research paper use of et al

How Do You Use et al. in Scientific Papers? (with many examples)

Et al. in academic writing helps you cite a publication with multiple contributors. Exactly how and where to use it varies depending on the specific journal publication or prescribed style guide. Even experienced authors have trouble with “et al.” Here we help clarify its use across every major style guide.

Updated on June 15, 2022

In scholarly papers, citation rules definitely have some strange terms. Some aren't English, and some aren't words. The term “et al.”, for instance, isn't an English word. For someone who speaks a non-Latin-origin language, like Japanese or Arabic, it's especially confusing. This post explains the use of et al. and some common mistakes related to it.

You use “et al.” in academic writing to cite a publication that has multiple authors (or other contributors, such as editors). For example, instead of an in-text citation reading (Schouten, McAlexander, Smith, Rogers, & Koenig 2010), it would simply be (Schouten et al., 2010).

Et al. is used in manuscript body text and in reference lists and footnotes. Exactly how and where to use it varies depending on the prescribed style, such as APA, AMA, Harvard, Vancouver, or that of a specific publication. It's short for et alia (or the respective masculine and feminine plural et alii or et aliae) – Latin for “and others.” The abbreviation is required, but it also makes writing easier to read, helping the reader find the cited works faster.

Even experienced authors have trouble with “et al.” because many major academic writing style guides, as well as specific journals, use it slightly differently. Let's look at the main ones you'll typically see when you're seeking to publish your scientific manuscript. Some of these styles are updated regularly, so always be sure to check with your professor and/or with your target publication's guidelines.

Using et al. in the main academic referencing styles

The following sections will show how to use “et al.” in APA, MLA, Vancouver, and other main referencing styles, especially those found in journals.

APA (American Psychological Association) Style

APA is commonly used in the social sciences and medicine, both in universities and in publications. Keep up to date on the latest APA style as well.

For in-text citations in APA Style , when a source has two authors, list both authors by their last names, followed by the publication year. For three or more authors, cite the first author followed by “et al.”

Note that these rules are based on the Publication Manual of the American Psychological Association, Seventh Edition (APA 7). The previous versions required listing more authors in the in-text citations, and had some differences in the reference list requirements.

APA Style in-text citations

The main difference in APA Style in-text citations is their use of the ampersand (&) symbol. Et al. is now simply used for three-plus authors. It used to be more confusing, as up to five authors were listed at first reference and then et al. on second reference. Many will not be familiar with the current style, so be sure to check.

APA Style reference list

The “et al.” abbreviation is not used in the APA references list. But knowing how to prepare the list can help you know when to use et al. in the in-text citations.

For publications with 3–20 authors put all the authors. For example:

Eckhardt, G., Houston, M., Jiang, B., Lamberton, C., Rindfleisch, A. & Zervas, G. (2019). Marketing in the sharing economy. Journal of Marketing , 83(5), 5-27.

For a source with 20 or more authors put the first six authors, followed by an ellipsis (…) and then the final author. For example:

Pegion, K., Kirtman, B. P., Becker, E., Collins, D. C., LaJoie, E., Burgman, R., . . . Kim, H. (2019). The subseasonal experiment (SubX): A multimodel subseasonal prediction experiment. Bulletin of the American Meteorological Society , 100(10), 2043-2061.

APA Style is rather idiosyncratic with its combinations of spaces and commas. Be careful with those, especially if you have a picky adviser or run into a picky peer reviewer or journal editor.

MLA (Modern Language Association) Style

MLA Style is most commonly used in the humanities. Nothing makes it especially unique, but it has its own slight differences.

MLA Style in-text citations

Unlike APA Style, MLA Style doesn't use the year in the citation. Instead, it uses the authors' last names and the relevant page number.

Use “et al.” for sources with three or more authors for both in-text citations and in the references list.

MLA Style reference list

For the reference list, known as the Works Cited list in MLA Style, publications with three or more authors will look like this:

Wysocki, Anne Frances, et al. Writing New Media: Theory and Applications for Expanding the Teaching of Composition . Utah State University Press, 2004.

Vancouver Style

The Vancouver Style guide was developed in Canada by the International Committee of Medical Journal Editors (ICMJE) . It's now widely used for journal referencing in medicine, health sciences, and life sciences, and even in technology.

It's a concise style that works well for hyperlinking and with referencing software such as EndNote.

Vancouver Style in-text citations

Vancouver Style uses numbers for in-text citations, so using “et al.” is not a concern. However, if an author is named in a sentence, use “et al.” for publications with more than one author. For example:

“Holt et al. found that there was no histochemical evidence of mitochondrial myopathy.”

Vancouver Style reference list

For the reference list, put the names of up to six authors. For example:

Holt IJ, Miller DH, Harding AE. Genetic heterogeneity and mitochondrial DNA heteroplasmy in Leber's hereditary optic neuropathy. J Med Genet. 1989 Dec; 26 (12): 739-743 .

For seven or more authors put the first six and “et al.” For example:

Meakin CJ, King DA, White J, Scott JM, Handley H, Griffiths A, et al. Screening for depression in the medically ill. J Nerv Ment Dis 1991; 12: 45‐53 .

AMA (American Medical Association) Style

Also very common in medical referencing is AMA Style. AMA Style tends to be used for strictly clinical medical journals and the life sciences.

AMA Style In-text citations and reference list

The AMA system is similar to the Vancouver system in that it also uses numbers for in-text citations. The difference is found in the way AMA treats publications with seven or more authors in the reference list.

In AMA put the names of all the authors for up to six authors. For example:

Mizumoto K, Kagaya K, Zarebski A, Chowell G. Estimating the asymptomatic proportion of coronavirus disease 2019 (COVID-19) cases on board the Diamond Princess cruise ship, Yokohama, Japan, 2020. Euro Surveill. 2020;25(10):2000180.

For seven or more authors put the first three, followed by “et al.” For example:

Ahn DG, Shin HJ, Kim MH, et al. Current Status of Epidemiology, Diagnosis, Therapeutics, and Vaccines for Novel Coronavirus Disease 2019 (COVID-19). J Microbiol Biotechnol. 2020;30(3):313-324.

Chicago/Turabian Style

Chicago Style (and the very similar Turabian Style) is an American English style guide that is widely used in books in the social sciences and humanities, as well as journalism. It's less commonly used in journals.

The massive and comprehensive book called The Chicago Manual of Style (CMOS) has two referencing systems: author-date and notes and bibliography (which, by the way, LaTex can handle automatically).

Chicago Style in-text citations

Use of “et al.” is the same in both of the above referencing styles. For in-text citations put all last names when there are up to three authors. For four or more authors put the first author's name followed by “et al.”

For footnotes, but the full author name(s). Note that relevant page numbers are also usually given in Chicago Style. Also, unlike APA Style, the word “and” is used instead of the & ampersand symbol. Footnotes are usually indicated in the text with a superscript number.

Chicago Style reference list

For the reference list in Chicago Style, use all authors' full names if the source has up to 10 authors. For example:

Sechzer, Jeri A., S. M. Pfaffilin, F. L. Denmark, A. Griffin, and S. J. Blumenthal, eds. Women and Mental Health . Baltimore: Johns Hopkins University Press, 1996.

For more than 10 authors put the first seven, followed by “et al.”

Harvard Style

This style guide will be familiar for students who have studied in the US or under US professors. It's commonly used from the high school level upward. It's less common in scientific publications.

Harvard Style in-text citations

For in-text citations in Harvard Style put all names if the source has three or fewer authors. Use “et al.” if there are four or more authors. Just to make things even more confusing, Harvard usually does not put a comma between the author name or between “et al.” and the year.

Harvard Style reference list

For the reference list in Harvard Style put the names of all the authors, no matter how many there are. For example:

Lupien, S.J., McEwen, B.S., Gunnar, M.R. and Heim, C., 2009. Effects of stress throughout the lifespan on the brain, behaviour and cognition. Nature Reviews Neuroscience , 10(6), pp. 434-445.

Harvard style is primarily used in university settings, and each school may have its own variations. Be sure to check, because Harvard shows a lot of variety in punctuation and capitalization depending on the university or publication using it.

Specific journal variations

Despite the great number of referencing styles available, some journals prefer to use their own style of referencing. These are almost never 100% unique. Most often, they are based on a popular style, but with a few alterations.

Most commonly, Vancouver Style is used as a basis for making a publication's or journal's “house style” (see more on that topic below). Some add spaces. Some change the punctuation. Some use superscript numbers while others use numbers in parentheses or brackets.

For instance, the popular online open-access (OA) journal PLOS ONE states it uses Vancouver Style. It does, but it also places citation numbers in brackets and it removes spaces in some punctuation in the reference list. These are small differences, but an author must do them correctly or they risk having their submission rejected by their target journal .

Another example, the American Society of Agricultural and Biological Engineers (ASABE) , which produced journals including Transactions of the ASABE , uses a variation of APA Style 6th Edition. Why? We may never know. But if you're submitting to them, you must follow their guidelines.

To be sure you satisfy the guidelines you can hire a professional scientific editor who has done this task hundreds, even thousands, of times. We're skilled at spotting tiny differences in styles. It's part of an editor job.

Common mistakes in using et al. in academic writing

There are several common mistakes that authors of any level should be aware of when using et al.

Using et al. when you shouldn't

Knowing where you should and should not put et al. depends on the style guide you're following. That's all. However, some authors simply put use et al. when there's more than one author. That's just wrong.

The recent APA Style update also made things confusing for students and publication-seeking researchers, because some professors and journal reviewers will be following APA 6 while others will be updated to APA 7. Still others may not care. If you're not sure, ask.

Using the period in et al.

Maybe the most common problem in using et al. is knowing where to put the period. It should be after the “al.” and not after the “et”. This is because, as mentioned, “et al.” is an abbreviation of the Latin phrase “et alia.” The “et” is itself a word.

The “et al.” may be followed by any other punctuation. For example:

(Aaker et al., 2004)

Or it may not. It depends on the publication.

When et al. ends a sentence, use only one period. For example:

“This leads to a 40% reduction in food waste, as shown by Simpson et al.”

“Et al.” vs. “etc.”

“Et al.” and “etc.” are sometimes confused with each other. But they're completely different.

The abbreviation “et al.” is used for lists of authors (or other contributors). That's all. However, “etc.” ( et cetera , which is the Latin word for “and other similar things”) is used for lists or related items. For example:

“Riches et al. (2017) suggest that subcultures form around a variety of popular music styles (punk, hip hop, etc.), each with its own aesthetics and ethos.”

Final words on et al.

Although the basic concept behind using “et al.” is easy, each system is different. For journal submission, check the specifics. The journal may use a common style such as APA or Vancouver, but with a few custom differences. Some journals are very picky about this, some are not.

Even though the abbreviation is required, it adds readability. Modern scientific writing should be accessible and readable; so et al., though tricky, is a good thing .

If you need formatting for your manuscript to be sure you're using the right guidelines, scientific editors can do that for you. Journal guidelines are notoriously quirky and if English isn't your first language, they're even harder.

Professional scientific editors are trained in dealing with this. Many of us even enjoy it! Get a professional edit if you want to be sure you have your references totally consistent and pleasing to the journal editor's discerning eyes.

About the author

Adam Goulston is a U.S.-born, Asia-based science marketer, writer, and editor. His company, Scize , helps scientific businesses and researchers communicate their value globally. He has edited more than 3,000 scientific manuscripts.

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How to Use ‘‘et al.’’ in APA Style (7th Edition)

The term ‘‘et al.’’ is the abbreviated form of the Latin term ‘‘et alia,’’ which means ‘‘and others.’’ It is used in academic in-text citations when referring to a source with multiple authors. In APA style, for a source with three or more authors, list the first author’s last name and “et al.” for all citations, including the first citation.

The Term ‘‘et al.’’ is the Abbreviation of Latin Term ‘‘et elia,’’ Meaning ‘‘and others’’

The term ‘‘et al.’’ is the abbreviated form of the Latin term ‘‘ et alia,’’ which means ‘‘and others.’’ It is used in academic in-text citations when referring to a source with multiple authors. In APA style, for a source with three or more authors , list the first author’s last name and “et al.” for all citations, including the first citation. Note that this rule has changed from APA 6th edition guidelines on using ‘‘et al.’’  which recommend listing all author names in the first citation up to five authors but then using ‘‘et al.’’  for the second and subsequent citations.

In October 2019, the American Psychological Association (APA) introduced the 7th edition of the APA Publication Manual, which replaces the 6th edition. The in-intext citation for works with three or more authors is now abbreviated right from the first citation. You only include the first author’s name and  “et al.”

For two authors: Always cite both authors' names in-text everytime you reference them.

Here is how this would look for a source authored by Parker, Robin, and Williams published in 2018.

( Parker et al., 2018)

            or

Parker et al. (2018) claimed that…

Note that there will be no comma between the surname and  ‘‘et al.’’  but a comma should be placed before the date in parentheses citation.  Also, the period goes only after the  ‘‘al.’’     even when it falls in the middle of a sentence.

The Correct Use of ‘‘et al.’’

Authors make several mistakes when using ‘‘et al.’’ in academic writings. The “al” in “et al.” is always followed by a period because the period shows that it is the abbreviated form of the term ‘‘et alia.’’

Thus, the following forms are not correct: ‘‘ et al’’, ‘‘et. al’’, ‘‘et. al.’’

The proper use of the abbreviation is ‘‘et al.’’

Also, “et al.” can be directly followed by another punctuation where necessary. However, the period always comes first:

(Parker et al., 2018)

When “et al.” is used right at the end of a sentence, only one period is used:

... by Parker et al. (2018)

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For more information about the citation styles and APA style, read the following articles:  

The 9 Most Important Changes in the 7th Edition of the APA Manual

APA Manual 7th Edition: In-Text Citation

How to Present Tables and Figures in APA Style (7th edition)

How to Use et al. in APA Style (7th Edition)?

APA Style: In-Text Citation | Reference List Entry

How to Cite Sources in APA Referencing Style? | With APA 7th Edition Update

How and When to Use ”et al.” in APA In-Text Citations?

Citation Styles | Which Citation Style Should I Use?

APA Formatting Guide for Academic Manuscripts

This handout discusses how and when to use et al. in APA style (7th edition). To give you an opportunity to practice your proofreading, we have left a few spelling, punctuation, or grammatical errors in the text. See if you can spot them! If you spot the errors correctly, you will be entitled to a 10% discount.

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How to Use Et Al. in Every Format—Et Al. Meaning

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Written by  Scribendi

Have you ever come across "et al." and wondered what it meant? Or how to use it?

If so, you're not alone. This Latin phrase is commonly used in academic writing and can be confused with other Latin phrases like "etc."

Things get even more complex when you realize that the placement of et al. changes depending on what style guide you're using.

Read on for a simplified breakdown of how to use et al. in every format, so you never get stuck.

Et Al. Meaning

Before we get into the nitty-gritty details, it helps to first understand the literal definition of et al. That way, you'll know exactly what you're saying when you use the term.

The phrase "et al." is derived from the Latin phrase "et alia," which means "and others." You are likely to encounter et al. in the references, in-text citations, and reference lists of academic texts.

For example, you might see the phrase, "Horowitz et al. (2012) published groundbreaking research," which means that Horowitz and others published the research.

Why Is Et Al. Used?

Et al. is used to simplify citations within your text or reference list. It lets the reader know that other authors have contributed to the work you're citing, without you having to list every author.

Et al. is also used to simplify subsequent references to groups of coauthors that have already been cited in full. For example, if you're citing the same group over and over, using et al. can simplify that citation throughout your paper.

How to Write Et Al.

Where should i put the period.

The period in et al. should go at the end of "al" because "al" is an abbreviation for "alia," meaning "others."

There is no period after "et" because "et" isn't an abbreviation. It's a full word in Latin, meaning "and."

Remember, "et al." is the only correct way to type this phrase.

A trick for remembering to include the period after "al" is to think of another common abbreviation, "etc."

"Etc." abbreviates et cetera, meaning "and the rest," and it always requires a period at the end. So et al., which is similar, always takes a period at the end too.

Here are a few common misspellings of et al.:

When you use other punctuation with et al., like a comma, it goes after the period. But if you're ending a sentence with et al., you don't need an additional period.

Should I Italicize Et Al.?

Most major style guides (including APA, MLA, the Chicago Manual of Style, and Harvard) do not require et al. to be italicized. However, some field-specific publications do require the italicization of the phrase, so it's always a good idea to double-check.

Using et al. in a sentence appropriately varies among style guides. Check out the overviews of different style guides below to make sure you're using this tricky phrase correctly.

How to Use Et Al., with Examples

APA format, established by the American Psychological Association, is commonly used for publications, essays, reports, and books in the fields of psychology and social science.

Also called APA style, this format has established specific standards for scientific and scholarly writing. It encourages uniformity and consistency in the way content is organized and references are cited.

APA in-text citations, reference lists, and title pages adhere to formatting requirements that differ from those of other styles.

For example, APA includes the author's surname and publication year in in-text citations, using an ampersand if there are two authors:

(Smith, 2012)

(Smith & Jones, 2012)

Another differentiator between APA and other styles is that APA requires a cover page, called a Title Page, and uses the title "References" above the citation list at the end of papers or manuscripts.

Traditionally, APA format is used for a range of subjects in the social and behavioral sciences, including:

Linguistics

When to Use Et Al. in APA

When dealing with a work by three or more authors in APA format (seventh edition), use the first author's last name in the signal phrase or parenthesis, followed by et al.

(McKenzie et al., 2020)

McKenzie et al. (2020)

Keep in mind that et al. wouldn't be needed if you were citing just two authors. If you were citing two authors and you replaced one of their names with et al., meaning "and others," this would be incorrect.

Use et al. in APA in-text citations only if you're citing at least three authors, and remember that et al. is never used in the reference list in APA.

Et Al. Example in APA Format

The use of et al. in APA format differs from other styles when it comes to the References.

Its format requires listing the surnames and first initials of up to 20 authors, placing an ampersand before the final author.

Karloff, J., McMahon, S., Watson, C., Williamson, M., Russell, S., Holden, R., Williams, B., Messier, A., Nesbo, J., Lamott, A., Shaffer, M., Barrows, A., Perry, T., Rooney, K., Cruz, M., Warren, G., Granville, D., Gonzalez, R., Johnson, S., & Galloway, J.

For more than 20 authors, you would replace all authors after the 19th with ellipses, followed by the final author's name.

Karloff, J., McMahon, S., Watson, C., Williamson, M., Russell, S., Holden, R., Williams, B., Messier, A., Nesbo, J., Lamott, A., Shaffer, M., Barrows, A., Perry, T., Rooney, K., Cruz, M., Warren, G., Granville, D., Gonzalez, R., Johnson, S., … Galloway, J.

Et Al. in APA In-Text Citations with Multiple Authors

When citing three or more authors in text with APA (seventh edition), you can use et al. upon the first and subsequent references to a source.

Before the seventh edition of APA, the names of up to five authors had to be spelled out in the text. Et al. could only be used upon subsequent references.

Luckily, the seventh edition has been simplified. Here is an example of how to use et al. for in-text citations in APA.

Three or more authors:

Parenthetical: (Johnson et al., 2020)

Nonparenthetical: Johnson et al. (2020)

MLA format was developed by the Modern Language Association. It provides specific guidelines for students and researchers writing academically in the fields of language and literature.

Often called MLA style, this format allows for an easy reading experience. It offers a uniform and consistent method of adding citations to books or literature.

Using et al. in MLA is different from APA and other styles in its requirements for the use of et al. MLA has different standards for layout, citations, and abbreviations.

There are also slight differences in the way authors are cited. But the spelling of et al. is always the same, regardless of the style guide being used, with lowercase letters and no punctuation after "et"—the only punctuation is the period after "al."

MLA format is traditionally used by writers and students creating work in the following disciplines:

Language and literature

Comparative literature

Literary criticism

Cultural studies

If you're formatting an essay or paper in MLA, the most updated edition is the ninth, published in April 2021.

When to Use Et Al. in MLA

You can use et al. in MLA when referring to multiple authors—three or more, to be exact. And you can add et al. to both your in-text citations and your Works Cited page (the name for the reference list).

Et Al. Example in MLA Format

Let's look at how to cite multiple authors in MLA in your Works Cited page with et al.

See the following two examples for citing a collection of poems and a collection of stories using et al. in MLA.

O'Hara, Frank, et al. The Collected Poems of Frank O'Hara . University of California Press, 1995.

Levine, Robert S., et al. The Norton Anthology of American Literature . Ninth ed., W.W. Norton &

Company, 2022.

Note that the second line of the citation is indented by half an inch.

Et Al. in MLA In-Text Citations with Multiple Authors

Now, we'll review how to cite multiple authors using et al. in MLA in-text citations.

MLA format requires the inclusion of the first author's surname, then et al., and then the page number.

(Lackey et al. 56)

The above is an example of a parenthetical in-text citation with et al. Here is an example of how to incorporate it within your prose:

According to Gilbert et al., "Today, however, we can see more clearly just how complex and multifaceted Woolf's set of women writers really is" (23).

The Chicago Manual of Style, often called CMS, CMOS, or Chicago, is a style guide used by authors, editors, indexers, designers, and publishers to prepare manuscripts and to aid in the revision of grammar, punctuation, and usage.

Dubbed the "editor's bible," the Chicago Manual of Style is typically used with material intended for publication. It's the style most often applied to novels, blogs, and creative nonfiction.

A key differentiator of Chicago style is that it offers two systems for source citations: notes and bibliography or author-date.

The notes and bibliography system is used by scholars and writers working in the humanities, and the author-date system is preferred by writers in the fields of science and social science.

That being said, here are a few of the most common fields in which Chicago style is used:

Social science

Natural science

The most recent edition is the 17th, which was published in September 2017. Let's look at how to use et al. in Chicago style.

When to Use Et Al. in Chicago Style

In essays adhering to Chicago style, you can use et al. when citing a source with four or more authors.

The format and placement of et al. can vary because, as we mentioned earlier, Chicago uses two systems for source citation: notes and bibliography and author-date. So the placement really depends on which system you're using!

But as a general rule, you can use et al. in your in-text citations, in your footnotes and endnotes, and in your reference list at the end of your document.

Note that bibliographies go with the notes and bibliography system, and reference lists go with the author-date system.

Et Al. Example in Chicago Style

You will use et al. in bibliographic form in Chicago Style for sources with more than 10 authors. In such cases, you'll list the first seven authors, followed by et al.

The citation format in your bibliography will change depending on whether you're using the notes and bibliography system or the author-date system, but the placement and format of et al. are the same.

Notes and bibliography system:

Jackson, Tiffany D., Nic Stone, Ashley Woodfolk, Dhonielle Clayton, Angie Thomas, Nicola Yoon,

Natasha Schrader, et al. Blackout . New York, NY: Quill Tree Books, an imprint of

HarperCollins Publishers, 2021.

Author-date system:

Natasha Schrader, et al. 2021. Blackout . New York, NY: Quill Tree Books, an imprint of

HarperCollins Publishers.

Et Al. in Chicago Style In-Text Citations with Multiple Authors

When using et al. in an in-text citation of four or more authors, et al. can be formatted in a few different ways, depending on which source citation system you're using. Take a look at the examples below.

In the author-date system, et al. goes after the first author's surname in an in-text citation.

(Johnson et al. 2021, 465)

In the notes and bibliography system, et al. can go in a short or long footnote. Here's how the format breaks down for each type:

Short footnote: Johnson et al.

Long footnote: David Johnson et al.

Turabian style is similar to Chicago style when it comes to how to write et al. Published by Kate L. Turabian in 1937, this style was created for researchers and students. Its official title is A Manual for Writers of Research Papers, Theses, and Dissertations.

You can think of it as a student's version of Chicago style. Turabian style places greater emphasis on student needs regarding the formatting of papers and citations, and this is its biggest differentiator.

This manual is also shorter and contains fewer instructions than others. Another differentiator of Turabian is that it covers a wide spectrum of disciplines, including:

Art history

Social studies

Global studies

Religious studies

If you're looking for the latest edition, be sure to use the ninth, published in 2018.

When to Use Et Al. in Turabian Style

As in Chicago style, you can use et al. in a sentence in Turabian when citing four or more authors.

You can also use et al. when citing sources in both the main text and the bibliography, and this is true of both the notes and bibliography and the author-date citation systems.

Where you should put et al. and how you should format it will vary depending on which citation system you use. Just keep in mind that you can use et al. in Turabian style whenever you have four or more authors to cite.

Et Al. Example in Turabian Style

The great thing about using Turabian style is that if you understand how to use et al. in Chicago style, using it in Turabian will be a breeze.

Below are some examples of how to write et al. in either your bibliography (notes and bibliography system) or reference list (author-date system) in Turabian style.

Notes and bibliography system (book):

Using the Turabian citation system, you'll follow the same format for et al. Only the placement of the publication date changes. See the examples below.

Kitamura, Katie, Allen Johnson, Birk Meyer, Alex Fritas, Joan Bigsby, Becca Thomas, Greg 

Lewis, et al. A Separation . New York: Riverhead Books. 2017. 

Author-date citation system (book):

For more than 10 authors, list the first seven authors and follow them up with et al.

Kitamura, Katie, Allen Johnson, Birk Meyer, Alex Fritas, Joan Bigsby, Becca Thomas, Greg Lewis,       

et al. 2017. A Separation . New York: Riverhead Books. 

Et Al. in Turabian In-Text Citations with Multiple Authors

Using et al. in your in-text citations is the same in Turabian as it is in Chicago style. You'll put et al. in your footnotes (short and long) and within your text. Below are examples of each.

(Johnson et al. 2017, 45)

In the notes and bibliography system, et al. could go in a short or long footnote. Here's how the format breaks down for each type of footnote.

Short footnote: Weber et al.

Long footnote: Jesse N. Weber et al.

Harvard style is a popular formatting style across many universities. It's been known to go by a couple of different names, including the Harvard Referencing System and Author-Date Referencing.

There's no official connection between Harvard style and Harvard University. This style is simply another way for students to cite their sources and format their papers uniformly.

Common disciplines that use this style include the following:

Behavioral sciences

The thing to remember about Harvard style is that it isn't as cut-and-dried as other styles—different schools have different requirements. This means that using et al. in Harvard style can change depending on what school you go to.

Be sure to refer to your professor's instructions before using et al. in your papers.

For the purposes of this post, we'll be talking about how to use et al. following Harvard Business School's Citation Guide.

When to Use Et Al. in Harvard Style

While some aspects of Harvard style can vary across institutions, one thing everyone seems to agree on is that et al. should be used to cite four or more authors.

So you should use et al. when you're citing four or more authors in both your footnotes and in your bibliography. You can also use the term in both parenthetical statements and as a signal phrase.

Et Al. Example in Harvard Style

In the bibliography section of your paper, you can use et al. for academic citations of sources with four or more authors .

Unlike Chicago, you don't have to list a certain number of authors before you list et al.—you can simply use et al. after the first author's name.

Here are two examples, one for a book citation and one for a web citation:

Christensen, C. Roland, et al. Business Policy: Text and Cases . 5th ed. Homewood, IL: Richard 

D. Irwin, Inc., 1982.

Enright, Michael J., et al. "Daewoo and the Korean Chaebol." University of Hong Kong case no. 

HKU143 (University of Hong Kong, August 2001). Harvard Business Publishing. 

https://hbsp.harvard.edu/, accessed March 2007.

Et Al. in Harvard Style In-Text Citations with Multiple Authors

When it comes to using et al. in Harvard style in-text citations, you can use it in your footnotes, parenthetical phrases, and signal phrases.

See examples of each below.

³C. Roland Christensen et al., Business Policy: Text and Cases, 5th ed. (Homewood, IL:

Richard D. Irwin, Inc., 1982), p. 101.

Parenthetical phrase:

(Johnson et al. 2007)

Signal phrase:

Johnson et al. (2007)

Again, keep in mind that Harvard style gives your instructor leeway in their guidelines for how to format et al., so be sure to follow their instructions.

An additional way to cite references is to use Vancouver style. This style was developed in Vancouver in 1978 by medical journal editors. It is most commonly used in medicine and science.

The biggest difference between Vancouver and other styles is its use of numbers. Often called the Numbering System, Vancouver cites sources by placing numbers within parentheses or superscripts in the main text.

These citation numbers are tied to entries in your reference list. Like in other styles, your reference list in Vancouver style will have all of the sources you've cited within your text.

Some common fields that use Vancouver are as follows:

Biomedicine

As in Harvard style, keep in mind that some universities and organizations have their own specific formatting requirements when it comes to citing work with et al. in Vancouver style.

When to Use Et Al. in Vancouver Style

With Vancouver style, you can use et al. for both in-text citations and within the reference list.

You should use et al. in your reference list when citing more than six authors. If you're citing just six authors, you'll need to spell out each author's surname and first initial, separating each author with a comma.

You should use et al. within the main text when citing multiple authors. Some universities differ in terms of how many authors, so it's best to check with your institution to confirm its preferences for this style.

Et Al. Example in Vancouver Style

Let's start our et al. examples for Vancouver with those in bibliographic form.

In Vancouver style, the bibliography is called a reference list. You'll add et al. to reference entries only if you're listing more than six authors. List the first six authors, then add et al.

Here's an example of a book citation with et al. in the reference list:

Doornbos MM, Groenhout ER, Hotz GK, Brandsen C, Cusveller B, Flikkema M, et al. 

Transforming care: a Christian vision of nursing practice. Grand Rapids, Michigan: 

William B. Eerdmans Publishing Company; 2005.

Note that the authors' surnames are followed by their first and (in many cases) middle initials, without punctuation.

Here's an example for an electronic journal article:

Aho M, Irshad B, Ackerman SJ, Lewis M, Leddy R, Pope T, et al. Correlation of sonographic

features of invasive ductal mammary carcinoma with age, tumor grade, and 

hormone-receptor status. J Clin Ultrasound [Internet]. 2013 Jan [cited 2015 Apr 

27];41(1):10-7. Available from: https://onlinelibrary.wiley.com/doi/10.1002/jcu.21990/full 

DOI: 10.1002/jcu.21990

Et Al. in Vancouver Style In-Text Citations with Multiple Authors

As far as in-text citations go in Vancouver style, you can use et al. directly in the text, followed by a reference number.

Because Vancouver references sources within parentheses or superscripts, here are examples using et al. in-text with both systems:

Harrison et al. (5) agree that only one solution is viable.

Harrison et al. 5 agree that only one solution is viable.

Et Alibi, Et Alii, and Others

Sometimes, et al. can be confused with other Latin phrases like et alibi and et alii. This is understandable because the terms all begin with the same letters!

Don't worry. Over the next few sections, we'll break down what each of these phrases means. That way, if you need to use them in your next paper or article, you won't use them incorrectly.

Et alia is the Latin phrase for "and others," and the phrase "et al." is its abbreviated form.

Et alia is meant to be used when a list contains too many people or things to name. In academic writing, it is used when citing sources with multiple authors.

However, the full phrase "et alia" isn't typically spelled out in academic writing. In papers, journals, and manuscripts, the abbreviated form "et al." is used, with a period after "al."

Et alibi means "and elsewhere" in Latin. It's used in academic writing to show that the information you're citing is mentioned in other parts of a text, too.

For example, if you're citing a passage from the Bible that can also be found in other locations of the text, that would be a perfect instance for using et alibi.

Keep in mind that "et al." is the abbreviated form of both et alibi and et alia.

Et aliae also means "and others" but in the feminine plural form. This means that et aliae refers specifically to a group of women or girls.

However, you won't need to differentiate between feminine or masculine forms when using et al. in your writing. You would simply use "et al."—the abbreviated form of both.

The Latin phrase et alii means "and others" in the masculine plural form. It’s used to refer to a group of men or boys.

But the abbreviated form, "et al.," is still what you would use to cite multiple authors.

As long as you can remember how to write the abbreviation et al. in your papers, you're good to go!

Difference between Et Al. and Etc.

Do you ever confuse et al. with etc.? You're not alone. The two are very similar.

While et al. means "and others" in Latin, etc. is short for the Latin et cetera and means "and the rest."

Both phrases indicate that something has been omitted from the text, and both are abbreviations. However, there are key differences to keep in mind to avoid using them incorrectly in your paper.

You use etc. to shorten a list. Its use lets the reader know that there are more items or examples you could list but that the shortened list allows the reader to get the idea.

For example, if you were to write, "The event is at the beach, so bring your swimsuits, towels, sunscreen, sandals, etc.," readers know they need to bring all beach items, not just the ones mentioned.

Similarly, you use et al. to shorten a list of authors or collaborators.

Common Mistakes

Spelling and formatting Latin phrases is no walk in the park—especially when you need to get them right to earn a passing grade.

It also doesn't help that each style guide has its own formatting or that many Latin phrases can sound the same. It's enough to make your head spin!

Below, we'll cover common mistakes made when using et al. and why using it is so important for clear and concise academic writing.

Spelling Latin phrases can be tricky, but abbreviating them correctly can be even trickier.

When using et al. in your papers, be sure to abbreviate it correctly and to use the right punctuation.

Et al. is always spelled as two separate words—"et" and "al"—with a period after "al."

The best way to remember how to punctuate and spell it is to remember that it's an abbreviation.

Here are a few common misspellings of et al. so you know to avoid them:

Using the Incorrect Style

Spelling et al. correctly is only half the battle. You'll also need to be sure you're using et al. in the style required by your university, institution, or professor.

As we mentioned earlier, there are many style guides to choose from, including MLA, Chicago, APA, and Turabian.

Each style has its own specific format for et al., so be sure to study its guidelines carefully before adding et al. to your references.

You'll especially want to take note of how et al. is used in both in-text and reference list citations and how many authors necessitate its use.

Not Using Et Al.

Using et al. is a clear and concise way of communicating your source information to readers without overwhelming them or taking away from your work.

It lets readers know that multiple authors or collaborators contributed to the source without having to list them all. Also, when referencing a source with several authors or collaborators multiple times, the use of et al. keeps the writing neat and tidy.

Not using et al. would make academic writing awkwardly long and arduous within the main text while extending bibliographies and reference lists unnecessarily.

Et al. helps academic writers and authors reference their sources in a clean-cut way.

How to Cite a Tweet

Nowadays, it's not uncommon for students or researchers to turn to social platforms like Twitter for their research.

Because of this, styles like MLA, APA, and Chicago have stayed current by offering standards for formatting citations of Tweets in research papers and scholarly articles.

Each style has its own formatting requirements for citing a Tweet, and these can vary among different editions of the same style.

Below are instructions for citing Tweets in each of the three major styles.

To cite a Tweet in MLA (ninth edition), you'll cite the first name and surname of the account holder (or the name of the organization) in addition to the Twitter handle.

Here is the basic structure:

Surname, First name [Username]. "Tweet message." Twitter , date posted, URL.

Here's an example:

Swift, Taylor [@taylorswift13]. "I'm so proud of this song and the memories I have with you guys 

because of it." Twitter , 22 November 2021, 

twitter.com/taylorswift13/status/1462908809542787072.

To cite a Tweet from an organization in MLA, you'll use this structure:

Organization or Account Name [Username]. "Tweet message". Twitter , date posted, URL.

The Wall Street Journal [@WSJ]. "Activist hedge fund Trian has acquired a stake in Unilever, 

people familiar with the matter say, adding pressure on the consumer-goods company." 

Twitter , 23 January 2022, twitter.com/WSJ/status/1485356694972551171.

To cite a Tweet in APA style (seventh edition), you'll do things a little differently from MLA. APA requires only the author's full surname with the first name initialized.

You'll also include only the first 20 words of the Tweet in your reference.

Surname, Initials [@username]. (Year, Month Day). Text of Tweet [Tweet]. Twitter. URL

Gates, B. [@BillGates]. (2019, September 7). Today, it's difficult for researchers to diagnose 

#Alzheimers patients early enough to intervene. A reliable, easy and accurate diagnostic 

would [Thumbnail with link attached] [Tweet]. Twitter.  

https://twitter.com/BillGates/status/1170305718425137152

To cite a Tweet in Chicago style, you'll include many of the same elements as Tweet citations in other styles, but you'll also add a timestamp.

The general structure is as follows:

First name Surname (@TwitterHandle), "Text of Tweet," Twitter, Month Day, Year, 00:00 

a.m., link to Tweet.

Here's an example from the Chicago Manual of Style:

Conan O'Brien (@ConanOBrien), "In honor of Earth Day, I'm recycling my Tweets," Twitter, April 

22, 2015, 11:10 a.m., https://twitter.com/ConanOBrien/status/590940792967016448.

If you'd like to cite a Tweet within your text, here's an example using the above Tweet:

Conan O'Brien's Tweet was characteristically deadpan: "In honor of Earth Day, I'm recycling my Tweets" (@ConanOBrien, April 22, 2015).

Frequently Asked Questions

What does et al. mean in a citation.

In a citation, et al. indicates that multiple authors are being cited within a reference in an academic work but that not all of their names are listed.

It's not uncommon for some sources to have 10 or even 20 authors, given the collaborative nature of research in the fields of medicine and science. Using et al. is a way of ensuring that all authors are referenced without crowding the content.

When Should Et Al. Be Used in APA Style?

Use et al. in APA in-text citations with multiple authors, as well as in the References. Specifically, use it when dealing with a work by three to five authors. You'll use the first author's surname in the signal phrase, parenthetical statement, or bibliographic entry, followed by et al.

Keep in mind that you should use et al. only for three or more authors, not two. Since et al. is an abbreviation for "and others," it must stand in for more than one person. If you were trying to cite two authors and you used et al. after the first one, et al. would represent one person as opposed to several "others," which would be incorrect.

What Is Et Al. in MLA?

In MLA style, et al. is an abbreviated Latin phrase meaning "and others." It indicates that multiple authors contributed to the source being cited but that not all of them are listed.

MLA recommends using et al. for sources with three or more authors. Et al. can be used both within the main text and on the Works Cited page. It's punctuated in the same way as in other styles, with a period after "al" only.

Here is a citation example using et al. in MLA:

(Gubar et al. 56)

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How to Use Et Al. Effectively in Your Research Paper

Discover how to use et al correctly and easily with this step-by-step guide. Learn the rules and examples of using et al in academic writing.

Academic writing is full of various citation styles and abbreviations , and one of the most commonly used ones is “et al.” But what does it really mean, and how should you use it? 

When there are three or more writers, this Latin phrase, short for “et alia,” is used instead of mentioning all of them. While it may appear simple, correctly using “et al.” can be difficult, and many writers struggle to understand when and how to use it.

This article will go over everything you need to know about utilizing “et al.” in your research paper, from what it is to how to cite it.

What Is Et Al.? 

“Et al.” is a common acronym in academic writing to denote the presence of other writers who are not expressly mentioned. It comes from the Latin phrase “et alia” (which means “and others” in English). The use of Latin terms in academic writing extends back to the medieval period when Latin was the main scholarly language in Europe.

When a source contains three or more authors, it might be difficult to list all of them in a citation, especially when there is a large list of authors. In these specific situations, “et al.” might be used to indicate the presence of other authors who are not identified.

It’s worth noting that the use of “et al.” differs based on the citation style. In certain styles, such as APA and Chicago , “et al.” is used for sources with three or more authors, however, in MLA style, “et al.” is only used for sources with four or more writers in others.

How To Use Et Al.?

Here are some guidelines for effectively using “et al.” in academic writing:

• Use “et al.” when a source has a large list of authors: When there are several authors of a source, the term “et al.” is used to shorten the citation, and it is commonly used when there are three or more writers; nevertheless, verify your citation style guidelines. 
• After the first author’s name, add “et al.” Most citation styles, including APA and MLA, include “et al.” after the first author’s name in the citation. 
• The period should come after “al.”. For instance, “Smith et al.” is correct, however, “Smith et. al” is wrong.
• In academic writing, “et al.” is italicized but not capitalized. 
• Understand the citation style guidelines: The use of “et al.” varies depending on the citation style. Make sure to follow the citation style guidelines specified for your academic writing.

In general, “et al.” is a useful abbreviation that simplifies citations in research papers, and mastering its correct usage is crucial for producing clear and precise academic writing.

Et Alibi, Et Alii, And Others

One important piece of information concerning et al. is the different forms it may take. Here’s some more information on all the different forms of “et al.” and their meanings:

Et alia is the most fundamental and widespread form of “et al.” in academic writing, meaning “and others.” When the number of authors of a source exceeds the maximum allowed by a citation style, this phrase is commonly used in citations to denote multiple authors.

Et Alibi 

Another Latin term for “and elsewhere.” It is used to highlight that further information about a topic is available from another source or location. For example, if you’re referencing a source and there’s more material on the same issue in another source, you might say “et alibi” to indicate that other sources are available. 

In Latin, this is the feminine plural form of “et al.” It is used to show that a source has numerous female authors. For instance, if a source includes numerous female authors and you wish to highlight this in your citation, you may use “et aliae” rather than “et al.”

In Latin, this is the male plural form of “et al.” It is used to show that a source has numerous male authors. For instance, if a source includes numerous male authors and you wish to highlight this in your citation, you may use “et alii” rather than “et al.”

Difference Between Et Al. And Etc.

Et al. and etc. are two separate abbreviations used in academic writing.

Et al. is an abbreviation of the Latin term “et alia,” which translates as “and others.”, as previously stated. It is used in citations to show many authors of a source and is usually used amid a citation, after the first author’s name. Simply put, you may use “et al.” to indicate that there are other authors aside from the name mentioned. 

Etc. is an abbreviation of the Latin term “et cetera,” which means “and so forth” or “and other things.” It is used to show that a list of things extends beyond those specifically mentioned. For instance, if you’re presenting several examples of a specific topic, you may use “etc.” to show that there are more examples. The expression “Etc.” is commonly used at the conclusion of a list and is preceded by a comma. It is frequently followed by a period and, depending on the citation style, italicized.

In summary, “et al.” indicates numerous authors of a source in a citation, whereas “etc.” indicates a continuation of a list of items.

Common Mistakes

• Using “et al.” to indicate a list continuation: As previously stated, “et al.” should be used to denote multiple authors of a source and should not be used to suggest a list continuation.
• Using “etc.” to denote many authors: “Etc.” should never be used to denote multiple authors of a source. This is the responsibility of “et al.” and using “etc.” instead is considered wrong and deceptive.
• Capitalizing “et al.” and “etc.”: Both “et al.” and “etc.” are abbreviations and should be written in lowercase characters, unless at the beginning of a phrase.
• Using “and others” instead of “et al.”: It is more suitable in academic writing to use “et al.” instead of “and others” to denote multiple authors of a source. Using “and others” can be informal and may violate the citation style.
• Using “et cetera” instead of “etc.”: The acceptable abbreviation for “et cetera” is “etc.” and should be used instead. Using the entire sentence may be considered needless, and it may also take up precious space in a citation or text.

How To Cite Et Al.

Here’s how to properly quote “et al.” in several citation styles:

In MLA style, “et al.” is used after the first author’s name on the paper’s reference page. For example, if a source has three or more authors, you would list the first author’s name followed by “et al.”, example:

Smith, John, et al. “The Effects of Climate Change on Biodiversity .” Environmental Science Journal, vol. 27, no. 2, 2020, pp. 25-34.

For in-text citations, you would include the first author’s name followed by “et al.” and at the end, the page number should be enclosed in parentheses, for example: 

(Smith et al. 36).

In the references page, put “et al.” after the first author’s name. If a source includes three or more authors, you would list the first author’s name followed by “et al.”, example:

Smith, J., Johnson, A., Williams, K., & Brown, M. (2019). “The Impact of Social Media on Adolescent Mental Health.” Journal of Adolescent Health, 65(3), 42-51.

In-text citations would include the first author’s name in parenthesis, followed by “et al.” and the year of publication, for example:

(Smith et al., 2019).

Chicago Format

On the reference page, “et al.” is used after the first author’s name in Chicago style. If a source includes four or more authors, you would list the first author’s name followed by “et al.”, for example:

Jones, S., et al. “The History of the American Civil War.” Civil War History, vol. 55, no. 2, 2009, pp. 34-47.

In-text citations would include the first author’s name in parenthesis, followed by “et al.” and the page number:

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• Writing Tips

“Et al.” Meaning and Examples

4-minute read

• 11th October 2023

In the world of academic writing , you’ve likely come across the term et al . at some point. What exactly does it mean, where did it come from, and how should you use it?

In this blog post, we’ll delve into the fascinating history and usage of et al . to help you become a more confident and effective scholarly writer.

What Is “Et al.”?

Et al . is an abbreviation of the Latin phrase et alia or et alii , which translates to and others or and colleagues . The use of Latin abbreviations in academic writing dates back to the Renaissance period when Latin was the lingua franca of scholars. Et al . became a shorthand way to indicate multiple authors without the need for lengthy lists.

In academic writing, it refers to a group of authors when citing a source. Essentially, it’s a convenient way to acknowledge all the contributors without listing each name individually, especially when there are several authors involved.

When to Use “Et al.”

Using et al . correctly is essential to maintaining clarity and professionalism in your writing. Nowadays, the main circumstance in which you’ll use it or come across it is in in-text citations .

Many referencing systems use et al . for in-text citations when listing more than a certain number of authors. Commonly, it’s used when there are more than two authors, but this depends on which system you’re following. In-text citations with et al . usually look something like this:

To Italicize or Not to Italicize

The question of whether to italicize et al. is one that often perplexes writers, as Latin terms are often given in italics. The general rule for et al ., though, is that it should not be italicized.

Et al . has become an integral part of academic writing conventions, so like with other Latin phrases, such as et cetera (etc.) and id est (i.e.), we’ve dropped the italics over time.

Referencing Systems That Use “Et Al.”

Different referencing systems have their own guidelines for using et al . Here’s a brief overview of some of them:

APA (American Psychological Association)

In APA style , et al . is used for both in-text citations and reference list entries. When citing a source with three or more authors for the first time, include the first author’s name followed by et al . and the year:

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MLA (Modern Language Association)

Similarly, in the MLA style , et al. is used in in-text citations. If a source has three or more authors, include the first author’s name followed by et al. and the page number:

Chicago Manual of Style

Chicago style allows for the use of et al . in both footnotes and the author-date style for sources with more than three authors. For in-text citations, if there are four or more authors, list the first author followed by et al .:

The same applies to Chicago footnotes:

1. Rachel Johnson et al., Architecture Styles (Miami: Classic Press, 2021).

Understanding how to use et al . with your referencing style is crucial to maintaining consistency and clarity in your academic writing. It streamlines references to sources with multiple authors and ensures your writing remains clear and concise. So, the next time you encounter multiple authors in your research, remember to embrace et al . as your ally in academic communication.

And if you’d like an expert to check your references and citations to make sure they’re top-notch, send us a copy of your work. We’ll ensure perfect referencing as well as grammar, spelling, punctuation, word choice, and more. Try it for free today.

How do you punctuate “et al.”?

Et al . should always have a period at the end of it. A comma is not needed after et al . in running text, but some referencing systems do require a comma after et al . if it’s in a parenthetical citation.

Is “et al.” used in casual writing?

Et al . is mainly used in formal writing.

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Home / Guides / Citation Guides / Harvard Referencing / Harvard Referencing Style Examples / When to use “et al.” in Harvard referencing style

When to use “et al.” in Harvard referencing style

“ Et al. ” is used in Harvard style to indicate that a source has four or more authors. By using “ et al. ”, writers can also avoid having very long citations that list every single author.  

For more help creating Harvard-style citations that use “ et al. ”, try the EasyBib Harvard referencing generator !

What is “ et al. ” and what does it mean?

“ Et al. ” is a Latin term and the short form of “ et alia ”, which literally means ”and others”. It is used in academic citations for sources that have multiple authors.

The ” al ” in “ et al. ” is always followed by a full stop. Other punctuation marks, such as a comma, can follow the full stop after ” al ”.

Usage of “ et al. ” in an in-text citation

When providing a citation for a source with four or more authors, the following format is used in Harvard style:

(Surname of the first author et al. , Year of publication)

“Continuous flow LVAS rely on pressure gradients between the left ventricular cavity and the aorta” (Jameson et al. , 2018).

Usage of “ et al. ” in a reference list

Depending on your institution, “ et al. ” may or may not be used in a reference list entry. Below, we’ll give examples of both.

References with “ et al. ”

If you have a choice, consider using “ et al. ” in your reference list. This is preferable since it helps keep your references succinct.  

To use “ et al. ” in your references, state the name of the first listed author and follow it by “et al.” in italics in the author section of the citation.  

Example reference structure (journal):

1 st author’s surname, Initial. et al. (Year published) ‘Article title’, Name of Journal, Volume(Issue), pp. 00-00.

Example reference (journal):

Bogaerts, W. et al. (2020) ‘Programmable photonic circuits’, Nature, 586(7828), pp. 207-216.

References that do not use “ et al. ”

Since references are usually where all the source details are shown, your institution may prefer to have all the author names included in references. If this is the case, do the following:

• List author names in the order they are shown in the source and not alphabetically.
• Each author name is formatted as last name, first-name initial. Example: Smith, J.
• Separate each name with a comma until you get to the last two names. Add the word “and” instead of a comma between the last two names.

Example author structure:

1 st author’s surname, Initial., 2 nd author’s surname, Initial., 3 rd author’s surname, Initial. and 4 th author’s surname, Initial.

1 st author’s surname, Initial., 2 nd author’s surname, Initial., 3 rd author’s surname, Initial., 4 th author’s surname, Initial., 5 th author’s surname, Initial., 6 th author’s surname, Initial. and 7 th author’s surname, Initial. (Year published) ‘Article title’, Name of Journal, Volume(Issue), pp. 00-00.

Example reference:

Bogaerts, W., Pérez, D., Capmany, J., Miller, D.A.B., Poon, J., Englund, D., Morichetti, F. and Melloni, A. (2020) ‘Programmable photonic circuits’, Nature, 586(7828), pp. 207-216.

Published October 29, 2020.

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You should use et al . in your citations when a source you have used has 'four or more' (ie more than three) authors.  You should list all of the authors in your reference.

What is et al. .

et al. stands for ' and others ' and it should be used in your   in-text citations  only,  to indicate that a work has multiple authors.  In your reference list at the end of your work, you should include  all of the authors.

It should  only  be used if the source you are citing has  four or more  authors (ie more than three). Where a source has one, two or three authors, you should name them all in both your in-text citation and your reference.

et al . should always be written in italics, with a full stop at the end of  al .

Previously, if you were a student at St George's ,  you were required to use et al . in both your citation and your reference list, so this is a change.

Find some examples of the correct use below:

Books or ebooks with four or more authors (more than three)

You should use Davey  et al ., 2015 in your citation but list all of the authors in your reference list.  For example: Citation: Davey et al . (2015) discuss the mechanisms of antibacterial drugs....

Davey, P., Wilcox, M.H, Irving, W. and Thwaites, G. (2015) Antimicrobial chemotherapy . 7th edn. Oxford: Oxford University Press.

Articles with four or more authors (more than three)

You should use Glavin  et al ., 2021 in your citation but list all of the authors in your reference list. For example:

Citation: Chronotype is a biological factor that affects sleep (Glavin et al ., 2021, p.2637).

Glavin, E.E., Ceneus, M., Chanowitz, M., Kantillerakis, J., Mendelow, E., Mosquera, J. and Spaeth, A.M. (2021) 'Relationships between sleep, exercise timing, and chronograph in young adults' Journal of Health Psychology, 26(13), pp. 2636-2647.

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Citations: Using et al.

Using et al..

For a work with one or two authors, include the name(s) in every citation. Here is how this could look:

(Dusek & Bakke, 2019)

According to Lai and Sookochoff (2018)…

In APA 7, for a work with three or more authors, list the first author and “et al.” for all citations, including the first citation, unless doing so would create ambiguity. (Note that this rule has changed from APA 6 guidelines on using "et al.," which recommend listing all author names in the first citation up to five authors but then using "et al." for the second and subsequent citations.)

Here is how this would look for a source authored by Sookochoff, Lai, and Bakke published in 2017:

(Sookochoff et al., 2017)

According to Sookochoff et al. (2017)...

Remember that there is no comma between the surname and "et al.," and the period goes only after the "al." The English translation of "et al." is "and others."

A helpful table of this rule can be found in APA 7, Table 8.1.

Shortening Citations With et al. Video

• APA Formatting & Style: Shortening Citations With et al. (video transcript)

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When to Use Author “et al.” in Citation and References

We publish because we want to share our knowledge and because we want recognition for our work. We acknowledge people’s ideas and findings by providing citations. Unfortunately, however, the rules regarding this common practice are not always easy to decipher, even for the best of us! We have published a number of other articles that help you navigate citation requirements, for example on the best citation format for science papers, how many references you should include in your research paper, and the general differences between common citation styles .

This article focuses on how to name the authors of cited works, including when to use the abbreviated Latin term “et al.” that usually accompanies the phrase “author et al.” Please make sure to follow the relevant journal guidelines concerning punctuation, citation style, etc., as publishers do not always follow the exact same formatting rules. Let’s start with some general definitions, and then look at specific rules of the most common style guides .

Table of Contents:

• What are the main types of citations? 
• Why do we use “et al.” in citations? 
• Using “et al.” vs “etc.”
• When Do We Use “et al.” in Citations? 

How to Cite “et al.” in APA Style

• How to Cite “et al.” in Chicago
• How to Cite “et al.” in MLA Citations

What are the main types of citations?

When referring to published literature, you need to provide details so that others can find and review the original material you base your ideas and claims on. In your research paper, you can make references to source materials using either endnotes and footnotes (i.e., numbers in the text that refer to the bottom of the page or the end of the paper) or in-text citations. Both styles require you to also provide a reference list at the end of the document.

In-text (or parenthetical) citations

When referencing other literature by author name or title in the text paragraphs of your paper, you are using in-text citations . Another similar method of citing is using parenthetical citations , as the referencing information is usually placed within parentheses. Both of these citation types are common in APA style.

Endnotes and footnotes

Endnotes and footnotes help declutter your writing. They are simple notation systems that allow you to use numbers in the body of a text to reference a cited work. Each number corresponds to further information or a citation entry found at the end of a manuscript (for endnotes) or at the bottom of the page where the cited reference is mentioned (for footnotes).

Footnotes are rarely found in scientific writing but are frequently used in the humanities and social sciences. Additionally, endnotes often replace parenthetical in-text citations in scientific journals these days – make sure you pay attention to the journal guidelines when you prepare your manuscript so that you don’t have to suddenly change your entire citation style before submitting or during the review process.

Reference lists

A reference list compiles all the works cited within a document for ease of reference and is included at the end of a manuscript. It must be included regardless of how the source material is acknowledged within the main body of your article. The author guidelines of your target journal will tell you whether the list has to be ordered alphabetically or in order of appearance in the text (when using a numbered system), and what general style it has to adhere to.

Why do we use “et al.” in citation?

The Latin term “et al.” is short for “et alii” and means “and others.” The abbreviation is used when citing a source with multiple authors. Its function is similar to that of “et cetera”, another common Latin phrase that is usually abbreviated as “etc.” and means “and other similar things.”

Using “et al.” vs “etc.” in Citation and References

As stated above, “et al.” is used strictly when talking about people, while “etc.” is only used for things. Apart from this key difference, they have the same function: replacing a list.

When to Use “et al.” in Reference and Citation

We cannot stress this enough, but always double-check your journal or relevant style guide regarding Latin terms and citations. There is no uniform rule on when to use “et al.”, but at least the phrase’s spelling is consistent. Always write “et al.” in lowercase and include a period after “al.”, even when it appears in the middle of a sentence.

The abbreviation “et al.” replaces author names in endnotes, footnotes, and in-text citations; it depends on the target journal whether “author et al.” citation style can also be used in the reference list or whether all author names need to be spelled out in that section . In the following section, you will find further information on how to cite references according to the most common citation styles and examples.

The APA style is frequently used in social science publications. Examples of book and journal citations are provided below. For information about other sources and special cases, see the Publication Manual of the American Psychological Association , Seventh Edition (2020) .

In-text or parenthetical citations (author-date system)

APA style uses the author-date notation, and the in-text citation rules apply to both digital and print editions of books and journals. Also, while providing page number references is optional for paraphrased statements, the APA recommends including them. Also, note that APA style uses the ampersand (&) to list author names in parentheses.

The same author rules apply to all source media including books, print periodicals, electronic journals, etc. Also, since reading electronic journals has become the norm for academics, the APA recommends including a DOI number for each journal article referenced, even if you accessed the document in print. Do not include a period (.) after the DOI information. Also note that APA reference lists should not contain “et al.”, and that the author-number thresholds for formatting rules in the reference list are different from those for in-text citations specified above.

The APA style does not use footnotes and strongly discourages the use of endnotes, which should only provide tangential information. However, sometimes content notes are necessary. In such cases, use the notation covered in Section 2.12 of the  APA Publication Manual .

How to Cite “et al.” in Chicago Style

The Chicago style is commonly used in the humanities. Below, we only comment on general book and journal citation formats. For additional information, see Wordvice’s guide on the Chicago Manual of Style , 17th edition . For an example of an annotated paper that uses bibliographic notation (i.e., numbers that refer to sources in a list), see the Pu rdue Owl’s NB sampler. See an example of an author-date paper.

Note that for formally published online sources, such as electronic academic journals, you do not need to include access date information except if required by your publisher or discipline. If no DOI is available, provide the uniform resource locator (URL). Unlike APA style, Chicago style does NOT use the ampersand (&) in name lists; instead, use “and.” Additionally, an author’s given names (first and middle) should be written in full (no initials) unless the author consistently publishes using initials.

Using “et al.” in in-text or parenthetical citations (author-date system)

Parenthetical citations are more commonly adopted by authors in the social, physical, and natural sciences. The same notation is used for digital and print editions of books and journals.

Don’t use “et al.” in reference lists

Using author “et al.” in books

Using author “et al.” in journals

Using “et al.” in endnotes and footnotes (bibliographic system)

How to Cite “et al.” in MLA Style

The MLA style is commonly used by writers in the humanities. General book and journal citation formations are highlighted below. For information regarding other media and special cases, see Wordvices guide on the MLA Handbook style rules .

Using “et al.” in in-text (parenthetical) citations

The MLA style uses an author-page style instead of an author-date style.

Using “et al.” in the reference list (works cited page)

Using “et al.” in endnotes and footnotes

The MLA style does not generally encourage endnotes and footnotes; however, it does accommodate their use when needed to clarify points that don’t otherwise belong in the main body of your work. The formats for these notes are similar to the format used for in-text citations, but without the parentheses:

One author : See [last name] [page range]

See Johnson 5-15 for a further discussion of this phenomenon.

Multiple authors/studies:  

[Comment]. See [last name] [page range], [last name] [page range], [last name] [page range]

Several other studies make the same argument. See, for example, Walker and Francis 112-118, Thomson 20-43, and Muller 78-90.

Regarding [content topic], see [last name] [page range] and [last name] [page range]; for [content topic], see [last name] [page range], [last name] [page range], and [last name] [page range].

Regarding this phenomenon’s impact on trauma caretakers, see Miller 54-68 and Willis 23-25; for alternative explanations, see Jones 23-25, Thompson 64-55, and Smith 12-15.

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What does ‘et al.’ mean and How to Use ‘et al.’ in a Research Paper

A majority of researchers wonder how to use et al. in a research paper. Et al. is one of the most commonly used Latin abbreviations, just like as,  etc. ,  versus ,  circa ,  ibid.  and  id. , and often crops up in academic writing. While the English phrases of all these above mentioned words are acceptable, researchers use Latin abbreviations as they take less time and fewer characters to write. Yet it’s not always easy to get these right.

In this article, we focus on one such abbreviation – et al. by explaining what does et al. mean and how to use et al. in a research paper correctly

Table of Contents

Et al. definition: what does et al. mean in academic writing, how to use et al. in a research paper, how to use et al. in a research paper: common mistakes to avoid.

The number of co-authors in an academic publication is, in principle, unlimited. Imagine having to write the names of all the authors in your bibliography. This is where et al. comes into play to indicate other authors in an academic work.

Et al. is the abbreviated form of et alia (or et alii or et aliae, the masculine and feminine plural, respectively). According to the Cambridge Dictionary, 1 the synonyms for et al. are “also,” “extra,” and “in addition.” Et al. is mostly used to indicate more than two people; it can also simplify subsequent references to groups of co-authors already cited in full. For example, when citing the same group of authors multiple times in your paper, using et al. can simplify the citations.

The number of authors to be listed before et al. can vary depending on the style guides. A few guidelines on the proper use of et al. in citations and references are given below. 2

• APA Style Guide
• Reference list : Et al. is never used in the reference list in APA.
• In-text Citation : Use et al. only if citing at least three authors (seventh edition). Use the first author’s last name in the signal phrase or parenthesis, followed by et al. For example,

Parenthetical: (Smith et al., 2020)

Nonparenthetical: Smith et al. (2020)

• MLA Style Guide
• Reference list : Use et al. when referencing work with three or more authors; include only the first author, followed by a comma, and the words et al, ending with a period.
• In-text Citation : Use et al. when citing a work with three or more authors. The author name is followed by the page number in place of the year. For example,

Parenthetical: …(James et al. 157-65).

Nonparenthetical: James et al. (157-65)

• Chicago Style Guide
• Reference list : When a source has more than 10 authors, list the first seven followed by “et al.” Otherwise, list every author.
• In-text Citation : When a source has four or more authors, give only the first author’s name followed by “et al.” For example,

(Bay et al. 2017, 465)

• Vancouver Style Guide
• Reference list : When a source has more than six authors, list the first six followed by “et al.” Otherwise, list every author.
• In-text Citation : When a source has three or more authors, give only the first author’s name followed by “et al.” Use et al. directly in the text, followed by the reference number. For example,

Doornbos et al. (5) agree that only one solution is viable.

• Plural vs. singular: Wondering if et al. is a plural or singular verb? Whenever this confuses you, remember that because a phrase ending in “et al.” refers to a group of people, you will use plural verbs when the “et al.” phrase is the subject.

Incorrect: Smith et al. (2015) states that …

Correct: Smith et al. (2015) state that …

Also, “et al.” is plural and indicates at least two people. So, you cannot use et al. to substitute for only one author. For example, if you are dealing with three authors and have typed out two names, the last author cannot be replaced with et al.

• Punctuation: “Et al.” is commonly misspelled as “et all,” “et. al.,” “et. al,” or “et-al.” Remember, “et al.” is composed of two words, with the “al” always followed by a period. The period indicates that the term is an abbreviation.
• Using the incorrect style: Decide on the style guide to follow before you start your writing. The use of et al. in a sentence can vary if using APA, MLA, etc.
• Possessive noun: When using a possessive noun, use “ ’s ” after “et al.”

Correct: In Smith et al.s’ study.

Correct: In Smith et al.’s study.

But, it’s best to avoid possessive phrasing when using et al. Instead, change it “Smith et al. (2015) found that . . .” or “In a study by Smith et al.”

• Italics: Italicizing is unnecessary when using “et al.” But this is more of a style guideline and can vary.
• “Et Al.” vs. “Etc.” and “Et Alibi”: “Et al.,” is sometimes confused with “Etc.” and “et alibi” but they mean different things and have other usages. “Etc.” meaning “rest,” is used at the end when listing things rather than people. “Et Alibi” means “and elsewhere” and is used when listing places or locations.

Finally, remember that when you think of the meaning of et al. in research, it is a word used to indicate other authors in the list. It is not intended to highlight the first author’s contribution as more important than the others, but simply to save space and time.

• Cambridge Dictionary https://dictionary.cambridge.org/dictionary/english/et-al
• Purdue Online Writing Lab. APA Formatting and Style Guide (7 th edition) https://owl.purdue.edu/owl/research_and_citation/apa_style/apa_formatting_and_style_guide/general_format.html

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• Know the Difference: Quoting, Paraphrasing and Summarizing 
• 3 Easy Ways for Researchers to Improve Their Academic Vocabulary
• 7 Common Writing Mistakes to Avoid in Your Research Paper 

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How to Use "et al."

What is the meaning of “et al.”.

"Et al." is an abbreviation for the Latin phrase "et alii" or "et alia," which translates to "and others" in English. It is used to indicate that there are additional authors or contributors beyond those explicitly mentioned.

In academic and scholarly writing, "et al." is commonly used in citations, reference lists, and bibliographies to represent multiple authors (three or more) when citing a source. It is an efficient way to acknowledge all contributors without listing all of the names, especially when there are numerous authors involved.

For example, if a research paper has several authors, the first citation may include all authors’ names, but all following in-text citations may use "et al." to refer to them collectively. This means that the first time the article is referenced, the author would state “Williams, Clark, and Fisher (2010)”. Every time that same article is mentioned after that, the author would write “Williams et al. (2010)”.

How to Use “et al.” in Citations

Here's another example of how “et al.” is used in a citation:

- First citation: Anong, Johnson, Anderson, and Brown (2022)

- Subsequent citations: Anong et al. (2022)

By using “et al.”, the reader understands that there are three or more additional authors not explicitly listed in the citation.

It’s important to note that the usage and formatting of “et al.” varies depending on the citation style or guidelines you are following. Each style guide, such as APA, MLA, or Chicago, has its own rules for using “et al.” for in-text citations and reference lists. You need to consult the appropriate style guide for the specific rules and conventions of your chosen citation style.

Some journals do not require you to follow a specific style guide, but do request that you keep your reference formatting consistent. If you’re submitting to the Journal of Economic Psychology , for example, “references can be in any style or format as long as the style is consistent.”

Using “et al.” in Reference Lists

In a reference list or bibliography, “et al.” is sometimes used to indicate multiple authors for a particular source. This applies for some , but not all, style guides. Here's an example:

   - For an article with multiple authors: Anong, S., Solis, O., et al. (2022). Title of the article. Journal Name , Volume (Issue), Page range.

   Note: The first few authors’ names (up to and including three authors) are listed, followed by “et al.” to indicate additional authors.

It’s important to follow the specific citation style recommended by your academic institution or the guidelines provided by the publication you are writing for. Different citation styles, such as APA, MLA, or Chicago, may have specific rules for using “et al.” in citations. Make sure to consult the appropriate style guide for the specific formatting and citation requirements.

APA Style “et al.”

In APA (American Psychological Association) style, “et al.” is used to represent multiple authors in in-text citations and reference lists. Here's how “et al.” is used in APA style:

1. Et al. in-text citations:

For sources with three or more authors: In the first in-text citation, list all the authors’ names. In subsequent citations, use the first author's last name followed by “et al.” and the publication year. For example:

     - First citation: (Anong, West, Anderson, & Brown, 2022)

     - Subsequent citations: (Anong et al., 2022)

 For sources with two authors: Always include both authors’ names in the in-text citation, connected by an ampersand (&). For example:

     - (Anong & West, 2022)

2. Reference list:

   - List up to 20 authors: Include the names of all authors in the reference list.

   - List more than 20 authors: After the 19th author's name, use an ellipsis (...) and then include the last author's name. For example:

     Anong, S., Johnson, A., Anderson, B., ... Brown, C.

Remember to follow the specific APA guidelines for your particular source type, such as journal articles, books, or websites. This is important because there may be slight variations in formatting and punctuation for each type.

It’s necessary to consult the official APA Publication Manual (currently the 7th edition) or online resources provided by the APA for comprehensive guidance on citing sources and using “et al.” correctly in APA style.

“Et al.” in a Sentence

One example of using “et al.” in a sentence following APA Style if the authors are Zhong, Xiao, and Su is: “Zhong et al. (2005) found a gender difference in behavior.” This could also be written as “Research has shown a gender difference in behavior (Zhong et al., 1995). Note that the first time the paper by Zhong et al. (2005) is noted, all authors’ names would be included: “Zhong, Xiao, and Su (2005) found a gender difference in behavior.”

Frequently asked questions

When should i use “et al.” in apa in-text citations.

The abbreviation “ et al. ” (meaning “and others”) is used to shorten APA in-text citations with three or more authors . Here’s how it works:

Only include the first author’s last name, followed by “et al.”, a comma and the year of publication, for example (Taylor et al., 2018).

Frequently asked questions: APA Style

APA footnotes use superscript numbers and should appear in numerical order. You can place footnotes at the bottom of the relevant pages, or on a separate footnotes page at the end:

• For footnotes at the bottom of the page, you can use your word processor to automatically insert footnotes .
• For footnotes at the end of the text in APA, place them on a separate page entitled “Footnotes,” after the r eference page . Indent the first line of each footnote, and double-space them.

For both approaches, place a space between the superscript number and the footnote text.

APA Style requires you to use APA in-text citations , not footnotes, to cite sources .

However, you can use APA footnotes sparingly for two purposes:

• Giving additional information
• Providing copyright attribution

Yes, APA language guidelines state that you should always use the serial comma (aka Oxford comma ) in your writing.

This means including a comma before the word “and” at the end of a list of three or more items: “spelling, grammar, and punctuation.” Doing this consistently tends to make your lists less ambiguous.

Yes, it’s perfectly valid to write sentences in the passive voice . The APA language guidelines do caution against overusing the passive voice, because it can obscure your meaning or be needlessly long-winded. For this reason, default to the active voice in most cases.

The passive voice is most useful when the point of the sentence is just to state what was done, not to emphasize who did it. For example, “The projector was mounted on the wall” is better than “James and I mounted the projector on the wall” if it’s not particularly important who mounted the projector.

Yes, APA language guidelines encourage you to use the first-person pronouns “I” or “we” when referring to yourself or a group including yourself in your writing.

In APA Style, you should not refer to yourself in the third person. For example, do not refer to yourself as “the researcher” or “the author” but simply as “I” or “me.” Referring to yourself in the third person is still common practice in some academic fields, but APA Style rejects this convention.

If you cite several sources by the same author or group of authors, you’ll distinguish between them in your APA in-text citations using the year of publication.

If you cite multiple sources by the same author(s) at the same point , you can just write the author name(s) once and separate the different years with commas, e.g., (Smith, 2020, 2021).

To distinguish between sources with the same author(s) and  the same publication year, add a different lowercase letter after the year for each source, e.g., (Smith, 2020, 2021a, 2021b). Add the same letters to the corresponding reference entries .

According to the APA guidelines, you should report enough detail on inferential statistics so that your readers understand your analyses.

Report the following for each hypothesis test:

• the test statistic value
• the degrees of freedom
• the exact p value (unless it is less than 0.001)
• the magnitude and direction of the effect

You should also present confidence intervals and estimates of effect sizes where relevant.

The number of decimal places to report depends on what you’re reporting. Generally, you should aim to round numbers while retaining precision. It’s best to present fewer decimal digits to aid easy understanding.

Use one decimal place for:

• Standard deviations
• Descriptive statistics based on discrete data

Use two decimal places for:

• Correlation coefficients
• Proportions
• Inferential test statistics such as t values, F values, and chi-squares.

No, including a URL is optional in APA Style reference entries for legal sources (e.g. court cases , laws ). It can be useful to do so to aid the reader in retrieving the source, but it’s not required, since the other information included should be enough to locate it.

Generally, you should identify a law in an APA reference entry by its location in the United States Code (U.S.C.).

But if the law is either spread across various sections of the code or not featured in the code at all, include the public law number in addition to information on the source you accessed the law in, e.g.:

You should report methods using the past tense , even if you haven’t completed your study at the time of writing. That’s because the methods section is intended to describe completed actions or research.

In your APA methods section , you should report detailed information on the participants, materials, and procedures used.

• Describe all relevant participant or subject characteristics, the sampling procedures used and the sample size and power .
• Define all primary and secondary measures and discuss the quality of measurements.
• Specify the data collection methods, the research design and data analysis strategy, including any steps taken to transform the data and statistical analyses.

With APA legal citations, it’s recommended to cite all the reporters (publications reporting cases) in which a court case appears. To cite multiple reporters, just separate them with commas in your reference entry . This is called parallel citation .

Don’t repeat the name of the case, court, or year; just list the volume, reporter, and page number for each citation. For example:

In APA Style , when you’re citing a recent court case that has not yet been reported in print and thus doesn’t have a specific page number, include a series of three underscores (___) where the page number would usually appear:

In APA style, statistics can be presented in the main text or as tables or figures . To decide how to present numbers, you can follow APA guidelines:

• To present three or fewer numbers, try a sentence,
• To present between 4 and 20 numbers, try a table,
• To present more than 20 numbers, try a figure.

Since these are general guidelines, use your own judgment and feedback from others for effective presentation of numbers.

In an APA results section , you should generally report the following:

• Participant flow and recruitment period.
• Missing data and any adverse events.
• Descriptive statistics about your samples.
• Inferential statistics , including confidence intervals and effect sizes.
• Results of any subgroup or exploratory analyses, if applicable.

When citing a podcast episode in APA Style , the podcast’s host is listed as author , accompanied by a label identifying their role, e.g. Glass, I. (Host).

When citing a whole podcast series, if different episodes have different hosts, list the executive producer(s) instead. Again, include a label identifying their role, e.g. Lechtenberg, S. (Producer).

Like most style guides , APA recommends listing the book of the Bible you’re citing in your APA in-text citation , in combination with chapter and verse numbers. For example:

Books of the Bible may be abbreviated to save space; a list of standard abbreviations can be found here . Page numbers are not used in Bible citations.

Yes, in the 7th edition of APA Style , versions of the Bible are treated much like other books ; you should include the edition you used in your reference list .

Previously, in the 6th edition of the APA manual, it was recommended to just use APA 6 in-text citations to refer to the Bible, and omit it from the reference list.

To make it easy for the reader to find the YouTube video , list the person or organization who uploaded the video as the author in your reference entry and APA in-text citation .

If this isn’t the same person responsible for the content of the video, you might want to make this clear in the text. For example:

When you need to highlight a specific moment in a video or audio source, use a timestamp in your APA in-text citation . Just include the timestamp from the start of the part you’re citing. For example:

To include a direct quote in APA , follow these rules:

• Quotes under 40 words are placed in double quotation marks .
• Quotes of 40 words or more are formatted as block quote .
• The author, year, and page number are included in an APA in-text citation .

APA doesn’t require you to include a list of tables or a list of figures . However, it is advisable to do so if your text is long enough to feature a table of contents and it includes a lot of tables and/or figures .

A list of tables and list of figures appear (in that order) after your table of contents, and are presented in a similar way.

Copyright information can usually be found wherever the table or figure was published. For example, for a diagram in a journal article , look on the journal’s website or the database where you found the article. Images found on sites like Flickr are listed with clear copyright information.

If you find that permission is required to reproduce the material, be sure to contact the author or publisher and ask for it.

If you adapt or reproduce a table or figure from another source, you should include that source in your APA reference list . You should also include copyright information in the note for the table or figure, and include an APA in-text citation when you refer to it.

Tables and figures you created yourself, based on your own data, are not included in the reference list.

An APA in-text citation is placed before the final punctuation mark in a sentence.

• The company invested over 40,000 hours in optimizing its algorithm (Davis, 2011) .
• A recent poll suggests that EU membership “would be backed by 55 percent of Danish voters” in a referendum (Levring, 2018) .

In an APA in-text citation , you use the phrase “ as cited in ” if you want to cite a source indirectly (i.e., if you cannot find the original source).

Parenthetical citation: (Brown, 1829, as cited in Mahone, 2018) Narrative citation: Brown (1829, as cited in Mahone, 2018) states that…

On the reference page , you only include the secondary source (Mahone, 2018).

Popular word processors like Microsoft Word and Google Docs can order lists in alphabetical order, but they don’t follow the APA Style alphabetization guidelines .

If you use Scribbr’s APA Citation Generator to create citations, references are ordered automatically based on the APA guidelines, taking into account all the exceptions.

Order numerals as though they were spelled out:

• “20 tips to relax” is ordered on the “T” of “Twenty”.
• “100 cities you should visit” is ordered on the “O” of “One hundred”.

Read more about alphabetizing the APA reference page .

If the author of a work is unknown, order the reference by its title. Disregard the words “A”, “An”, and “The” at the beginning of the title.

• The privacy concerns around social media
• Teens, social media, and privacy

Yes, if relevant you can and should include APA in-text citations in your appendices . Use author-date citations as you do in the main text.

Any sources cited in your appendices should appear in your reference list . Do not create a separate reference list for your appendices.

When you include more than one appendix in an APA Style paper , they should be labeled “Appendix A,” “Appendix B,” and so on.

When you only include a single appendix, it is simply called “Appendix” and referred to as such in the main text.

Appendices in an APA Style paper appear right at the end, after the reference list and after your tables and figures if you’ve also included these at the end.

An appendix contains information that supplements the reader’s understanding of your research but is not essential to it. For example:

• Interview transcripts
• Questionnaires
• Detailed descriptions of equipment

Something is only worth including as an appendix if you refer to information from it at some point in the text (e.g. quoting from an interview transcript). If you don’t, it should probably be removed.

If you adapt or reproduce a table or figure from another source, you should include that source in your APA reference list . You should also acknowledge the original source in the note or caption for the table or figure.

APA doesn’t require you to include a list of tables or a list of figures . However, it is advisable to do so if your text is long enough to feature a table of contents and it includes a lot of tables and/or figures.

A list of tables and list of figures appear (in that order) after your table of contents , and are presented in a similar way.

In an APA Style paper , use a table or figure when it’s a clearer way to present important data than describing it in your main text. This is often the case when you need to communicate a large amount of information.

Before including a table or figure in your text, always reflect on whether it’s useful to your readers’ understanding:

• Could this information be quickly summarized in the text instead?
• Is it important to your arguments?
• Does the table or figure require too much explanation to be efficient?

If the data you need to present only contains a few relevant numbers, try summarizing it in the text (potentially including full data in an appendix ). If describing the data makes your text overly long and difficult to read, a table or figure may be the best option.

In an APA Style paper , the abstract is placed on a separate page after the title page (page 2).

An APA abstract is around 150–250 words long. However, always check your target journal’s guidelines and don’t exceed the specified word count.

In APA Style , all sources that are not retrievable for the reader are cited as personal communications . In other words, if your source is private or inaccessible to the audience of your paper , it’s a personal communication.

Common examples include conversations, emails, messages, letters, and unrecorded interviews or performances.

Interviews you conducted yourself are not included in your reference list , but instead cited in the text as personal communications .

Published or recorded interviews are included in the reference list. Cite them in the usual format of the source type (for example, a newspaper article , website or YouTube video ).

To cite a public post from social media , use the first 20 words of the post as a title, include the date it was posted and a URL, and mention the author’s username if they have one:

Dorsey, J. [@jack]. (2018, March 1). We’re committing Twitter to help increase the collective health, openness, and civility of public conversation, and to hold ourselves publicly [Tweet]. Twitter. https://twitter.com/jack/status/969234275420655616

To cite content from social media that is not publicly accessible (e.g. direct messages, posts from private groups or user profiles), cite it as a personal communication in the text, but do not include it in the reference list :

When contacted online, the minister stated that the project was proceeding “according to plan” (R. James, Twitter direct message, March 25, 2017).

When you quote or paraphrase a specific passage from a source, you need to indicate the location of the passage in your APA in-text citation . If there are no page numbers (e.g. when citing a website ) but the text is long, you can instead use section headings, paragraph numbers, or a combination of the two:

(Caulfield, 2019, Linking section, para. 1).

Section headings can be shortened if necessary. Kindle location numbers should not be used in ebook citations , as they are unreliable.

If you are referring to the source as a whole, it’s not necessary to include a page number or other marker.

When no individual author name is listed, but the source can clearly be attributed to a specific organization—e.g., a press release by a charity, a report by an agency, or a page from a company’s website—use the organization’s name as the author in the reference entry and APA in-text citations .

When no author at all can be determined—e.g. a collaboratively edited wiki or an online article published anonymously—use the title in place of the author. In the in-text citation, put the title in quotation marks if it appears in plain text in the reference list, and in italics if it appears in italics in the reference list. Shorten it if necessary.

APA Style usually does not require an access date. You never need to include one when citing journal articles , e-books , or other stable online sources.

However, if you are citing a website or online article that’s designed to change over time, it’s a good idea to include an access date. In this case, write it in the following format at the end of the reference: Retrieved October 19, 2020, from https://www.uva.nl/en/about-the-uva/about-the-university/about-the-university.html

The 7th edition APA Manual , published in October 2019, is the most current edition. However, the 6th edition, published in 2009, is still used by many universities and journals.

The APA Manual 7th edition can be purchased at Amazon as a hardcover, paperback or spiral-bound version. You can also buy an ebook version at RedShelf .

The American Psychological Association anticipates that most people will start using the 7th edition in the spring of 2020 or thereafter.

It’s best to ask your supervisor or check the website of the journal you want to publish in to see which APA guidelines you should follow.

If you’re citing from an edition other than the first (e.g. a 2nd edition or revised edition), the edition appears in the reference, abbreviated in parentheses after the book’s title (e.g. 2nd ed. or Rev. ed.).

In the 7th edition of the APA manual, no location information is required for publishers. The 6th edition previously required you to include the city and state where the publisher was located, but this is no longer the case.

In an APA reference list , journal article citations include only the year of publication, not the exact date, month, or season.

The inclusion of volume and issue numbers makes a more specific date unnecessary.

In an APA journal citation , if a DOI (digital object identifier) is available for an article, always include it.

If an article has no DOI, and you accessed it through a database or in print, just omit the DOI.

If an article has no DOI, and you accessed it through a website other than a database (for example, the journal’s own website), include a URL linking to the article.

You may include up to 20 authors in a reference list entry .

When an article has more than 20 authors, replace the names prior to the final listed author with an ellipsis, but do not omit the final author:

Davis, Y., Smith, J., Caulfield, F., Pullman, H., Carlisle, J., Donahue, S. D., James, F., O’Donnell, K., Singh, J., Johnson, L., Streefkerk, R., McCombes, S., Corrieri, L., Valck, X., Baldwin, F. M., Lorde, J., Wardell, K., Lao, W., Yang, P., . . . O’Brien, T. (2012).

Include the DOI at the very end of the APA reference entry . If you’re using the 6th edition APA guidelines, the DOI is preceded by the label “doi:”. In the 7th edition , the DOI is preceded by ‘https://doi.org/’.

• 6th edition: doi: 10.1177/0894439316660340
• 7th edition: https://doi.org/ 10.1177/0894439316660340

APA citation example (7th edition)

Hawi, N. S., & Samaha, M. (2016). The relations among social media addiction, self-esteem, and life satisfaction in university students. Social Science Computer Review , 35 (5), 576–586. https://doi.org/10.1177/0894439316660340

When citing a webpage or online article , the APA in-text citation consists of the author’s last name and year of publication. For example: (Worland & Williams, 2015). Note that the author can also be an organization. For example: (American Psychological Association, 2019).

If you’re quoting you should also include a locator. Since web pages don’t have page numbers, you can use one of the following options:

• Paragraph number: (Smith, 2018, para. 15).
• Heading or section name: ( CDC, 2020, Flu Season section)
• Abbreviated heading:  ( CDC, 2020, “Key Facts” section)

Always include page numbers in the APA in-text citation when quoting a source . Don’t include page numbers when referring to a work as a whole – for example, an entire book or journal article.

If your source does not have page numbers, you can use an alternative locator such as a timestamp, chapter heading or paragraph number.

Instead of the author’s name, include the first few words of the work’s title in the in-text citation. Enclose the title in double quotation marks when citing an article, web page or book chapter. Italicize the title of periodicals, books, and reports.

No publication date

If the publication date is unknown , use “n.d.” (no date) instead. For example: (Johnson, n.d.).

APA Style papers should be written in a font that is legible and widely accessible. For example:

• Times New Roman (12pt.)
• Arial (11pt.)
• Calibri (11pt.)
• Georgia (11pt.)

The same font and font size is used throughout the document, including the running head , page numbers, headings , and the reference page . Text in footnotes and figure images may be smaller and use single line spacing.

The easiest way to set up APA format in Word is to download Scribbr’s free APA format template for student papers or professional papers.

Alternatively, you can watch Scribbr’s 5-minute step-by-step tutorial or check out our APA format guide with examples.

You need an APA in-text citation and reference entry . Each source type has its own format; for example, a webpage citation is different from a book citation .

Use Scribbr’s free APA Citation Generator to generate flawless citations in seconds or take a look at our APA citation examples .

APA format is widely used by professionals, researchers, and students in the social and behavioral sciences, including fields like education, psychology, and business.

Be sure to check the guidelines of your university or the journal you want to be published in to double-check which style you should be using.

Yes, page numbers are included on all pages, including the title page , table of contents , and reference page . Page numbers should be right-aligned in the page header.

To insert page numbers in Microsoft Word or Google Docs, click ‘Insert’ and then ‘Page number’.

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How to Use Et Al

Last Updated: May 18, 2024 Fact Checked

This article was co-authored by Michelle Golden, PhD . Michelle Golden is an English teacher in Athens, Georgia. She received her MA in Language Arts Teacher Education in 2008 and received her PhD in English from Georgia State University in 2015. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 404,921 times.

Latin abbreviations, like etc. and et al. are used frequently and often incorrectly. Et al. means “and others”, and abbreviates people in a list, while etc. can be used to abbreviate almost anything. [1] X Research source A period is always used after et al., since the term is used to abbreviate the Latin term “et alii.” There are several rules, however, both formal and informal, that are required for proper usage of et al.

Using Et Al. Formally

• If Lewis, Gilbert, and Lamar wrote something about teamwork, the reference could be: ”Lewis et al. (2006) demonstrated teamwork environment is critical to success.”

• First citations: (Dobbs, Almond, & Chen, 2009)
• Subsequent citations: (Dobbs, Almond, & Chen, 2009)
• First citations: (Dobbs, Almond, Chen, Brown, & Ender, 2009)
• Subsequent citations: (Dobbs, Almond, Chen, et al., 2009)
• All citations are (Wilson, Dobbs, & Almond, 2009), and do not coincide or conflict in any way with the previous two citations because Wilson is the lead author, and different from the lead author (i.e. Dobbs) on the other two.

• Not using the Oxford comma, “Moe, Curly, Larry and Shemp” would be “Moe, Curly et al.”
• Using the Oxford comma, “John, Paul, George, and Ringo” would be “John, Paul, et al.”

Differentiating Et Al. Based on the Number of Authors

• First citation – (Balboa, Creed, & Drago, 1985)
• Subsequent citations – (Balboa et al., 1985)

• First citation – (Highway et al., 1986)
• Subsequent citations – (Highway et al., 1986)

Using Et Al. Informally

• ”We should go to the work overtime this weekend Jim, Jesse, Brian et al. to get the project done.”
• ”If David et al. get the financing, we can move forward with the prototype.”

• ”The Bulls would have lost the game if not for Jordan and the other guards.”
• ”Woody, Buzz Lightyear, and the rest made it safely to the day care.”

• Try substituting an appropriate plural word for the group you’re addressing, instead of forcing et al. into a greeting.

Community Q&A

You Might Also Like

• ↑ https://grammar.yourdictionary.com/grammar/style-and-usage/what-s-the-difference-between-etc-and-et-al.html
• ↑ https://academicguides.waldenu.edu/writingcenter/apa/citations/etal
• ↑ https://owl.purdue.edu/owl/research_and_citation/apa_style/apa_formatting_and_style_guide/in_text_citations_author_authors.html
• ↑ https://blog.apastyle.org/apastyle/2011/11/the-proper-use-of-et-al-in-apa-style.html
• ↑ https://grammarist.com/usage/et-al/
• ↑ https://www.businesswritingblog.com/business_writing/2009/11/dear-john-et-al.html

About This Article

To use et al., keep in mind that the Latin phrase means "and others" to help you decide where and when to use it. You can use et al. formally when you're creating in-text citations and parenthetical remarks so that you don't have to list a long string of names. You can also use the phrase in less formal situations, like when you need to refer to a group of coworkers in a work email. Et al. works best when written, so try to avoid using it in general, everyday conversations. To learn more about using et al. correctly in citations, read on! Did this summary help you? Yes No

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In-Text Citations: Author/Authors

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Though the APA's author-date system for citations is fairly straightforward, author categories can vary significantly from the standard "one author, one source" configuration. There are also additional rules for citing authors of indirect sources, electronic sources, and sources without page numbers.

A Work by One Author 

The APA manual recommends the use of the author-date citation structure for in-text citation references. This structure requires that any in-text citation (i.e., within the body of the text) be accompanied by a corresponding reference list entry. In the in-text citation provide the surname of the author but do not include suffixes such as "Jr.". 

Citing Non-Standard Author Categories

A work by two authors.

Name both authors in the signal phrase or in parentheses each time you cite the work. Use the word "and" between the authors' names within the text and use the ampersand in parentheses.

A Work by Three or More Authors

List only the first author’s name followed by “et al.” in every citation, even the first, unless doing so would create ambiguity between different sources.

In  et al. , et  should not be followed by a period. Only "al" should be followed by a period.

If you’re citing multiple works with similar groups of authors, and the shortened “et al” citation form of each source would be the same, you’ll need to avoid ambiguity by writing out more names. If you cited works with these authors:

They would be cited in-text as follows to avoid ambiguity:

Since et al. is plural, it should always be a substitute for more than one name. In the case that et al. would stand in for just one author, write the author’s name instead.

Unknown Author

If the work does not have an author, cite the source by its title in the signal phrase or use the first word or two in the parentheses. Titles of books and reports are italicized; titles of articles, chapters, and web pages are in quotation marks. APA style calls for capitalizing important words in titles when they are written in the text (but not when they are written in reference lists).

Note : In the rare case that "Anonymous" is used for the author, treat it as the author's name (Anonymous, 2001). In the reference list, use the name Anonymous as the author.

Organization as an Author

If the author is an organization or a government agency, mention the organization in the signal phrase or in the parenthetical citation the first time you cite the source, just as you would an individual person.

If the organization has a well-known abbreviation, you may include the abbreviation in brackets the first time the source is cited and then use only the abbreviation in later citations. However, if you cite work from multiple organizations whose abbreviations are the same, do not use abbreviations (to avoid ambiguity).

Two or More Works in the Same Parentheses

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Note:  Never use the page numbers of webpages you print out; different computers print webpages with different pagination. Do not use Kindle location numbers; instead, use the page number (available in many Kindle books) or the method above. 

Other Sources

The  APA Publication Manual  describes how to cite many different kinds of authors and content creators. However, you may occasionally encounter a source or author category that the manual does not describe, making the best way to proceed unclear.

In these cases, it's typically acceptable to apply the general principles of APA citation to the new kind of source in a way that's consistent and sensible. A good way to do this is to simply use the standard APA directions for a type of source that resembles the source you want to cite. For example, a sensible way to cite a virtual reality program would be to mimic the APA's guidelines for computer software.

You may also want to investigate whether a third-party organization has provided directions for how to cite this kind of source.

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Use of et al. – for referencing in an academic paper

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“Et al.” is a popular expression used by college and university students when citing a research source having more than one author. Included in this article is its definition, how to use it when using different citation styles, and the most frequently asked questions regarding the use of et al. The information contained here is vital, as it will assist you to know how to use the term correctly, which may, in the long run, help in boosting your grades.

Inhaltsverzeichnis

• 1 Use of et al. - FAQ
• 2 Use of et al.: Definition
• 3 Use of et al. in Citation
• 4 Use of et al. Common Mistakes
• 5 In a Nutshell

Use of et al. - FAQ

When do you need to use et al..

Et al. is an abbreviation of et al. ii, a Latin expression, which means ‘and others’. You often need to make use of et al. in a citation that has three or more authors. Its purpose is to assist in making the citations manageable. If you are using the author’s name, you have to ensure you add a full stop after writing et al.

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How do you punctuate et al.?

Some college students don’t know how to make the right use of et al. Whenever you have to use the term, you have to note that the “al” should always have a period after it. The period is vital because et al. is an abbreviation . Including the period helps to show this to the reader.

How do you read et al.?

Learning the use of et al. also means learning how to pronounce it. If reading it aloud, you will be required to pronounce the term in full, i.e., “et alia” or “et al. ii”. On the other hand, you could also choose to say “and others.” It’s the same way you would opt to say “for example,” as opposed to reading the abbreviation “e.g.”

Can you start an email with et al.?

Not sure how to make use of et al. in an email? It’s possible to do so. For example, in the greeting section, you could say Dear Daniel et al., Hello, Kevin et al., Remember that the expression stands for “and others.”

Should et al. be Italicized?

When using et al., you shouldn’t underline or italicize it. You have to write it without either of the two. As a rule, the most commonly used Latin abbreviations and words shouldn’t be italicized.

Use of et al.: Definition

Definition 1: et al. and others: It’s an abbreviation of ‘et alii’ which is used when the author is referring to a group of people. Definition 2: et al. and elsewhere: Authors use it when they want to refer to other occurrences in the text. Why it’s used: When citing papers that use the name and dating system, it can prove awkward when the author provides a long string containing numerous names. It’s the reason why many scientific journals recommend that authors make use of et al. When it’s used: Its recommended to try to make use of et al. when an author doesn’t want to have to name all the things or people in a list. The abbreviation works in the same manner as “etc.”

Use of et al. in Citation

Using Et Al. in APA Citation

APA citation happens to have a few quirks, with one of them being in the use of et al. While the abbreviation is used when citing sources having many authors, the 7th APA citation edition happens to differ from the rest in terms of how to make use of et al.

Only make use of et al. when using in-text citations

The 7th edition states that et al. should only be used when one is using in-text citations. It’s a significant change from the previous edition where authors could use et al. in the reference list. This means that the reference list in the 7th edition doesn’t support the use of et al.

In-text citation format using et al.

Et al. should only be used in in-text citations when an author wants to reference a source having three or more authors. Here, you can make use of et al. by including the authors first name, and then including et al. in every other Citation.

Exceptions: Multiple works sharing a single author

There are instances when making use of et al. could lead to unwanted problems. For example, when numerous works share the same three authors and year of publication, simply writing “et al.” could muddy the waters. When dealing with such a case, it’s recommended to write as many names as possible to help differentiate the references. You can then make use of et al. for any remaining names.

Using Et Al. in MLA Citation

For MLA citation , it’s recommended that you make use of et al. whenever there are sources with more than three sources. It’s a rule that applies to both the Works Cited list and the in-text citations.

Using Et Al. in Chicago Citation

Chicago Style Citation traditionally has two citation systems: author-date style and notes and bibliography style. The use of et al. doesn’t differ in both styles. When working with sources with one, two, or three plus authors, you will need to list all their names in your in-text citations (author-date or footnotes).

In case you have a source with four-plus authors, then it’s advisable to use et al. by listing the first name and following it up with et al. In the Chicago style bibliography or reference list, you will need to list up to ten authors. For any source with over ten authors, you should list the first seven and then follow this with et al.

For example, Harold Peters, McDonnel, Anne Elliot, Frederick, Robert Davis, Molly Davidson, Ronald Clobus, Jessica Singh, et al.

Use of et al. Common Mistakes

I. Most students tend to make use of et al. with works that don’t have multiple sources. Remember, you only need to use it when the source has more than three authors. II. Punctuation Mistakes: the “al” in “et al.” should always have a period after it. The reason for using the period is because “et al.” is an abbreviation. It’s why you need the period.

• Where necessary, it can also be followed by another punctuation mark where deemed necessary. However, make sure that the period comes first, before the other punctuation mark.

III. Et al. vs etc. Some students end up confusing “etc.” with et al. This shouldn’t happen as “etc.” is used for concepts and lists of things whereas “et al.” is primarily used when dealing with lists of people.

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In a Nutshell

• Et al. is an abbreviation for a Latin term “et alia” which means “and others.”
• The expression is commonly used in academic papers when a writer wants to cite more than one author
• Each citation style has its own rules on how to use et al. in both the in-text citations and in the works cited section.
•  Common FAQs on making use of et al. have to do with reading it aloud and punctuating it correctly.

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Tasks At Work: Comparative Advantage, Technology and Labor Demand

This chapter reviews recent advances in the task model and shows how this framework can be put to work to understand the major labor market trends of the last several decades. Production in each industry necessitates the completion of a range of tasks, which can be allocated to workers of different skill types or to capital. Factors of production have well-defined comparative advantage across tasks, which governs the pattern of substitution between skill groups. Technological change can: (1) augment a specific labor type—e.g., increase the productivity of labor in tasks it is already performing; (2) augment capital; (3) automate work by enabling capital to perform tasks previously allocated to labor; (4) create new tasks. The task model clarifies that these different types of technological changes have distinct effects on labor demand, factor shares and productivity, and their full impact depends on the pattern of substitution between different factors which arises endogenously in the task framework. We explore the implications of the task framework using reduced-form evidence, which highlights the central role of automation and new tasks in recent labor market trends. We also explain how general equilibrium effects ignored in these reduced-form approaches can be estimated structurally.

We thank the editors Christian Dustmann and Thomas Lemieux for their detailed comments. Acemoglu gratefully acknowledges support from the Hewlett and Smith Richardson Foundations, Kong from the Bradley Foundation, and Restrepo from the National Science Foundation (Award No. 2049427). The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.

Restrepo received compensation for advising internal research at OpenAI on the economic effects of LLMs.

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• Published: 22 July 2024

Neural general circulation models for weather and climate

• Dmitrii Kochkov   ORCID: orcid.org/0000-0003-3846-4911 1   na1 ,
• Janni Yuval   ORCID: orcid.org/0000-0001-7519-0118 1   na1 ,
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• Peter Düben   ORCID: orcid.org/0000-0002-4610-3326 3 ,
• Sam Hatfield 3 ,
• Peter Battaglia 4 ,
• Alvaro Sanchez-Gonzalez 4 ,
• Matthew Willson   ORCID: orcid.org/0000-0002-8730-1927 4 ,
• Michael P. Brenner 1 , 5 &
• Stephan Hoyer   ORCID: orcid.org/0000-0002-5207-0380 1   na1  

Nature volume  632 ,  pages 1060–1066 ( 2024 ) Cite this article

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• Atmospheric dynamics
• Climate and Earth system modelling
• Computational science

General circulation models (GCMs) are the foundation of weather and climate prediction 1 , 2 . GCMs are physics-based simulators that combine a numerical solver for large-scale dynamics with tuned representations for small-scale processes such as cloud formation. Recently, machine-learning models trained on reanalysis data have achieved comparable or better skill than GCMs for deterministic weather forecasting 3 , 4 . However, these models have not demonstrated improved ensemble forecasts, or shown sufficient stability for long-term weather and climate simulations. Here we present a GCM that combines a differentiable solver for atmospheric dynamics with machine-learning components and show that it can generate forecasts of deterministic weather, ensemble weather and climate on par with the best machine-learning and physics-based methods. NeuralGCM is competitive with machine-learning models for one- to ten-day forecasts, and with the European Centre for Medium-Range Weather Forecasts ensemble prediction for one- to fifteen-day forecasts. With prescribed sea surface temperature, NeuralGCM can accurately track climate metrics for multiple decades, and climate forecasts with 140-kilometre resolution show emergent phenomena such as realistic frequency and trajectories of tropical cyclones. For both weather and climate, our approach offers orders of magnitude computational savings over conventional GCMs, although our model does not extrapolate to substantially different future climates. Our results show that end-to-end deep learning is compatible with tasks performed by conventional GCMs and can enhance the large-scale physical simulations that are essential for understanding and predicting the Earth system.

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Solving the equations for Earth’s atmosphere with general circulation models (GCMs) is the basis of weather and climate prediction 1 , 2 . Over the past 70 years, GCMs have been steadily improved with better numerical methods and more detailed physical models, while exploiting faster computers to run at higher resolution. Inside GCMs, the unresolved physical processes such as clouds, radiation and precipitation are represented by semi-empirical parameterizations. Tuning GCMs to match historical data remains a manual process 5 , and GCMs retain many persistent errors and biases 6 , 7 , 8 . The difficulty of reducing uncertainty in long-term climate projections 9 and estimating distributions of extreme weather events 10 presents major challenges for climate mitigation and adaptation 11 .

Recent advances in machine learning have presented an alternative for weather forecasting 3 , 4 , 12 , 13 . These models rely solely on machine-learning techniques, using roughly 40 years of historical data from the European Center for Medium-Range Weather Forecasts (ECMWF) reanalysis v5 (ERA5) 14 for model training and forecast initialization. Machine-learning methods have been remarkably successful, demonstrating state-of-the-art deterministic forecasts for 1- to 10-day weather prediction at a fraction of the computational cost of traditional models 3 , 4 . Machine-learning atmospheric models also require considerably less code, for example GraphCast 3 has 5,417 lines versus 376,578 lines for the National Oceanic and Atmospheric Administration’s FV3 atmospheric model 15 (see Supplementary Information section  A for details).

Nevertheless, machine-learning approaches have noteworthy limitations compared with GCMs. Existing machine-learning models have focused on deterministic prediction, and surpass deterministic numerical weather prediction in terms of the aggregate metrics for which they are trained 3 , 4 . However, they do not produce calibrated uncertainty estimates 4 , which is essential for useful weather forecasts 1 . Deterministic machine-learning models using a mean-squared-error loss are rewarded for averaging over uncertainty, producing unrealistically blurry predictions when optimized for multi-day forecasts 3 , 13 . Unlike physical models, machine-learning models misrepresent derived (diagnostic) variables such as geostrophic wind 16 . Furthermore, although there has been some success in using machine-learning approaches on longer timescales 17 , 18 , these models have not demonstrated the ability to outperform existing GCMs.

Hybrid models that combine GCMs with machine learning are appealing because they build on the interpretability, extensibility and successful track record of traditional atmospheric models 19 , 20 . In the hybrid model approach, a machine-learning component replaces or corrects the traditional physical parameterizations of a GCM. Until now, the machine-learning component in such models has been trained ‘offline’, by learning parameterizations independently of their interaction with dynamics. These components are then inserted into an existing GCM. The lack of coupling between machine-learning components and the governing equations during training potentially causes serious problems, such as instability and climate drift 21 . So far, hybrid models have mostly been limited to idealized scenarios such as aquaplanets 22 , 23 . Under realistic conditions, machine-learning corrections have reduced some biases of very coarse GCMs 24 , 25 , 26 , but performance remains considerably worse than state-of-the-art models.

Here we present NeuralGCM, a fully differentiable hybrid GCM of Earth’s atmosphere. NeuralGCM is trained on forecasting up to 5-day weather trajectories sampled from ERA5. Differentiability enables end-to-end ‘online training’ 27 , with machine-learning components optimized in the context of interactions with the governing equations for large-scale dynamics, which we find enables accurate and stable forecasts. NeuralGCM produces physically consistent forecasts with accuracy comparable to best-in-class models across a range of timescales, from 1- to 15-day weather to decadal climate prediction.

Neural GCMs

A schematic of NeuralGCM is shown in Fig. 1 . The two key components of NeuralGCM are a differentiable dynamical core for solving the discretized governing dynamical equations and a learned physics module that parameterizes physical processes with a neural network, described in full detail in Methods , Supplementary Information sections  B and C , and Supplementary Table 1 . The dynamical core simulates large-scale fluid motion and thermodynamics under the influence of gravity and the Coriolis force. The learned physics module (Supplementary Fig. 1 ) predicts the effect of unresolved processes, such as cloud formation, radiative transport, precipitation and subgrid-scale dynamics, on the simulated fields using a neural network.

a , Overall model structure, showing how forcings F t , noise z t (for stochastic models) and inputs y t are encoded into the model state x t . The model state is fed into the dynamical core, and alongside forcings and noise into the learned physics module. This produces tendencies (rates of change) used by an implicit–explicit ordinary differential equation (ODE) solver to advance the state in time. The new model state x t +1 can then be fed back into another time step, or decoded into model predictions. b , The learned physics module, which feeds data for individual columns of the atmosphere into a neural network used to produce physics tendencies in that vertical column.

The differentiable dynamical core in NeuralGCM allows an end-to-end training approach, whereby we advance the model multiple time steps before employing stochastic gradient descent to minimize discrepancies between model predictions and reanalysis (Supplementary Information section  G.2 ). We gradually increase the rollout length from 6 hours to 5 days (Supplementary Information section  G and Supplementary Table 5 ), which we found to be critical because our models are not accurate for multi-day prediction or stable for long rollouts early in training (Supplementary Information section  H.6.2 and Supplementary Fig. 23 ). The extended back-propagation through hundreds of simulation steps enables our neural networks to take into account interactions between the learned physics and the dynamical core. We train deterministic and stochastic NeuralGCM models, each of which uses a distinct training protocol, described in full detail in Methods and Supplementary Table 4 .

We train a range of NeuralGCM models at horizontal resolutions with grid spacing of 2.8°, 1.4° and 0.7° (Supplementary Fig. 7 ). We evaluate the performance of NeuralGCM at a range of timescales appropriate for weather forecasting and climate simulation. For weather, we compare against the best-in-class conventional physics-based weather models, ECMWF’s high-resolution model (ECMWF-HRES) and ensemble prediction system (ECMWF-ENS), and two of the recent machine-learning-based approaches, GraphCast 3 and Pangu 4 . For climate, we compare against a global cloud-resolving model and Atmospheric Model Intercomparison Project (AMIP) runs.

Medium-range weather forecasting

Our evaluation set-up focuses on quantifying accuracy and physical consistency, following WeatherBench2 12 . We regrid all forecasts to a 1.5° grid using conservative regridding, and average over all 732 forecasts made at noon and midnight UTC in the year 2020, which was held-out from training data for all machine-learning models. NeuralGCM, GraphCast and Pangu compare with ERA5 as the ground truth, whereas ECMWF-ENS and ECMWF-HRES compare with the ECMWF operational analysis (that is, HRES at 0-hour lead time), to avoid penalizing the operational forecasts for different biases than ERA5.

Model accuracy

We use ECMWF’s ensemble (ENS) model as a reference baseline as it achieves the best performance across the majority of lead times 12 . We assess accuracy using (1) root-mean-squared error (RMSE), (2) root-mean-squared bias (RMSB), (3) continuous ranked probability score (CRPS) and (4) spread-skill ratio, with the results shown in Fig. 2 . We provide more in-depth evaluations including scorecards, metrics for additional variables and levels and maps in Extended Data Figs. 1 and 2 , Supplementary Information section  H and Supplementary Figs. 9 – 22 .

a , c , RMSE ( a ) and RMSB ( c ) for ECMWF-ENS, ECMWF-HRES, NeuralGCM-0.7°, NeuralGCM-ENS, GraphCast 3 and Pangu 4 on headline WeatherBench2 variables, as a percentage of the error of ECMWF-ENS. Deterministic and stochastic models are shown in solid and dashed lines respectively. e , g , CRPS relative to ECMWF-ENS ( e ) and spread-skill ratio for the ENS and NeuralGCM-ENS models ( g ). b , d , f , h , Spatial distributions of RMSE ( b ), bias ( d ), CRPS ( f ) and spread-skill ratio ( h ) for NeuralGCM-ENS and ECMWF-ENS models for 10-day forecasts of specific humidity at 700 hPa. Spatial plots of RMSE and CRPS show skill relative to a probabilistic climatology 12 with an ensemble member for each of the years 1990–2019. The grey areas indicate regions where climatological surface pressure on average is below 700 hPa.

Deterministic models that produce a single weather forecast for given initial conditions can be compared effectively using RMSE skill at short lead times. For the first 1–3 days, depending on the atmospheric variable, RMSE is minimized by forecasts that accurately track the evolution of weather patterns. At this timescale we find that NeuralGCM-0.7° and GraphCast achieve best results, with slight variations across different variables (Fig. 2a ). At longer lead times, RMSE rapidly increases owing to chaotic divergence of nearby weather trajectories, making RMSE less informative for deterministic models. RMSB calculates persistent errors over time, which provides an indication of how models would perform at much longer lead times. Here NeuralGCM models also compare favourably against previous approaches (Fig. 2c ), with notably much less bias for specific humidity in the tropics (Fig. 2d ).

Ensembles are essential for capturing intrinsic uncertainty of weather forecasts, especially at longer lead times. Beyond about 7 days, the ensemble means of ECMWF-ENS and NeuralGCM-ENS forecasts have considerably lower RMSE than the deterministic models, indicating that these models better capture the average of possible weather. A better metric for ensemble models is CRPS, which is a proper scoring rule that is sensitive to full marginal probability distributions 28 . Our stochastic model (NeuralGCM-ENS) running at 1.4° resolution has lower error compared with ECMWF-ENS across almost all variables, lead times and vertical levels for ensemble-mean RMSE, RSMB and CRPS (Fig. 2a,c,e and Supplementary Information section  H ), with similar spatial patterns of skill (Fig. 2b,f ). Like ECMWF-ENS, NeuralGCM-ENS has a spread-skill ratio of approximately one (Fig. 2d ), which is a necessary condition for calibrated forecasts 29 .

An important characteristic of forecasts is their resemblance to realistic weather patterns. Figure 3 shows a case study that illustrates the performance of NeuralGCM on three types of important weather phenomenon: tropical cyclones, atmospheric rivers and the Intertropical Convergence Zone. Figure 3a shows that all the machine-learning models make significantly blurrier forecasts than the source data ERA5 and physics-based ECMWF-HRES forecast, but NeuralCGM-0.7° outperforms the pure machine-learning models, despite its coarser resolution (0.7° versus 0.25° for GraphCast and Pangu). Blurry forecasts correspond to physically inconsistent atmospheric conditions and misrepresent extreme weather. Similar trends hold for other derived variables of meteorological interest (Supplementary Information section  H.2 ). Ensemble-mean predictions, from both NeuralGCM and ECMWF, are closer to ERA5 in an average sense, and thus are inherently smooth at long lead times. In contrast, as shown in Fig. 3 and in Supplementary Information section  H.3 , individual realizations from the ECMWF and NeuralGCM ensembles remain sharp, even at long lead times. Like ECMWF-ENS, NeuralGCM-ENS produces a statistically representative range of future weather scenarios for each weather phenomenon, despite its eight-times-coarser resolution.

All forecasts are initialized at 2020-08-22T12z, chosen to highlight Hurricane Laura, the most damaging Atlantic hurricane of 2020. a , Specific humidity at 700 hPa for 1-day, 5-day and 10-day forecasts over North America and the Northeast Pacific Ocean from ERA5 14 , ECMWF-HRES, NeuralGCM-0.7°, ECMWF-ENS (mean), NeuralGCM-ENS (mean), GraphCast 3 and Pangu 4 . b , Forecasts from individual ensemble members from ECMWF-ENS and NeuralGCM-ENS over regions of interest, including predicted tracks of Hurricane Laura from each of the 50 ensemble members (Supplementary Information section  I.2 ). The track from ERA5 is plotted in black.

We can quantify the blurriness of different forecast models via their power spectra. Supplementary Figs. 17 and 18 show that the power spectra of NeuralCGM-0.7° is consistently closer to ERA5 than the other machine-learning forecast methods, but is still blurrier than ECMWF’s physical forecasts. The spectra of NeuralGCM forecasts is also roughly constant over the forecast period, in stark contrast to GraphCast, which worsens with lead time. The spectrum of NeuralGCM becomes more accurate with increased resolution (Supplementary Fig. 22 ), which suggests the potential for further improvements of NeuralGCM models trained at higher resolutions.

Water budget

In NeuralGCM, advection is handled by the dynamical core, while the machine-learning parameterization models local processes within vertical columns of the atmosphere. Thus, unlike pure machine-learning methods, local sources and sinks can be isolated from tendencies owing to horizontal transport and other resolved dynamics (Supplementary Fig. 3 ). This makes our results more interpretable and facilitates the diagnosis of the water budget. Specifically, we diagnose precipitation minus evaporation (Supplementary Information section  H.5 ) rather than directly predicting these as in machine-learning-based approaches 3 . For short weather forecasts, the mean of precipitation minus evaporation has a realistic spatial distribution that is very close to ERA5 data (Extended Data Fig. 4c–e ). The precipitation-minus-evaporation rate distribution of NeuralGCM-0.7° closely matches the ERA5 distribution in the extratropics (Extended Data Fig. 4b ), although it underestimates extreme events in the tropics (Extended Data Fig. 4a ). It is noted that the current version of NeuralGCM directly predicts tendencies for an atmospheric column, and thus cannot distinguish between precipitation and evaporation.

Geostrophic wind balance

We examined the extent to which NeuralGCM, GraphCast and ECMWF-HRES capture the geostrophic wind balance, the near-equilibrium between the dominant forces that drive large-scale dynamics in the mid-latitudes 30 . A recent study 16 highlighted that Pangu misrepresents the vertical structure of the geostrophic and ageostrophic winds and noted a deterioration at longer lead times. Similarly, we observe that GraphCast shows an error that worsens with lead time. In contrast, NeuralGCM more accurately depicts the vertical structure of the geostrophic and ageostrophic winds, as well as their ratio, compared with GraphCast across various rollouts, when compared against ERA5 data (Extended Data Fig. 3 ). However, ECMWF-HRES still shows a slightly closer alignment to ERA5 data than NeuralGCM does. Within NeuralGCM, the representation of the geostrophic wind’s vertical structure only slightly degrades in the initial few days, showing no noticeable changes thereafter, particularly beyond day 5.

Generalizing to unseen data

Physically consistent weather models should still perform well for weather conditions for which they were not trained. We expect that NeuralGCM may generalize better than machine-learning-only atmospheric models, because NeuralGCM employs neural networks that act locally in space, on individual vertical columns of the atmosphere. To explore this hypothesis, we compare versions of NeuralCGM-0.7° and GraphCast trained to 2017 on 5 years of weather forecasts beyond the training period (2018–2022) in Supplementary Fig. 36 . Unlike GraphCast, NeuralGCM does not show a clear trend of increasing error when initialized further into the future from the training data. To extend this test beyond 5 years, we trained a NeuralGCM-2.8° model using only data before 2000, and tested its skill for over 21 unseen years (Supplementary Fig. 35 ).

Climate simulations

Although our deterministic NeuralGCM models are trained to predict weather up to 3 days ahead, they are generally capable of simulating the atmosphere far beyond medium-range weather timescales. For extended climate simulations, we prescribe historical sea surface temperature (SST) and sea-ice concentration. These simulations feature many emergent phenomena of the atmosphere on timescales from months to decades.

For climate simulations with NeuralGCM, we use 2.8° and 1.4° deterministic models, which are relatively inexpensive to train (Supplementary Information section  G.7 ) and allow us to explore a larger parameter space to find stable models. Previous studies found that running extended simulations with hybrid models is challenging due to numerical instabilities and climate drift 21 . To quantify stability in our selected models, we run multiple initial conditions and report how many of them finish without instability.

Seasonal cycle and emergent phenomena

To assess the capability of NeuralGCM to simulate various aspects of the seasonal cycle, we run 2-year simulations with NeuralGCM-1.4°. for 37 different initial conditions spaced every 10 days for the year 2019. Out of these 37 initial conditions, 35 successfully complete the full 2 years without instability; for case studies of instability, see Supplementary Information section  H.7 , and Supplementary Figs. 26 and 27 . We compare results from NeuralGCM-1.4° for 2020 with ERA5 data and with outputs from the X-SHiELD global cloud-resolving model, which is coupled to an ocean model nudged towards reanalysis 31 . This X-SHiELD run has been used as a target for training machine-learning climate models 24 . For comparison, we evaluate models after regridding predictions to 1.4° resolution. This comparison slightly favours NeuralGCM because NeuralGCM was tuned to match ERA5, but the discrepancy between ERA5 and the actual atmosphere is small relative to model error.

Figure 4a shows the temporal variation of the global mean temperature to 2020, as captured by 35 simulations from NeuralGCM, in comparison with the ERA5 reanalysis and standard climatology benchmarks. The seasonality and variability of the global mean temperature from NeuralGCM are quantitatively similar to those observed in ERA5. The ensemble-mean temperature RMSE for NeuralGCM stands at 0.16 K when benchmarked against ERA5, which is a significant improvement over the climatology’s RMSE of 0.45 K. We find that NeuralGCM accurately simulates the seasonal cycle, as evidenced by metrics such as the annual cycle of the global precipitable water (Supplementary Fig. 30a ) and global total kinetic energy (Supplementary Fig. 30b ). Furthermore, the model captures essential atmospheric dynamics, including the Hadley circulation and the zonal-mean zonal wind (Supplementary Fig. 28 ), as well as the spatial patterns of eddy kinetic energy in different seasons (Supplementary Fig. 31 ), and the distinctive seasonal behaviours of monsoon circulation (Supplementary Fig. 29 ; additional details are provided in Supplementary Information section  I.1 ).

a , Global mean temperature for ERA5 14 (orange), 1990–2019 climatology (black) and NeuralGCM-1.4° (blue) for 2020 using 35 simulations initialized every 10 days during 2019 (thick line, ensemble mean; thin lines, different initial conditions). b , Yearly global mean temperature for ERA5 (orange), mean over 22 CMIP6 AMIP experiments 34 (violet; model details are in Supplementary Information section  I.3 ) and NeuralGCM-2.8° for 22 AMIP-like simulations with prescribed SST initialized every 10 days during 1980 (thick line, ensemble mean; thin lines, different initial conditions). c , The RMSB of the 850-hPa temperature averaged between 1981 and 2014 for 22 NeuralGCM-2.8° AMIP runs (labelled NGCM), 22 CMIP6 AMIP experiments (labelled AMIP) and debiased 22 CMIP6 AMIP experiments (labelled AMIP*; bias was removed by removing the 850-hPa global temperature bias). In the box plots, the red line represents the median. The box delineates the first to third quartiles; the whiskers extend to 1.5 times the interquartile range (Q1 − 1.5IQR and Q3 + 1.5IQR), and outliers are shown as individual dots. d , Vertical profiles of tropical (20° S–20° N) temperature trends for 1981–2014. Orange, ERA5; black dots, Radiosonde Observation Correction using Reanalyses (RAOBCORE) 41 ; blue dots, mean trends for NeuralGCM; purple dots, mean trends from CMIP6 AMIP runs (grey and black whiskers, 25th and 75th percentiles for NeuralGCM and CMIP6 AMIP runs, respectively). e – g , Tropical cyclone tracks for ERA5 ( e ), NeuralGCM-1.4° ( f ) and X-SHiELD 31 ( g ). h – k , Mean precipitable water for ERA5 ( h ) and the precipitable water bias in NeuralGCM-1.4° ( i ), initialized 90 days before mid-January 2020 similarly to X-SHiELD, X-SHiELD ( j ) and climatology ( k ; averaged between 1990 and 2019). In d – i , quantities are calculated between mid-January 2020 and mid-January 2021 and all models were regridded to a 256 × 128 Gaussian grid before computation and tracking.

Next, we compare the annual biases of a single NeuralGCM realization with a single realization of X-SHiELD (the only one available), both initiated in mid-October 2019. We consider 19 January 2020 to 17 January 2021, the time frame for which X-SHiELD data are available. Global cloud-resolving models, such as X-SHiELD, are considered state of the art, especially for simulating the hydrological cycle, owing to their resolution being capable of resolving deep convection 32 . The annual bias in precipitable water for NeuralGCM (RMSE of 1.09 mm) is substantially smaller than the biases of both X-SHiELD (RMSE of 1.74 mm) and climatology (RMSE of 1.36 mm; Fig. 4i–k ). Moreover, NeuralGCM shows a lower temperature bias in the upper and lower troposphere than X-SHiELD (Extended Data Fig. 6 ). We also indirectly compare precipitation bias in X-SHiELD with precipitation-minus-evaporation bias in NeuralGCM-1.4°, which shows slightly larger bias and grid-scale artefacts for NeuralGCM (Extended Data Fig. 5 ).

Finally, to assess the capability of NeuralGCM to generate tropical cyclones in an annual model integration, we use the tropical cyclone tracker TempestExtremes 33 , as described in Supplementary Information section   I.2 , Supplementary Fig. 34 and Supplementary Table 6 . Figure 4e–g shows that NeuralGCM, even at a coarse resolution of 1.4°, produces realistic trajectories and counts of tropical cyclone (83 versus 86 in ERA5 for the corresponding period), whereas X-SHiELD, when regridded to 1.4° resolution, substantially underestimates the tropical cyclone count (40). Additional statistical analyses of tropical cyclones can be found in Extended Data Figs. 7 and 8 .

Decadal simulations

To assess the capability of NeuralGCM to simulate historical temperature trends, we conduct AMIP-like simulations over a duration of 40 years with NeuralGCM-2.8°. Out of 37 different runs with initial conditions spaced every 10 days during the year 1980, 22 simulations were stable for the entire 40-year period, and our analysis focuses on these results. We compare with 22 simulations run with prescribed SST from the Coupled Model Intercomparison Project Phase 6 (CMIP6) 34 , listed in Supplementary Information section  I.3 .

We find that all 40-year simulations of NeuralGCM, as well as the mean of the 22 AMIP runs, accurately capture the global warming trends observed in ERA5 data (Fig. 4b ). There is a strong correlation in the year-to-year temperature trends with ERA5 data, suggesting that NeuralGCM effectively captures the impact of SST forcing on climate. When comparing spatial biases averaged over 1981–2014, we find that all 22 NeuralGCM-2.8° runs have smaller bias than the CMIP6 AMIP runs, and this result remains even when removing the global temperature bias in CMIP6 AMIP runs (Fig. 4c and Supplementary Figs. 32 and 33 ).

Next, we investigated the vertical structure of tropical warming trends, which climate models tend to overestimate in the upper troposphere 35 . As shown in Fig. 4d , the trends, calculated by linear regression, of NeuralGCM are closer to ERA5 than those of AMIP runs. In particular, the bias in the upper troposphere is reduced. However, NeuralGCM does show a wider spread in its predictions than the AMIP runs, even at levels near the surface where temperatures are typically more constrained by prescribed SST.

Lastly, we evaluated NeuralGCM’s capability to generalize to unseen warmer climates by conducting AMIP simulations with increased SST (Supplementary Information section  I.4.2 ). We find that NeuralGCM shows some of the robust features of climate warming response to modest SST increases (+1 K and +2 K); however, for more substantial SST increases (+4 K), NeuralGCM’s response diverges from expectations (Supplementary Fig. 37 ). In addition, AMIP simulations with increased SST show climate drift, underscoring NeuralGCM’s limitations in this context (Supplementary Fig. 38 ).

NeuralGCM is a differentiable hybrid atmospheric model that combines the strengths of traditional GCMs with machine learning for weather forecasting and climate simulation. To our knowledge, NeuralGCM is the first machine-learning-based model to make accurate ensemble weather forecasts, with better CRPS than state-of-the-art physics-based models. It is also, to our knowledge, the first hybrid model that achieves comparable spatial bias to global cloud-resolving models, can simulate realistic tropical cyclone tracks and can run AMIP-like simulations with realistic historical temperature trends. Overall, NeuralGCM demonstrates that incorporating machine learning is a viable alternative to building increasingly detailed physical models 32 for improving GCMs.

Compared with traditional GCMs with similar skill, NeuralGCM is computationally efficient and low complexity. NeuralGCM runs at 8- to 40-times-coarser horizontal resolution than ECMWF’s Integrated Forecasting System and global cloud-resolving models, which enables 3 to 5 orders of magnitude savings in computational resources. For example, NeuralGCM-1.4° simulates 70,000 simulation days in 24 hours using a single tensor-processing-unit versus 19 simulated days on 13,824 central-processing-unit cores with X-SHiELD (Extended Data Table 1 ). This can be leveraged for previously impractical tasks such as large ensemble forecasting. NeuralGCM’s dynamical core uses global spectral methods 36 , and learned physics is parameterized with fully connected neural networks acting on single vertical columns. Substantial headroom exists to pursue higher accuracy using advanced numerical methods and machine-learning architectures.

Our results provide strong evidence for the disputed hypothesis 37 , 38 , 39 that learning to predict short-term weather is an effective way to tune parameterizations for climate. NeuralGCM models trained on 72-hour forecasts are capable of realistic multi-year simulation. When provided with historical SSTs, they capture essential atmospheric dynamics such as seasonal circulation, monsoons and tropical cyclones. However, we will probably need alternative training strategies 38 , 39 to learn important processes for climate with subtle impacts on weather timescales, such as a cloud feedback.

The NeuralGCM approach is compatible with incorporating either more physics or more machine learning, as required for operational weather forecasts and climate simulations. For weather forecasting, we expect that end-to-end learning 40 with observational data will allow for better and more relevant predictions, including key variables such as precipitation. Such models could include neural networks acting as corrections to traditional data assimilation and model diagnostics. For climate projection, NeuralGCM will need to be reformulated to enable coupling with other Earth-system components (for example, ocean and land), and integrating data on the atmospheric chemical composition (for example, greenhouse gases and aerosols). There are also research challenges common to current machine-learning-based climate models 19 , including the capability to simulate unprecedented climates (that is, generalization), adhering to physical constraints, and resolving numerical instabilities and climate drift. NeuralGCM’s flexibility to incorporate physics-based models (for example, radiation) offers a promising avenue to address these challenges.

Models based on physical laws and empirical relationships are ubiquitous in science. We believe the differentiable hybrid modelling approach of NeuralGCM has the potential to transform simulation for a wide range of applications, such as materials discovery, protein folding and multiphysics engineering design.

Differentiable atmospheric model

NeuralGCM combines components of the numerical solver and flexible neural network parameterizations. Simulation in time is carried out in a coordinate system suitable for solving the dynamical equations of the atmosphere, describing large-scale fluid motion and thermodynamics under the influence of gravity and the Coriolis force.

Our differentiable dynamical core is implemented in JAX, a library for high-performance code in Python that supports automatic differentiation 42 . The dynamical core solves the hydrostatic primitive equations with moisture, using a horizontal pseudo-spectral discretization and vertical sigma coordinates 36 , 43 . We evolve seven prognostic variables: vorticity and divergence of horizontal wind, temperature, surface pressure, and three water species (specific humidity, and specific ice and liquid cloud water content).

Our learned physics module uses the single-column approach of GCMs 2 , whereby information from only a single atmospheric column is used to predict the impact of unresolved processes occurring within that column. These effects are predicted using a fully connected neural network with residual connections, with weights shared across all atmospheric columns (Supplementary Information section  C.4 ).

The inputs to the neural network include the prognostic variables in the atmospheric column, total incident solar radiation, sea-ice concentration and SST (Supplementary Information section  C.1 ). We also provide horizontal gradients of the prognostic variables, which we found improves performance 44 . All inputs are standardized to have zero mean and unit variance using statistics precomputed during model initialization. The outputs are the prognostic variable tendencies scaled by the fixed unconditional standard deviation of the target field (Supplementary Information section  C.5 ).

To interface between ERA5 14 data stored in pressure coordinates and the sigma coordinate system of our dynamical core, we introduce encoder and decoder components (Supplementary Information section  D ). These components perform linear interpolation between pressure levels and sigma coordinate levels. We additionally introduce learned corrections to both encoder and decoder steps (Supplementary Figs. 4–6 ), using the same column-based neural network architecture as the learned physics module. Importantly, the encoder enables us to eliminate the gravity waves from initialization shock 45 , which otherwise contaminate forecasts.

Figure 1a shows the sequence of steps that NeuralGCM takes to make a forecast. First, it encodes ERA5 data at t  =  t 0 on pressure levels to initial conditions on sigma coordinates. To perform a time step, the dynamical core and learned physics (Fig. 1b ) then compute tendencies, which are integrated in time using an implicit–explicit ordinary differential equation solver 46 (Supplementary Information section  E and Supplementary Table 2 ). This is repeated to advance the model from t  =  t 0 to t  =  t final . Finally, the decoder converts predictions back to pressure levels.

The time-step size of the ODE solver (Supplementary Table 3 ) is limited by the Courant–Friedrichs–Lewy condition on dynamics, and can be small relative to the timescale of atmospheric change. Evaluating learned physics is approximately 1.5 times as expensive as a time step of the dynamical core. Accordingly, following the typical practice for GCMs, we hold learned physics tendencies constant for multiple ODE time steps to reduce computational expense, typically corresponding to 30 minutes of simulation time.

Deterministic and stochastic models

We train deterministic NeuralGCM models using a combination of three loss functions (Supplementary Information section  G.4 ) to encourage accuracy and sharpness while penalizing bias. During the main training phase, all losses are defined in a spherical harmonics basis. We use a standard mean squared error loss for prompting accuracy, modified to progressively filter out contributions from higher total wavenumbers at longer lead times (Supplementary Fig. 8 ). This filtering approach tackles the ‘double penalty problem’ 47 as it prevents the model from being penalized for predicting high-wavenumber features in incorrect locations at later times, especially beyond the predictability horizon. A second loss term encourages the spectrum to match the training data using squared loss on the total wavenumber spectrum of prognostic variables. These first two losses are evaluated on both sigma and pressure levels. Finally, a third loss term discourages bias by adding mean squared error on the batch-averaged mean amplitude of each spherical harmonic coefficient. For analysis of the impact that various loss functions have, refer to Supplementary Information section  H.6.1 , and Supplementary Figs. 23 and 24 . The combined action of the three training losses allow the resulting models trained on 3-day rollouts to remain stable during years-to-decades-long climate simulations. Before final evaluations, we perform additional fine-tuning of just the decoder component on short rollouts of 24 hours (Supplementary Information section  G.5 ).

Stochastic NeuralGCM models incorporate inherent randomness in the form of additional random fields passed as inputs to neural network components. Our stochastic loss is based on the CRPS 28 , 48 , 49 . CRPS consists of mean absolute error that encourages accuracy, balanced by a similar term that encourages ensemble spread. For each variable we use a sum of CRPS in grid space and CRPS in the spherical harmonic basis below a maximum cut-off wavenumber (Supplementary Information section  G.6 ). We compute CRPS on rollout lengths from 6 hours to 5 days. As illustrated in Fig. 1 , we inject noise to the learned encoder and the learned physics module by sampling from Gaussian random fields with learned spatial and temporal correlation (Supplementary Information section  C.2 and Supplementary Fig. 2 ). For training, we generate two ensemble members per forecast, which suffices for an unbiased estimate of CRPS.

Data availability

For training and evaluating the NeuralGCM models, we used the publicly available ERA5 dataset 14 , originally downloaded from https://cds.climate.copernicus.eu/ and available via Google Cloud Storage in Zarr format at gs://gcp-public-data-arco-era5/ar/full_37-1h-0p25deg-chunk-1.zarr-v3. To compare NeuralGCM with operational and data-driven weather models, we used forecast datasets distributed as part of WeatherBench2 12 at https://weatherbench2.readthedocs.io/en/latest/data-guide.html , to which we have added NeuralGCM forecasts for 2020. To compare NeuralGCM with atmospheric models in climate settings, we used CMIP6 data available at https://catalog.pangeo.io/browse/master/climate/ , as well as X-SHiELD 24 outputs available on Google Cloud storage in a ‘requester pays’ bucket at gs://ai2cm-public-requester-pays/C3072-to-C384-res-diagnostics. The Radiosonde Observation Correction using Reanalyses (RAOBCORE) V1.9 that was used as reference tropical temperature trends was downloaded from https://webdata.wolke.img.univie.ac.at/haimberger/v1.9/ . Base maps use freely available data from https://www.naturalearthdata.com/downloads/ .

Code availability

The NeuralGCM code base is separated into two open source projects: Dinosaur and NeuralGCM, both publicly available on GitHub at https://github.com/google-research/dinosaur (ref. 50 ) and https://github.com/google-research/neuralgcm (ref. 51 ). The Dinosaur package implements a differentiable dynamical core used by NeuralGCM, whereas the NeuralGCM package provides machine-learning models and checkpoints of trained models. Evaluation code for NeuralGCM weather forecasts is included in WeatherBench2 12 , available at https://github.com/google-research/weatherbench2 (ref. 52 ).

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Acknowledgements

We thank A. Kwa, A. Merose and K. Shah for assistance with data acquisition and handling; L. Zepeda-Núñez for feedback on the paper; and J. Anderson, C. Van Arsdale, R. Chemke, G. Dresdner, J. Gilmer, J. Hickey, N. Lutsko, G. Nearing, A. Paszke, J. Platt, S. Ponda, M. Pritchard, D. Rothenberg, F. Sha, T. Schneider and O. Voicu for discussions.

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These authors contributed equally: Dmitrii Kochkov, Janni Yuval, Ian Langmore, Peter Norgaard, Jamie Smith, Stephan Hoyer

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Google Research, Mountain View, CA, USA

Dmitrii Kochkov, Janni Yuval, Ian Langmore, Peter Norgaard, Jamie Smith, Griffin Mooers, James Lottes, Stephan Rasp, Michael P. Brenner & Stephan Hoyer

Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA

Milan Klöwer

European Centre for Medium-Range Weather Forecasts, Reading, UK

Peter Düben & Sam Hatfield

Google DeepMind, London, UK

Peter Battaglia, Alvaro Sanchez-Gonzalez & Matthew Willson

School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

Michael P. Brenner

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D.K., J.Y., I.L., P.N., J.S. and S. Hoyer contributed equally to this work. D.K., J.Y., I.L., P.N., J.S., G.M., J.L. and S. Hoyer wrote the code. D.K., J.Y., I.L., P.N., G.M. and S. Hoyer trained models and analysed the data. M.P.B. and S. Hoyer managed and oversaw the research project. M.K., S.R., P.D., S. Hatfield, P.B. and M.P.B. contributed technical advice and ideas. M.W. ran experiments with GraphCast for comparison with NeuralGCM. A.S.-G. assisted with data preparation. D.K., J.Y., I.L., P.N. and S. Hoyer wrote the paper. All authors gave feedback and contributed to editing the paper.

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Correspondence to Dmitrii Kochkov , Janni Yuval or Stephan Hoyer .

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Competing interests.

D.K., J.Y., I.L., P.N., J.S., J.L., S.R., P.B., A.S.-G., M.W., M.P.B. and S. Hoyer are employees of Google. S. Hoyer, D.K., I.L., J.Y., G.M., P.N., J.S. and M.B. have filed international patent application PCT/US2023/035420 in the name of Google LLC, currently pending, relating to neural general circulation models.

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Nature thanks Karthik Kashinath and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Extended data figures and tables

Extended data fig. 1 maps of bias for neuralgcm-ens and ecmwf-ens forecasts..

Bias is averaged over all forecasts initialized in 2020.

Extended Data Fig. 2 Maps of spread-skill ratio for NeuralGCM-ENS and ECMWF-ENS forecasts.

Spread-skill ratio is averaged over all forecasts initialized in 2020.

Extended Data Fig. 3 Geostrophic balance in NeuralGCM, GraphCast 3 and ECMWF-HRES.

Vertical profiles of the extratropical intensity (averaged between latitude 30°–70° in both hemispheres) and over all forecasts initialized in 2020 of (a,d,g) geostrophic wind, (b,e,h) ageostrophic wind and (c,f,i) the ratio of the intensity of ageostrophic wind over geostrophic wind for ERA5 (black continuous line in all panels), (a,b,c) NeuralGCM-0.7°, (d,e,f) GraphCast and (g,h,i) ECMWF-HRES at lead times of 1 day, 5 days and 10 days.

Extended Data Fig. 4 Precipitation minus evaporation calculated from the third day of weather forecasts.

(a) Tropical (latitudes −20° to 20°) precipitation minus evaporation (P minus E) rate distribution, (b) Extratropical (latitudes 30° to 70° in both hemispheres) P minus E, (c) mean P minus E for 2020 ERA5 14 and (d) NeuralGCM-0.7° (calculated from the third day of forecasts and averaged over all forecasts initialized in 2020), (e) the bias between NeuralGCM-0.7° and ERA5, (f-g) Snapshot of daily precipitation minus evaporation for 2020-01-04 for (f) NeuralGCM-0.7° (forecast initialized on 2020-01-02) and (g) ERA5.

Extended Data Fig. 5 Indirect comparison between precipitation bias in X-SHiELD and precipitation minus evaporation bias in NeuralGCM-1.4°.

Mean precipitation calculated between 2020-01-19 and 2021-01-17 for (a) ERA5 14 (c) X-SHiELD 31 and the biases in (e) X-SHiELD and (g) climatology (ERA5 data averaged over 1990-2019). Mean precipitation minus evaporation calculated between 2020-01-19 and 2021-01-17 for (b) ERA5 (d) NeuralGCM-1.4° (initialized in October 18th 2019) and the biases in (f) NeuralGCM-1.4° and (h) climatology (data averaged over 1990–2019).

Extended Data Fig. 6 Yearly temperature bias for NeuralGCM and X-SHiELD 31 .

Mean temperature between 2020-01-19 to 2020-01-17 for (a) ERA5 at 200hPa and (b) 850hPa. (c,d) the bias in the temperature for NeuralGCM-1.4°, (e,f) the bias in X-SHiELD and (g,h) the bias in climatology (calculated from 1990–2019). NeuralGCM-1.4° was initialized in 18th of October (similar to X-SHiELD).

Extended Data Fig. 7 Tropical Cyclone densities and annual regional counts.

(a) Tropical Cyclone (TC) density from ERA5 14 data spanning 1987–2020. (b) TC density from NeuralGCM-1.4° for 2020, generated using 34 different initial conditions all initialized in 2019. (c) Box plot depicting the annual number of TCs across different regions, based on ERA5 data (1987–2020), NeuralGCM-1.4° for 2020 (34 initial conditions), and orange markers show ERA5 for 2020. In the box plots, the red line represents the median; the box delineates the first to third quartiles; the whiskers extend to 1.5 times the interquartile range (Q1 − 1.5IQR and Q3 + 1.5IQR), and outliers are shown as individual dots. Each year is defined from January 19th to January 17th of the following year, aligning with data availability from X-SHiELD. For NeuralGCM simulations, the 3 initial conditions starting in January 2019 exclude data for January 17th, 2021, as these runs spanned only two years.

Extended Data Fig. 8 Tropical Cyclone maximum wind distribution in NeuralGCM vs. ERA5 14 .

Number of Tropical Cyclones (TCs) as a function of maximum wind speed at 850hPa across different regions, based on ERA5 data (1987–2020; in orange), and NeuralGCM-1.4° for 2020 (34 initial conditions; in blue). Each year is defined from January 19th to January 17th of the following year, aligning with data availability from X-SHiELD. For NeuralGCM simulations, the 3 initial conditions starting in January 2019 exclude data for January 17th, 2021, as these runs spanned only two years.

Supplementary information

Supplementary information.

Supplementary Information (38 figures, 6 tables): (A) Lines of code in atmospheric models; (B) Dynamical core of NeuralGCM; (C) Learned physics of NeuralGCM; (D) Encoder and decoder of NeuralGCM; (E) Time integration; (F) Evaluation metrics; (G) Training; (H) Additional weather evaluations; (I) Additional climate evaluations.

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Kochkov, D., Yuval, J., Langmore, I. et al. Neural general circulation models for weather and climate. Nature 632 , 1060–1066 (2024). https://doi.org/10.1038/s41586-024-07744-y

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Received : 13 November 2023

Accepted : 15 June 2024

Published : 22 July 2024

Issue Date : 29 August 2024

DOI : https://doi.org/10.1038/s41586-024-07744-y

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