Wikipedia:Scientific citation guidelines

The no original research and verifiability policies are of paramount importance to Wikipedia. Inline citations, which link specific reliable sources with specific pieces of information in the article, provide practical support for these policies by making it easier to check the article content.

This page applies the advice in the policies, and in the citing sources guideline, to referencing science and mathematics articles. The goal is to achieve a reasonable balance between ease of verification, readability and editability. This page also describes some sensible guidelines for dealing with issues that are specific to writing Wikipedia articles (compared to writing for the academic press).

Footnotes ( tags) are used in examples throughout this page. Parenthetical referencing was a different type of referencing used on Wikipedia until September 2020, when a community discussion reached a consensus to deprecate parenthetical referencing. Do not change any article's established citation style without discussing it first.

Uncontroversial knowledge
Some statements are uncontroversial and widely known among people familiar with a discipline. Such facts may be taught in university courses, found in textbooks, or contained in multiple references in the research literature (most importantly in review articles). Some examples are: These statements are not common knowledge, but the first should be known to anyone with an undergraduate background in physics, the second to anyone knowledgeable about condensed matter physics, and the third to anyone knowledgeable about string theory.
 * Special relativity combines Galilean relativity with the postulate that all observers will always measure the speed of light to be the same no matter what their state of uniform linear motion is.
 * A frustrated spin glass may have a large ground state degeneracy.
 * T-duality relates type IIA superstring theory to type IIB superstring theory.

The verifiability criteria require that such statements be sourced so that in principle anyone can verify them. However, in many articles it is cumbersome to provide an in-line reference for every statement. In addition, such dense referencing can obscure the logical interdependence of statements. Therefore, in sections or articles that present well-known and uncontroversial information – information that is readily available in most common and obvious books on the subject – it is acceptable to give an inline citation for one or two authoritative sources (and possibly a more accessible source, if one is available) in such a way as to indicate that these sources can be checked to verify statements for which no other in-line citation is provided. These inline citations are often inserted either after the first sentence of a paragraph or after the last sentence of the paragraph; a single convention should be chosen for each article.

For example, from aldol reaction: "The aldol reaction is an important carbon-carbon bond forming reaction in organic chemistry involving the addition of an enol or enolate anion to an aldehyde or ketone.  In the aldol addition, the reaction results in a β-hydroxy ketone (or aldehyde), also called an "aldol" (aldehyde + alcohol).  In the aldol condensation, the initial aldol adduct undergoes dehydration (loss of water) to form an α,β-unsaturated ketone (or aldehyde).

The enol or enolate is itself generated from a carbonyl compound, often an aldehyde or ketone, using acid or base. If the enol or enolate is formed in situ, the process can be considered as an acid or base-catalyzed reaction of one carbonyl compound with another. This may involve one aldehyde or ketone reacting with itself. Alternatively two different carbonyl compounds may be used, in which case the reaction is known as a crossed aldol reaction. In the scheme shown, the enol or enolate of a methyl ketone reacts with an aldehyde."

Five references are provided early on: two textbooks, a specialized monograph on aldol reactions, and two review articles. Most readers would assume that the bulk of the statements in the comparatively short Wikipedia article could be verified by checking any of these references, and so it may only be necessary to provide additional in-line references for controversial statements, for recent discoveries that are not covered in the standard references, for historical and academic attribution, and for verifying more specialized statements or subsections.

When quoting widely known numbers such as the speed of light or numbers published by the Particle Data Group or in the CRC Handbook of Chemistry and Physics, a reference might only be needed in the most relevant article. Wikipedia policy WP:V states that if an editor requests that a particular statement be sourced, that request should be fulfilled. In this case, it may be advisable to add an in-line citation if this would prevent future confusion. However, if the statement is easily found in the principal references already given in the article, a citation may instead be provided on the article's talk page.

Articles without in-line references
Sometimes, short articles (including many stubs) provide a list of references without any inline citations. This can satisfy the sourcing policies when the entire contents of the article can be verified from the sources listed. An example of a very short article covered by general references is provided by the linked revision of "low basis theorem".

As an article matures to include more than a few sentences, inline citations are added to make it clear which material in the article can be verified by which source. If a few general references cover the bulk of an article, consider using the technique described in the section Uncontroversial knowledge above. This can be done regardless of article length.

Some material, including direct quotations, contentious material about living people, and any material whose verifiability has been challenged, should always be accompanied by an inline citation, regardless of the length of the article. For more information on these special cases, see Verifiability and Biographies of living people.

Citation format
Since Wikipedia is not a paper encyclopedia, references do not need to be as concise as they are in journals. In particular, it may be helpful to give the title of a journal article, and to give the complete name of the journal (Astrophysical Journal instead of Ap. J.). It is important to provide linkage data such as the ISBN for books, and relevant database identifiers that link to papers or their bibliographic records. Such linkages facilitate the verification of sourced statements. Examples include the DOI for articles in many areas of science, the PMID for articles in medicine and the MR number for mathematics articles. For physics and mathematics, many articles are available as preprints on the arXiv, so it is helpful to provide the preprint number and a URL. For articles published before 1992, and many others, there is no arXiv preprint. Instead, consider linking to the ADS, SPIRES or MathSciNet entry, if one is available, or directly to the entry at the journal's website. The bibcode, arxiv and MathSciNet templates may prove useful for creating these database links in free-form citations, or such links can be automatically generated when using the, or  templates using the corresponding parameters.

For some topics the bibliography available may address different audiences, e.g. undergraduate vs. graduate, or levels or rigor, e.g. statistics textbooks for social scientists vs. those addressed to mathematicians. When the audience of a text in the further reading section is not self-evident, it may be useful to annotate it as discussed at WP:FURTHER.

Examples, derivations, and restatements
Wikipedia is neither a textbook nor a journal. Nonetheless, in mathematics and the mathematical sciences, it is frequently helpful to quote theorems, include simple derivations, and provide illustrative examples. For reasons of notation, clarity, consistency, or simplicity it is often necessary to state things in a slightly different way than they are stated in the references, to provide a different derivation, or to provide an example. This is standard practice in journals, and does not make any claim of novelty. In Wikipedia articles this does not constitute original research and is perfectly permissible – in fact, encouraged – provided that anyone who reads and understands the references can easily see how the material in the Wikipedia article can be inferred. Furthermore, copying extensively from a source with only minor modifications is not normally permitted by copyright law, unless the source has a free license.

Wikipedia's no-original-research policy allows routine calculations based on data from reliable sources. Routine calculations frequently involve converting units, rounding to appropriate levels of precision for the article, describing quantitative relationships in words, and other simple methods that both accurately describe the information from the source(s) and do not tend to advance a novel argument. As an example, the article on the Lambda-CDM model quotes values for Hubble parameter h and the fraction of the present universe made up of baryons, Ωb. For technical reasons having to do with their Fisher matrix, the WMAP collaboration quotes values for h and Ωbh2. The values quoted in the article are more useful for non-experts. Anyone who looks at the WMAP paper, and has a basic knowledge of error analyses, will understand how to go from one to the other.

If a calculation, although routine, takes more than one or two steps, it may be helpful to present the details of the calculation in a note to the text. For an example, see the detailed calculation in the article on Methane clathrate giving a derivation of the statement in the article's lead that one liter of methane clathrate solid at STP contains, on average, 168 liters of methane gas.

Attribution
Wikipedia's no original research policy requires that we make it clear assertions do not originate with Wikipedia's editors. This is achieved by providing sources for the material in Wikipedia articles. It is also important, however, for our articles to clearly indicate the person who first discovered an astronomical object, first proved a theorem, first performed an experiment, or was otherwise responsible for the idea being discussed. The process of giving credit to the original discoverer will be called attribution here.

Articles should provide attribution for experiments, theorems, astronomical objects, and similar topics, when the original discoverer is known. Many editors prefer to supply the original source for an idea when providing this attribution, for example: When the original reference is not suitable as an introduction to the idea, either because it is outdated or because it contains serious errors, it is helpful to note this in an annotation:
 * Supernova 1987A was discovered by Ian Shelton and Oscar Duhalde at the Las Campanas Observatory in Chile on February 24, 1987, and independently by Albert Jones in New Zealand.
 * Kervaire and Milnor showed that the oriented 7-sphere has 28 different smooth structures (or 15 ignoring orientations), and in higher dimensions there are usually many different smooth structures on a sphere. (from Poincaré conjecture)
 * Beginning with observations in 1912, Vesto Slipher discovered that most spiral nebulae had considerable redshifts. 

Numerical data can also be attributed to the person or group that obtained it. For example, from the neutrino article:
 * The strongest upper limit on the masses of neutrinos comes from cosmology: careful analysis of cosmological data, such as the cosmic microwave background radiation, galaxy surveys and the Lyman-alpha forest indicate that the sum of the neutrino masses must be less than 0.3 electron volts. 

This provides attribution for academic and historical purposes, and also makes it clear how readers can understand where a number comes from. This not only makes Wikipedia a more convenient resource for readers, but makes it easier to update when better data become available.

A related issue is the attribution of eponyms (terms derived from people's names) such as: If Wikipedia has an article about an eponymous topic – such as Michelson–Morley experiment, Sunyaev–Zel'dovich effect, Green–Schwarz mechanism, Alpher–Bethe–Gamow paper and Kaluza–Klein theory – then editors of this article should, if feasible, explain why the names are attached to the result or experiment. To this end, editors of these articles should consider researching and citing the original papers, even if those papers were not originally used as sources in writing the article. However, articles that only link to an eponymous article might not cite the original papers, depending on context. In this case, a reader looking for a reference may easily click the article link to find it.
 * ...the Michelson–Morley experiment ...
 * ...the Sunyaev–Zel'dovich effect ...
 * ...the Green–Schwarz anomaly cancellation mechanism ...
 * ...the &alpha;&beta;&gamma; neutron capture theory ...
 * ...the Kaluza–Klein theory of dimensional reduction  ...