Help:Displaying a formula

This screenshot shows the formula E = mc2 being edited using VisualEditor. The window is opened by typing "<math>" in VisualEditor. The visual editor shows a button that allows to choose one of three offered modes to display a formula.

There are three methods for displaying formulas in Wikipedia: raw HTML, HTML with math templates (abbreviated here as {{math}}), and a subset of LaTeX implemented with the HTML markup <math></math> (referred to as LaTeX in this article). Each method has some advantages and some disadvantages, which have evolved over the time with improvements of MediaWiki. The manual of style MOS:MATH has not always evolved accordingly. So the how-to recommendations that appear below may differ from those of the manual of style. In this case, they express a consensus resulting of the practice of most experienced members of WikiProject Mathematics and many discussions at Wikipedia talk:WikiProject Mathematics.

For example, the famous Einstein formula can be entered in raw HTML as {{nowrap|''E'' {{=}} ''mc''<sup>2</sup>}}, which is rendered as E = mc2 (the template {{nowrap}} is here only for avoiding a line break inside the formula). With {{math}}, it can be entered as {{math|''E'' {{=}} ''mc''{{sup|2}}}}, which is rendered as E = mc2. With LaTeX, it is entered as <math>E=mc^2</math>, and rendered as .

Use of raw HTML edit

Variable names and many symbols look very different with raw HTML and the other display methods. This may be confusing in the common case where several methods are used in the same article. Moreover, mathematicians who are used to reading and writing texts written with LaTeX often find the raw HTML rendering awful.

So, raw HTML should normally not be used for new content. However, raw HTML is still present in many mathematical articles. It is generally a good practice to convert it to {{math}} format, but coherency must be respected; that is, such a conversion must be done in a whole article, or at least in a whole section. Moreover, such a conversion must be identified as such in the edit summary, and making other changes in the same edit should be avoided. This is for helping other users to identify changes that are possibly controversial (the "diff" of a conversion may be very large, and may hide other changes).

Converting raw HTML to {{math}} is rather simple: when the formula is enclosed with {{nowrap}}, it suffices to change "nowrap" into "math". However, if the formula contains an equal sign, one has to add 1= just before the formula for avoiding confusion with the template syntax; for example, {{math|1=''E'' = ''mc''{{sup|2}}}}. Also, vertical bars, if any, must either be replaced with {{!}} or avoided by using {{abs}}.

LaTeX vs. {{math}} edit

These two ways of writing mathematical formulas each have their advantages and disadvantages. They are both accepted by the manual of style MOS:MATH. The rendering of variable names is very similar. So having a variable name displayed in the same paragraph with {{math}} and <math> is generally not a problem.

The disadvantages of LaTeX are the following: On some browser configurations, LaTeX inline formulas appear with a slight vertical misalignment, or with a font size that is slightly different from that of the surrounding text. This is not a problem with a block displayed formula. This is generally also not a real problem with inline formulas that exceed the normal line height (for example formulas with subscripts and superscripts). Also, the use of LaTeX in a piped link or in a section heading should appear in blue in the linked text or the table of content, but they do not. Moreover, links to section headings containing LaTeX formulas do not work always as expected. Finally, too many LaTeX formulas may significantly increase the processing time of a page. LaTeX formulas should be avoided in image captions, because when the image is clicked for a larger display, LaTeX in the caption will not render.

The disadvantages of {{math}} are the following: not all formulas can be displayed. While it is possible to render a complicated formula with {{math}}, it is often poorly rendered. Except for the most common ones, the rendering of non-alphanumeric Unicode symbols is often very poor and may depend on the browser configuration (misalignment, wrong size, ...). The spaces inside formulas are not managed automatically, and thus need some expertise for being rendered correctly. Except for short formulas, many more characters have to be typed for entering a formula, and the source is more difficult to read.

Therefore, the common practice of most members of WikiProject mathematics is the following:

  • Use of {{mvar}} and {{math}} for isolated variables and very simple inline formulas
  • Use of {{mvar}} and {{math}} for formulas in image captions, even if the rendering is mediocre
  • Use of LaTeX for displayed formulas and more complicated inline formulas
  • Use of LaTeX for formulas involving symbols that are not regularly rendered in Unicode (see MOS:BBB)
  • Avoid formulas in section headings, and when this is a problem, use raw HTML (see Finite field for an example)

The choice between {{math}} and LaTeX depends on the editor. So converting from a format to another one must be done with stronger reasons than editor preference.

Display format of LaTeX edit

By default SVG images with non-visible MathML are generated. The text-only form of the LaTeX can be set via user preferences at My Preferences – Appearance – Math.

The hidden MathML can be used by screen readers and other assistive technology. To display the MathML in Firefox:

In either case, you must have fonts that support MathML (see installed on your system. For copy-paste support in Firefox, you can also install MathML Copy.

Use of HTML templates edit

TeX markup is not the only way to render mathematical formulas. For simple inline formulas, the template {{math}} and its associated templates are often preferred. The following comparison table shows that similar results can be achieved with the two methods. See also Help:Special characters.

TeX syntax TeX rendering   HTML syntax HTML rendering
<math>\alpha</math>   {{math|''&alpha;''}}   or   {{mvar|&alpha;}} α   or   α
<math>f(x) = x^2</math>   {{math|''f''(''x'') {{=}} ''x''<sup>2</sup>}} f(x) = x2
<math>\{1,e,\pi\}</math>   {{math|{{mset|1, ''e'', ''&pi;''}}}} {1, e, π}
<math>|z + 1| \leq 2</math>   {{math|{{abs|''z'' + 1}} &le; 2}} |z + 1| ≤ 2

Here is a summary of the mathematical templates:

Care should be taken when writing sets within {{math}}, as braces, equal signs, and vertical bars can conflict with template syntax. The {{mset}} template is available for braces, as shown in the example above. Likewise, {{abs}} encloses its parameter inside vertical bars to help with the pipe character conflicting with template syntax. For a single vertical bar, use {{!}}, and for an equal sign, use {{=}}.

HTML entities edit

Though Unicode characters are generally preferred, sometimes HTML entities are needed to avoid problems with wiki syntax or confusion with other characters:

< > ·
&lt; &gt; &minus; &bull; &prime; &Prime; &sdot; &middot; &ndash; &mdash;

In the table below, the codes on the left produce the symbols on the right, but these symbols can also be entered directly in the wikitext either by typing them if they are available on the keyboard, by copy-pasting them, or by using menus below the edit windows. (When editing any Wikipedia page in a desktop web browser, use the "Insert" pulldown menu immediately below the article text, or the "Special characters" menu immediately above the article text.) Normally, lowercase Greek letters should be entered in italics, that is, enclosed between two single quotes ('').

HTML syntax Rendering
&alpha; &beta; &gamma; &delta; &epsilon; &zeta;
&eta; &theta; &iota; &kappa; &lambda; &mu; &nu;
&xi; &omicron; &pi; &rho; &sigma; &sigmaf;
&tau; &upsilon; &phi; &chi; &psi; &omega;

α β γ δ ε ζ
η θ ι κ λ μ ν
ξ ο π ρ σ ς
τ υ φ χ ψ ω

&Gamma; &Delta; &Theta; &Lambda; &Xi; &Pi;
&Sigma; &Phi; &Psi; &Omega;


&int; &sum; &prod; &minus; &plusmn; &infin;
&asymp; &prop; = &equiv; &ne; &le; &ge;
&times; &middot; &sdot; &divide; &part; &prime; &Prime;
&nabla; &permil; &deg; &there4; &empty;

∫ ∑ ∏ − ± ∞
≈ ∝ = ≡ ≠ ≤ ≥
× · ⋅ ÷ ∂ ′ ″
∇ ‰ ° ∴ ∅

&isin; &notin; &cap; &cup; &sub; &sup; &sube; &supe;
&not; &and; &or; &exist; &forall;
&rArr; &hArr; &rarr; &harr; &uarr; &darr;
&alefsym; - &ndash; &mdash;

∈ ∉ ∩ ∪ ⊂ ⊃ ⊆ ⊇
¬ ∧ ∨ ∃ ∀
⇒ ⇔ → ↔ ↑ ↓
ℵ - – —

Superscripts and subscripts edit

x2 x3 x2

Spacing edit

To avoid line-wrapping in the middle of a formula, use {{math}}. If necessary, a non-breaking space ( ) can be inserted with "&nbsp;".

Typically whitespace should be a regular space ( ) or none at all. In rare circumstances, such as where one character overlaps another due to one being in italics, a thin space can be added with {{thin space}}.

More edit

For more on Wikipedia howtos and math style guidelines:

For more on special characters:

LaTeX basics edit

Math markup goes inside <math>...</math>. Chemistry markup goes inside <math chem>...</math> or <chem>...</chem>. All these tags use TeX.

The TeX code has to be put literally: MediaWiki templates, predefined templates, and parameters cannot be used within math tags: pairs of double braces are ignored and "#" gives an error message. However, math tags work in the then and else part of #if, etc. See m:Template:Demo of attempt to use parameters within TeX (backlinks edit) for more information.

The now deprecated tag <ce> was considered too ambiguous, and it has been replaced by <chem>.[1]

LaTeX commands edit

LaTeX commands are case-sensitive, and take one of the following two formats:

  • They start with a backslash \ and then have a name consisting of letters only. Command names are terminated by a space, a number or any other "non-letter" character.
  • They consist of a backslash \ and exactly one non-letter.

Some commands need an argument, which has to be given between curly braces {} after the command name. Some commands support optional parameters, which are added after the command name in square brackets []. The general syntax is:


Special characters edit

The following symbols are reserved characters that either have a special meaning under LaTeX or are unavailable in all the fonts. If you enter them directly in your text, they will normally not render, but rather do things you did not intend.

# $ % ^ & _ { } ~ \

These characters can be entered by prefixing the escape character backslash \ or using special sequences:

\# \$ \% ^\wedge \& \_ \{ \} \sim \backslash



The backslash character \ can not be entered by adding another backslash in front of it (\\); this sequence is used for line breaking. For introducing a backslash in math mode, you can use \backslash instead which gives  .

The command \tilde produces a tilde which is placed over the next letter. For example, \tilde{a} gives  . To produce just a tilde character ~, use \tilde{} which gives  , placing a ~ over an empty box. Alternatively \sim produces  , a large centred ~ which may be more appropriate in some situations.

The command \hat produces a hat over the next character, for example \hat{o} produces  . For a stretchable version use \widehat{abc} giving  . The wedge \wedge is normally used as a mathematical operator  . The sequence ^\wedge produces   the best equivalent to the ASCII caret ^ character.

Spaces edit

"Whitespace" characters, such as blank or tab, are treated uniformly as "space" by LaTeX. Several consecutive whitespace characters are treated as one "space". See below for commands that produces spaces of different size.

LaTeX environments edit

Environments in LaTeX have a role that is quite similar to commands, but they usually have effect on a wider part of formula. Their syntax is:

   text to be influenced

Environments supported by Wikipedia include matrix, align, etc. See below.

Rendering edit

The font sizes and types are independent of browser settings or CSS. Font sizes and types will often deviate from what HTML renders. Vertical alignment with the surrounding text can also be a problem; a work-around is described in the "Alignment with normal text flow" section below. The CSS selector of the images is img.tex.

Apart from function and operator names, as is customary in mathematics, variables and letters are in italics; digits are not. For other text, (like variable labels) to avoid being rendered in italics like variables, use \text or \mathrm (formerly \rm). You can also define new function names using \operatorname{...}. For example, \text{abc} gives  . \operatorname{...} provides spacing before and after the operator name when appropriate, as when a\operatorname{sn}b is rendered as   (with space to the left and right of "sn") and a\operatorname{sn}(b+c) as   (with space to the left and not to the right). LaTeX's starred version, \operatorname* is not supported, but a workaround is to add \limits instead. For example, \operatorname{sn}_{b>c}(b+c) \qquad \operatorname{sn}\limits_{b>c}(b+c) renders as


LaTeX does not have full support for Unicode characters, and not all characters render. Most Latin characters with accents render correctly. However some do not, in particular those that include multiple diacritics (e.g. with Latin letters used in Vietnamese) or that cannot be precomposed into a single character (such as the uppercase Latin letter W with ring), or that use other diacritics (like the ogonek or the double grave accent, used in Central European languages like Polish, or the horn attached above some vowels in Vietnamese), or other modified letter forms (used in IPA notations, or African languages, or in medieval texts), some digram ligatures (like IJ in Dutch), or Latin letters borrowed from Greek, or small capitals, as well as superscripts and subscript letters. For example, \text{ð} and \text{þ} (used in Icelandic) will give errors.

The normal way of entering quotation marks in text mode (two back ticks for the left and two apostrophes for the right), such as \text{a ``quoted'' word} will not work correctly. As a workaround, you can use the Unicode left and right quotation mark characters, which are available from the "Symbols" dropdown panel beneath the editor: \text{a “quoted” word}.

Force-rerendering of formulas edit

MediaWiki stores rendered formulas in a cache so that the images of those formulas do not need to be created each time the page is opened by a user. To force the rerendering of all formulas of a page, you must open it with the getter variables action=purge&mathpurge=true. Imagine for example there is a wrong rendered formula in the article Integral. To force the re-rendering of this formula you need to open the URL

Afterwards you need to bypass your browser cache so that the new created images of the formulas are actually downloaded.

Formatting using TeX edit

Functions, symbols, special characters edit

Accents and diacritics edit

\dot{a}, \ddot{a}, \acute{a}, \grave{a}  
\check{a}, \breve{a}, \tilde{a}, \bar{a}  
\hat{a}, \widehat{a}, \vec{a}  

Standard numerical functions edit

\exp_a b = a^b, \exp b = e^b, 10^m  
\ln c = \log c, \lg d = \log_{10} d  
\sin a, \cos b, \tan c, \cot d, \sec f, \csc g  
\arcsin h, \arccos i, \arctan j  
\sinh k, \cosh l, \tanh m, \coth n  
\operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n  
\operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q  
\sgn r, \left\vert s \right\vert  
\min(x,y), \max(x,y)  

Bounds edit

\min x, \max y, \inf s, \sup t  
\lim u, \liminf v, \limsup w  
\dim p, \deg q, \det m, \ker\phi  

Projections edit

\Pr j, \hom l, \lVert z \rVert, \arg z  

Differentials and derivatives edit

dt, \mathrm{d}t, \partial t, \nabla\psi  
dy/dx, \mathrm{d}y/\mathrm{d}x, \frac{dy}{dx}, \frac{\mathrm{d}y}{\mathrm{d}x}  
\frac{\partial^2}{\partial x_1\partial x_2}y, \left.\frac{\partial^3 f}{\partial^2 x \partial y}\right\vert_{p_0}  
\prime, \backprime, f^\prime, f', f'', f^{(3)}, \dot y, \ddot y  

Letter-like symbols or constants edit

\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar, \N, \R, \Z, \C, \Q  
\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS, \S, \P, \AA  

Modular arithmetic edit

s_k \equiv 0 \pmod{m}  
a \bmod b  
\gcd(m, n), \operatorname{lcm}(m, n)  
\mid, \nmid, \shortmid, \nshortmid  

Radicals edit

\surd, \sqrt{2}, \sqrt[n]{2}, \sqrt[3]{\frac{x^3+y^3}{2}}  

Operators edit

+, -, \pm, \mp, \dotplus  
\times, \div, \divideontimes, /, \backslash  
\cdot, * \ast, \star, \circ, \bullet  
\boxplus, \boxminus, \boxtimes, \boxdot  
\oplus, \ominus, \otimes, \oslash, \odot  
\circleddash, \circledcirc, \circledast  
\bigoplus, \bigotimes, \bigodot  

Sets edit

\{ \}, \O \empty \emptyset, \varnothing  
\in, \notin \not\in, \ni, \not\ni  
\cap, \Cap, \sqcap, \bigcap  
\cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus  
\setminus, \smallsetminus, \times  
\subset, \Subset, \sqsubset  
\supset, \Supset, \sqsupset  
\subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq  
\supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq  
\subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq  
\supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq  

Relations edit

=, \ne, \neq, \equiv, \not\equiv  
\doteq, \doteqdot, \overset{\underset{\mathrm{def}}{}}{=}, :=  
\sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong  
\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto  
<, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot  
>, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot  
\le, \leq, \lneq, \leqq, \nleq, \nleqq, \lneqq, \lvertneqq  
\ge, \geq, \gneq, \geqq, \ngeq, \ngeqq, \gneqq, \gvertneqq  
\lessgtr, \lesseqgtr, \lesseqqgtr, \gtrless, \gtreqless, \gtreqqless  
\leqslant, \nleqslant, \eqslantless  
\geqslant, \ngeqslant, \eqslantgtr  
\lesssim, \lnsim, \lessapprox, \lnapprox  
\gtrsim, \gnsim, \gtrapprox, \gnapprox  
\prec, \nprec, \preceq, \npreceq, \precneqq  
\succ, \nsucc, \succeq, \nsucceq, \succneqq  
\preccurlyeq, \curlyeqprec  
\succcurlyeq, \curlyeqsucc  
\precsim, \precnsim, \precapprox, \precnapprox  
\succsim, \succnsim, \succapprox, \succnapprox  

Geometric edit

\parallel, \nparallel, \shortparallel, \nshortparallel  
\perp, \angle, \sphericalangle, \measuredangle, 45^\circ  
\Box, \square, \blacksquare, \diamond, \Diamond, \lozenge, \blacklozenge, \bigstar  
\bigcirc, \triangle, \bigtriangleup, \bigtriangledown  
\vartriangle, \triangledown  
\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright  

Logic edit

\forall, \exists, \nexists  
\therefore, \because, \And  
\lor \vee, \curlyvee, \bigvee

don't use \or which is now deprecated

\land \wedge, \curlywedge, \bigwedge

don't use \and which is now deprecated

\bar{q}, \bar{abc}, \overline{q}, \overline{abc},

\lnot \neg, \not\operatorname{R}, \bot, \top



\vdash \dashv, \vDash, \Vdash, \models  
\Vvdash \nvdash \nVdash \nvDash \nVDash  
\ulcorner \urcorner \llcorner \lrcorner  

Arrows edit

\Rrightarrow, \Lleftarrow  
\Rightarrow, \nRightarrow, \Longrightarrow, \implies  
\Leftarrow, \nLeftarrow, \Longleftarrow  
\Leftrightarrow, \nLeftrightarrow, \Longleftrightarrow, \iff  
\Uparrow, \Downarrow, \Updownarrow  
\rightarrow, \to, \nrightarrow, \longrightarrow  
\leftarrow, \gets, \nleftarrow, \longleftarrow  
\leftrightarrow, \nleftrightarrow, \longleftrightarrow  
\uparrow, \downarrow, \updownarrow  
\nearrow, \swarrow, \nwarrow, \searrow  
\mapsto, \longmapsto  
\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons  
\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \rightarrowtail \looparrowright  
\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \leftarrowtail \looparrowleft  
\hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow  

Special edit

\amalg \P \S \% \dagger \ddagger \ldots \cdots \vdots \ddots  
\smile \frown \wr \triangleleft \triangleright  
\diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp  

Unsorted (new stuff) edit

\diagup \diagdown \centerdot \ltimes \rtimes \leftthreetimes \rightthreetimes  
\eqcirc \circeq \triangleq \bumpeq \Bumpeq \doteqdot \risingdotseq \fallingdotseq  
\intercal \barwedge \veebar \doublebarwedge \between \pitchfork  
\vartriangleleft \ntriangleleft \vartriangleright \ntriangleright  
\trianglelefteq \ntrianglelefteq \trianglerighteq \ntrianglerighteq  

For a little more semantics on these symbols, see this brief TeX Cookbook.

Larger expressions edit

Subscripts, superscripts, integrals edit

Feature Syntax How it looks rendered
Superscript a^2, a^{x+3}  
Subscript a_2  
Grouping 10^{30} a^{2+2}  
a_{i,j} b_{f'}  
Combining sub & super without and with horizontal separation x_2^3  
Super super 10^{10^{8}}  
Preceding and/or additional sub & super \sideset{_1^2}{_3^4}\prod_a^b  
Stacking \overset{\alpha}{\omega}  
Derivatives x', y'', f', f''  
x^\prime, y^{\prime\prime}  
Derivative dots \dot{x}, \ddot{x}  
Underlines, overlines, vectors \hat a \ \bar b \ \vec c  
\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}  
\overline{g h i} \ \underline{j k l}  
Arc (workaround) \overset{\frown} {AB}  
Arrows A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C  
Overbraces \overbrace{ 1+2+\cdots+100 }^{5050}  
Underbraces \underbrace{ a+b+\cdots+z }_{26}  
Sum \sum_{k=1}^N k^2  
Sum (force \textstyle) \textstyle \sum_{k=1}^N k^2  
Sum in a fraction (default \textstyle) \frac{\sum_{k=1}^N k^2}{a}  
Sum in a fraction (force \displaystyle) \frac{\displaystyle \sum_{k=1}^N k^2}{a}  
Sum in a fraction (alternative limits style) \frac{\sum\limits^{^N}_{k=1} k^2}{a}  
Product \prod_{i=1}^N x_i  
Product (force \textstyle) \textstyle \prod_{i=1}^N x_i  
Coproduct \coprod_{i=1}^N x_i  
Coproduct (force \textstyle) \textstyle \coprod_{i=1}^N x_i  
Limit \lim_{n \to \infty}x_n  
Limit (force \textstyle) \textstyle \lim_{n \to \infty}x_n  
Integral \int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx  
Integral (alternative limits style) \int_{1}^{3}\frac{e^3/x}{x^2}\, dx  
Integral (force \textstyle) \textstyle \int\limits_{-N}^{N} e^x dx  
Integral (force \textstyle, alternative limits style) \textstyle \int_{-N}^{N} e^x dx  
Double integral \iint\limits_D dx\,dy  
Triple integral \iiint\limits_E dx\,dy\,dz  
Quadruple integral \iiiint\limits_F dx\,dy\,dz\,dt  
Line or path integral \int_{(x,y)\in C} x^3\, dx + 4y^2\, dy  
Closed line or path integral \oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy  
Intersections \bigcap_{i=1}^n E_i  
Unions \bigcup_{i=1}^n E_i  

Fractions, matrices, multilines edit

Feature Syntax How it looks rendered
Fractions \frac{2}{4}=0.5 or {2 \over 4}=0.5  
Small fractions (force \textstyle) \tfrac{2}{4} = 0.5  
Large (normal) fractions (force \displaystyle) \dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a  
Large (nested) fractions \cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a  
Cancellations in fractions \cfrac{x}{1 + \cfrac{\cancel{y}}{\cancel{y}}} = \cfrac{x}{2}  
Binomial coefficients \binom{n}{k}  
Small binomial coefficients (force \textstyle) \tbinom{n}{k}  
Large (normal) binomial coefficients (force \displaystyle) \dbinom{n}{k}  
-x & y \\
z & -v
-x & y \\
z & -v
-x & y \\
z & -v
0 & \cdots & 0 \\
\vdots & \ddots & \vdots \\
0 & \cdots & 0
x & y \\
z & v
x & y \\
z & v
\bigl( \begin{smallmatrix}
a&b\\ c&d
\end{smallmatrix} \bigr)
Case distinctions
f(n) =
n/2, & \text{if }n\text{ is even} \\
3n+1, & \text{if }n\text{ is odd}
Simultaneous equations
3x + 5y + z \\
7x - 2y + 4z \\
-6x + 3y + 2z
Multiline equations
f(x) & = (a+b)^2 \\
& = a^2+2ab+b^2 \\
f(x) & = (a-b)^2 \\
& = a^2-2ab+b^2 \\
Multiline equations with multiple alignments per row
f(a,b) & = (a+b)^2 && = (a+b)(a+b) \\
& = a^2+ab+ba+b^2  && = a^2+2ab+b^2 \\
f(a,b) & = (a+b)^2 && = (a+b)(a+b) \\
& = a^2+ab+ba+b^2  && = a^2+2ab+b^2 \\
Multiline equations (must define number of columns used ({lcl})) (should not be used unless needed)
z & = & a \\
f(x,y,z) & = & x + y + z
Multiline equations (more)
z & = & a \\
f(x,y,z) & = & x + y + z
Multiline alignment using & to left align (top example) versus && to right align (bottom example) the last column
F:\; && C(X) && \;\to\;     & C(X) \\
     && g    && \;\mapsto\; & g^2
F:\; && C(X) && \;\to\;     && C(X) \\
     && g    && \;\mapsto\; && g^2


Breaking up a long expression so that it wraps when necessary, at the expense of destroying correct spacing
<math>f(x) \,\!</math>
<math>= \sum_{n=0}^\infty a_n x^n </math>
<math>= a_0+a_1x+a_2x^2+\cdots</math>
\begin{array}{|c|c|c|} a & b & S \\
0 & 0 & 1 \\
0 & 1 & 1 \\
1 & 0 & 1 \\
1 & 1 & 0 \\

Parenthesizing big expressions, brackets, bars edit

Feature Syntax How it looks rendered
 NBad ( \frac{1}{2} )^n  
Good Y \left ( \frac{1}{2} \right )^n  

You can use various delimiters with \left and \right:

Feature Syntax How it looks rendered
Parentheses \left ( \frac{a}{b} \right )  
Brackets \left [ \frac{a}{b} \right ] \quad
\left \lbrack \frac{a}{b} \right \rbrack
Braces \left \{ \frac{a}{b} \right \} \quad
\left \lbrace \frac{a}{b} \right \rbrace
Angle brackets \left \langle \frac{a}{b} \right \rangle  
Bars and double bars \left | \frac{a}{b} \right \vert \quad
\left \Vert \frac{c}{d} \right \|
Floor and ceiling functions: \left \lfloor \frac{a}{b} \right \rfloor \quad
\left \lceil \frac{c}{d} \right \rceil
Slashes and backslashes \left / \frac{a}{b} \right \backslash  
Up, down, and up-down arrows \left \uparrow \frac{a}{b} \right \downarrow \quad
\left \Uparrow \frac{a}{b} \right \Downarrow \quad
\left \updownarrow \frac{a}{b} \right \Updownarrow
Delimiters can be mixed,
as long as \left and \right match
\left [ 0,1 \right )
\left \langle \psi \right |
Use \left. and \right. if you
do not want a delimiter to appear
\left . \frac{A}{B} \right \} \to X  
Size of the delimiters (add "l" or "r" to indicate the side for proper spacing) ( \bigl( \Bigl( \biggl( \Biggl( \dots \Biggr] \biggr] \Bigr] \bigr] ]  
\{ \bigl\{ \Bigl\{ \biggl\{ \Biggl\{ \dots
\Biggr\rangle \biggr\rangle \Bigr\rangle \bigr\rangle \rangle
\| \big\| \Big\| \bigg\| \Bigg\| \dots \Bigg| \bigg| \Big| \big| |  
\lfloor \bigl\lfloor \Bigl\lfloor \biggl\lfloor \Biggl\lfloor \dots
\Biggr\rceil \biggr\rceil \Bigr\rceil \bigr\rceil \ceil
\uparrow \big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots
\Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow \Downarrow
\updownarrow \big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots
\Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow \Updownarrow
/ \big/ \Big/ \bigg/ \Bigg/ \dots
\Bigg\backslash \bigg\backslash \Big\backslash \big\backslash \backslash

Display attribute edit

The <math> tag can take a display attribute with possible values of inline and block.

Inline edit

If the value of the display attribute is inline, the contents will be rendered in inline mode: there will be no new paragraph for the equation and the operators will be rendered to consume only a small amount of vertical space.

The sum   converges to 2.

The next line-width is not disturbed by large operators.

The code for the math example reads:

<math display="inline">\sum_{i=0}^\infty 2^{-i}</math>

The quotation marks around inline are optional and display=inline is also valid.[2]

Technical implementation edit

Technically the command \textstyle will be added to the user input before the TeX command is passed to the renderer. The result will be displayed without further formatting by outputting the image or MathMLelement to the page.

Block edit

In block-style the equation is rendered in its own paragraph and the operators are rendered consuming less horizontal space. The equation is indented.

The sum

converges to 2.

It was entered as

<math display="block">\sum_{i=0}^\infty 2^{-i}</math>
Technical implementation edit

Technically the command \displaystyle will be added to the user input (if the user input does not already contain the string \displaystyle or \align) before the TeX command is passed to the renderer. The result will be displayed in a new paragraph. Therefore, the style of the MathImage is altered i.e. the style attribute "display:block;margin:auto" is added. For MathML it is ensured that display=inline is replaced by display block which produces a new paragraph

Not specified edit

If nothing is specified the equation is rendered in the same display style as "block", but without using a new paragraph. If the equation does appear on a line by itself, it is not automatically indented.

The sum   converges to 2.

The next line-width is disturbed by large operators.


The sum


converges to 2.

In both cases, the math is coded as:

<math>\sum_{i=0}^\infty 2^{-i}</math>

Equation numbering edit

The templates {{NumBlk}} and {{EquationRef}} can be used to number equations. The template {{EquationNote}} can be used to refer to a numbered equation from surrounding text. For example, the following syntax:

{{NumBlk|:|<math>x^2 + y^2 + z^2 = 1</math>|{{EquationRef|1}}}}

produces the following result (note the equation number in the right margin):







Later on, the text can refer to this equation by its number using syntax like this:

As seen in equation ({{EquationNote|1}}), example text...

The result looks like this:

As seen in equation (1), example text...

The equation number produced by {{EquationNote}} is a link that the user can click to go immediately to the cited equation.

Alphabets and typefaces edit

Texvc cannot render arbitrary Unicode characters. Those it can handle can be entered by the expressions below. For others, such as Cyrillic, they can be entered as Unicode or HTML entities in running text, but cannot be used in displayed formulas.

Greek alphabet
\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta  
\Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi  
\Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega  
\alpha \beta \gamma \delta \epsilon \zeta \eta \theta  
\iota \kappa \lambda \mu \nu \xi \omicron \pi  
\rho \sigma \tau \upsilon \phi \chi \psi \omega  
\varGamma \varDelta \varTheta \varLambda \varXi \varPi \varSigma \varPhi \varUpsilon \varOmega  
\varepsilon \digamma \varkappa \varpi \varrho \varsigma \vartheta \varphi  
Hebrew symbols
\aleph \beth \gimel \daleth  
Blackboard bold/scripts
Boldface (Greek)
\boldsymbol{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta}  
\boldsymbol{\Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi}  
\boldsymbol{\Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega}  
\boldsymbol{\alpha \beta \gamma \delta \epsilon \zeta \eta \theta}  
\boldsymbol{\iota \kappa \lambda \mu \nu \xi \omicron \pi}  
\boldsymbol{\rho \sigma \tau \upsilon \phi \chi \psi \omega}  
Italics (default for Latin alphabet)
Greek italics (default for lowercase Greek)
\mathit{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta}  
\mathit{\Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi}  
\mathit{\Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega}  
Greek uppercase boldface italics
\boldsymbol{\varGamma \varDelta \varTheta \varLambda}  
\boldsymbol{\varXi \varPi \varSigma \varUpsilon \varOmega}  
Roman typeface
Sans serif
Sans serif Greek (capital only)
\mathsf{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta}  
\mathsf{\Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi}  
\mathsf{\Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega}  
Fraktur typeface
Small scriptstyle text

Mixed text faces edit

Feature Syntax How it looks rendered
Italicised characters (spaces are ignored) x y z  
Non-italicised characters \text{x y z}  
Mixed italics (bad) \text{if} n \text{is even}  
Mixed italics (good) \text{if }n\text{ is even}  
Mixed italics (alternative: ~ or "\ " forces a space) \text{if}~n\ \text{is even}  

Color edit

Equations can use color with the \color command. For example,

How it looks rendered Syntax Feature

The \color command colors all symbols to its right. However, if the \color command is enclosed in a pair of braces (e.g. {\color{Red}...}) then no symbols outside of those braces are affected.

How it looks rendered Syntax Feature
  x\color{red}\neq y=z

Colors red everything to the right of \color{red}. To only color the   symbol red, place braces around \color{red}\neq or insert \color{black} to the right of \neq.

  x{\color{red}\neq} y=z
  x\color{red}\neq\color{black} y=z
  \frac{-b\color{Green}\pm\sqrt{b^2\color{Blue}-4{\color{Red}a}c}}{2a}=x The outermost braces in {\color{Red}a}c limit the effect of \color{Red} to the symbol a. Similarly, \color{Blue} does not affect any symbols outside of the \sqrt{} that encloses it, and \color{Green} does not affect any symbols outside of the numerator.

There are several alternate notations styles

How it looks rendered Syntax Feature
  {\color{Blue}x^2}+{\color{Orange}2x}-{\color{LimeGreen}1} works with both texvc and MathJax
  \color{Blue}x^2\color{Black}+\color{Orange}2x\color{Black}-\color{LimeGreen}1 works with both texvc and MathJax
  \color{Blue}{x^2}+\color{Orange}{2x}-\color{LimeGreen}{1} only works with MathJax

Some color names are predeclared according to the following table, you can use them directly for the rendering of formulas (or for declaring the intended color of the page background).

Colors supported

Color should not be used as the only way to identify something, because it will become meaningless on black-and-white media or for color-blind people. See WP:Manual of Style (accessibility)#Color.

Latex does not have a command for setting the background color. The most effective way of setting a background color is by setting a CSS styling rule for a table cell:

{| class="wikitable" align="center"
| style="background-color: gray;"      | <math>x^2</math>
| style="background-color: Goldenrod;" | <math>y^3</math>

Rendered as:


Custom colors can be defined using:

\definecolor{myorange}{rgb}{1,0.65,0.4}\color{myorange}e^{i \pi}\color{Black} + 1 = 0

Formatting issues edit

Spacing edit

TeX handles most spacing automatically, but you may sometimes want manual control.

Feature Syntax How it looks rendered
double quad space a \qquad b  
quad space a \quad b  
text space a\ b  
text space in text mode a \text{ } b  
large space a\;b  
medium space a\<b Not supported
small space a\,b  
tiny space (use for multiplication of factors) ab  
tiny space (syntax space ignored) a b  
no space (use for multi-letter variables) \mathit{ab}  
small negative space a\!b  
zero-width space a\hspace{0pt}b Not supported

Automatic spacing may be broken in very long expressions (because they produce an overfull hbox in TeX):


This can be remedied by putting a pair of braces { } around the whole expression:


When relational symbols such as   are employed as ordinary symbols, for example in bra–ket notation, additional spacing may have to be avoided:

Feature Syntax How it looks rendered
without special formatting | \uparrow \rangle  
explicit opening and closing delimiter \left| \uparrow \right\rangle  
with additional braces | {\uparrow} \rangle  
arrow as ordinary symbol | \mathord\uparrow \rangle  
Empty horizontal or vertical spacing edit

The phantom commands create empty horizontal and/or vertical space the same height and/or width of the argument.

Feature Syntax How it looks rendered
Empty horizontal and vertical spacing \Gamma^{\phantom{i}j}_{i\phantom{j}k}  
Empty vertical spacing -e\sqrt{\vphantom{p'}p},\; -e'\sqrt{p'},\; \ldots  
Empty horizontal spacing \int u^2\,du=\underline{\hphantom{(2/3)u^3+C}}  

Alignment with normal text flow edit

Because of the default CSS

img.tex { vertical-align: middle; }

an inline expression like   should look good.

If you need to align it otherwise, use <math style="vertical-align:-100%;">...</math> and play with the vertical-align argument until you get it right; however, how it looks may depend on the browser and the browser settings.

If you rely on this workaround, if and when the rendering on the server gets fixed in a future release, this extra manual offset will suddenly make every affected formula align incorrectly. So use it sparingly, if at all.

Unimplemented elements and workarounds edit

The current Mathoid–MathJax backend has the following elements unimplemented (see also MathJax's own description of differences):

Special integral operators edit

The following integral operators that are not supported by the default font of MathJax 2.7 are available

 \oiint, \oiiint, \ointctrclockwise, \varointclockwise, \intbar, \intBar

they have poor horizontal spacing, generate cropped SVG images unless used with other tall characters, and appear different from the usual integral symbol \int:


cf. phab:T348587. However, they render fine when MathML is used.

\oiint and \oiiint edit

Elements which are not yet implemented are \oiint, namely a two-fold integral \iint ( ) with a circular curve through the centre of the two integrals, and similarly \oiiint, a circular curve through three integrals. In contrast, \oint ( ) exists for the single dimension (integration over a curved line within a plane or any space with higher dimension).

These elements appear in many contexts: \oiint denotes a surface integral over the closed 2d boundary of a 3d region (which occurs in much of 3d vector calculus and physical applications – like Maxwell's equations), likewise \oiiint denotes integration over the closed 3d boundary (surface volume) of a 4d region, and they would be strong candidates for the next TeX version. As such there are a lot of workarounds in the present version.

However, since no standardisation exists as yet, any workaround like this (which uses many \! symbols for backspacing) should be avoided, if possible. See below for a possibility using PNG image enforcement.

Note that \iint (the double integral) and \iiint (the triple integral) are still not kerned as they should preferably be, and are currently rendered as if they were successive \int symbols; this is not a major problem for reading the formulas, even if the integral symbols before the last one do not have bounds, so it's best to avoid backspacing "hacks" as they may be inconsistent with a possible future better implementation of integrals symbols (with more precisely computed kerning positions).

\oiint and \oiiint as PNG images edit

These symbols are available as PNG images which are also integrated into two templates, {{oiint}} and {{oiiint}}, which take care of the formatting around the symbols.

The templates have three parameters:

the text or formula immediately before the integral
the subscript below the integral
the text or formula immediately after the integral
Examples edit
  • Stokes' theorem: {{oiint | intsubscpt=<math>\scriptstyle S</math> | integrand=<math>( \nabla \times \mathbf{F} ) \cdot {\mathrm d}\mathbf{S} = \oint_{\partial S} \mathbf{F} \cdot {\mathrm d}\boldsymbol{\ell}</math>}}
  • Ampère's law + correction: {{oiint | preintegral=<math>\oint_C \mathbf{B} \cdot {\mathrm d} \boldsymbol{\ell} = \mu_0 </math> | intsubscpt = <math>{\scriptstyle S}</math> | integrand = <math>\left ( \mathbf{J} + \epsilon_0\frac{\partial \mathbf{E}}{\partial t} \right ) \cdot {\mathrm d}\mathbf{S}</math> }}
  • Continuity of 4-momentum flux (in general relativity):[3]{{oiiint | preintegral=<math>\mathbf{P} = </math> | intsubscpt=<math>\scriptstyle \partial \Omega</math> | integrand=<math>\mathbf{T} \cdot {\mathrm d}^3\boldsymbol{\Sigma}</math> <math>=0</math>}}


Oriented \oiint and \oiiint as PNG images edit

Some variants of \oiint and \oiiint have arrows on them to indicate the sense of integration, such as a line integral around a closed curve in the clockwise sense, and higher dimensional analogues. These are not implemented in TeX on Wikipedia either, although the template {{intorient}} is available - see link for details.

Arc notation \overarc edit

\overarc is not yet implemented to display the arc notation. However, there exists a workaround: use \overset{\frown}{AB}, which gives


For longer arcs, use {{Overarc}}:


Triple dot \dddot edit

\dddot is not implemented. For a workaround use \overset{...}{x}, which gives


Starred operatorname \operatorname* edit

The starred version of \operatorname is not currently supported. A workaround for

\operatorname*{median}_{j\,\ne\,i} X_{i,j}


\operatorname{\underset{\mathit{j\,\ne\,i}}{median}} X_{i,j}

Strikethrough edit

Strikethrough like \sout or \st is not implemented, nor is overlapping like \rlap. This means struck characters like ƛ are difficult to type, except the hardcoded \hbar. A workaround suffix for a normal strikethrough is q \!\!\!\frac{}{\ }, and for elevated strikethrough is \lambda \!\!\!^{{}^\underline{\ \ }}, which give


Formatting in \text edit

Formatting in \text is not supported. In other words, you can't use:

\text{\textsf{textual description of a variable}}

but have to use:

\mathsf{textual\ description\ of\ a\ variable}

More specifically, in Mathoid's MathJax, no processing is done to the contents of \text at all. The texvcjs component blocks the use of macros, but another way this behavior leaks through is in the processing of quotation marks, where the Unicode version must be used instead of `:

\text{`failed ``ascii'' quotes'},\ \text{‘okay “unicode” quotes’}

It is currently impossible to get straight (typewriter) quotes in MathJax.

Automatic line-breaking edit

The current image-based implementation precludes automatic line-breaking of inline formulae after binary operators and "=" as seen in TeX. The only workaround is to not write long formulae inline.

Readers wishing to enable automatic line-breaking can try to have the browser render the MathML itself or to use an alternate in-browser renderer.

Syntax to avoid edit

Unicode characters edit

Non-ASCII Unicode characters like π work in MathML and MathJax but not in texvc so should currently be avoided. In the long term it may become possible to use these characters.

Unicode is currently possible in \text{} due to Wikipedia's switch to Mathoid (server-side MathJax in SVG/PNG mode). However, Unicode text in math mode is still unavailable due to texvcjs considering it invalid. A formal feature request and discussion is required to fix this.

Deprecated syntax edit

The texvc processor accepted some non-standard syntax. These should be avoided as the MathJax based renderers do not support these syntax.

The following texvc commands are now deprecated and should be avoided. This is part of an effort to update the math engine see mw:Extension:Math/Roadmap for details. A bot User:Texvc2LaTeXBot will replace this syntax on the English Wikipedia.

Current syntax Suggested replacement Comment
$ \$ redefinition would involve changing the character code
 % \% redefinition would involve changing the character code
\or \lor causes teubner to fail[4]
\and \land causes normal align environment to fail
\pagecolor remove not needed and not working anymore, done manually
\part \partial acceptable if the document doesn't use sectioning with \part.
\ang \angle this only conflicts with siunitx package.
\C \Complex conflicts with puenc.def e.g. from hyperref package
\H \mathbb{H} conflicts with text command \H{0} which is ő.
\bold \mathbf
\Bbb \mathbb

Chemistry edit

There are three ways to render chemical sum formulas as used in chemical equations:

  • <chem>...</chem> (<ce>...</ce> is a deprecated alias for it)
  • <math chem>...</math>
  • {{chem}} and {{chem2}}

<chem>X</chem> is short for <math chem>\ce{X}</math> (where X is a chemical sum formula)

Technically, <math chem> is a math tag with the extension mhchem enabled, according to the MathJax documentation.

Wikipedia:Manual of Style/Chemistry advises avoiding the <chem> and <math chem> markup methods when possible.

Note, that the commands \cee and \cf are disabled, because they are marked as deprecated in the mhchem LaTeX package documentation.

If the formula reaches a certain "complexity", spaces might be ignored (<chem>A + B</chem> might be rendered as if it were <chem>A+B</chem> with a positive charge). In that case, write <chem>A{} + B</chem> (and not <chem>{A} + {B}</chem> as was previously suggested). This will allow auto-cleaning of formulas once the bug will be fixed and/or a newer mhchem version will be used.

Please note that there are still major issues with mhchem support in MediaWiki. Some issues can be solved by enabling the extension using <math chem> and formatting individual items with \ce. For example,

  • <math chem>\ce{pIC_{50}} = -\log_{10} \ce{(IC_{50})}</math>

Molecular and condensed formula edit

mhchem {{chem}} {{chem2}} Equivalent HTML
Markup Renders as






Markup Renders as






Markup Renders as






Markup Renders as






Bonds edit

mhchem Equivalent {{chem}} and HTML {{chem2}}
Markup Renders as




Markup Renders as





Markup Renders as




Charges edit

mhchem {{chem}} {{chem2}} Equivalent HTML
Markup Renders as












Markup Renders as












Markup Renders as












Markup Renders as












Addition compounds and stoichiometric numbers edit

mhchem {{chem}} {{chem2}}
Markup Renders as




<chem>CaSO4.1/2H2O + 1\!1/2 H2O -> CaSO4.2H2O</chem>


<chem>25/2 O2 + C8H18 -> 8 CO2 + 9 H2O</chem>


Markup Renders as




{{chem|Ca|S|O|4}}&middot;&frac12;{{chem|H|2|O}} + 1&frac12;{{chem|H|2|O}} → {{chem|Ca|S|O|4}}&middot;2{{chem|H|2|O}}

+ 1½H

{{frac|25|2}}{{chem|O|2}} + {{chem|C|8|H|18}} → 8{{chem|C|O|2}} + 9{{chem|H|2|O}}

+ C
→ 8CO
+ 9H

Markup Renders as




{{chem2|2CaSO4*H2O + 3H2O -> 2CaSO4*2H2O}}

2CaSO4·H2O + 3H2O → 2CaSO4·2H2O

{{chem2|25 O2 + 2 C8H18 -> 16 CO2 + 18 H2O}}

25 O2 + 2 C8H18 → 16 CO2 + 18 H2O

Wiki linking edit

25 {{chem|link=oxygen|O|2}} + 2 {{chem|link=octane|C|8|H|18}} → 16 {{chem|link=Carbon dioxide|C|O|2}} + 18 {{chem|link=water|H|2|O}}
Renders as 25 O
+ 2 C
→ 16 CO
+ 18 H
{{chem2|25 [[oxygen|O2]] + 2 [[octane|C8H18]] -> 16 [[Carbon dioxide|CO2]] + 18 [[water|H2O]]}}
Renders as 25 O2 + 2 C8H18 → 16 CO2 + 18 H2O

(Italic) Math edit

<chem>{C_\mathit{x}H_\mathit{y}} + \mathit{z}O2 -> {\mathit{x}CO2} + \frac{\mathit{y}}{2}H2O</chem>
Renders as