你谷之 KaTeX

· · 科技·工程

博客（不是专栏）应该是 v0.11.1，所以文档：

https://github.com/KaTeX/KaTeX/blob/v0.11.1/website/versioned_docs/version-0.11.0/supported.md

https://github.com/KaTeX/KaTeX/blob/v0.11.1/website/versioned_docs/version-0.11.0/support_table.md

云剪贴板应该是 v0.12.0，所以文档：

https://github.com/KaTeX/KaTeX/blob/v0.12.0/website/versioned_docs/version-0.12.0/supported.md

https://github.com/KaTeX/KaTeX/blob/v0.12.0/website/versioned_docs/version-0.12.0/support_table.md

而博客同步预览界面的 Markdown*Palettes 更离谱，一堆都不支持。不知道哪个渲染。

另附 MathJax 支持表：

https://docs.mathjax.org/en/latest/input/tex/macros/index.html

鉴于 GitHub 用 MathJax 渲染很糟糕，抄了份 v0.11.1 的 supported.md 过来（有一处反引号改为了全角）：

Accents
a' a' \tilde{a} \tilde{a} \mathring{g} \mathring{g}
a'' a'' \widetilde{ac} \widetilde{ac} \overgroup{AB} \overgroup{AB}
a^{\prime} a^{\prime} \utilde{AB} \utilde{AB} \undergroup{AB} \undergroup{AB}
\acute{a} \acute{a} \vec{F} \vec{F} \Overrightarrow{AB} \Overrightarrow{AB}
\bar{y} \bar{y} \overleftarrow{AB} \overleftarrow{AB} \overrightarrow{AB} \overrightarrow{AB}
\breve{a} \breve{a} \underleftarrow{AB} \underleftarrow{AB} \underrightarrow{AB} \underrightarrow{AB}
\check{a} \check{a} \overleftharpoon{ac} \overleftharpoon{ac} \overrightharpoon{ac} \overrightharpoon{ac}
\dot{a} \dot{a} \overleftrightarrow{AB} \overleftrightarrow{AB} \overbrace{AB} \overbrace{AB}
\ddot{a} \ddot{a} \underleftrightarrow{AB} \underleftrightarrow{AB} \underbrace{AB} \underbrace{AB}
\grave{a} \grave{a} \overline{AB} \overline{AB} \overlinesegment{AB} \overlinesegment{AB}
\hat{\theta} \hat{\theta} \underline{AB} \underline{AB} \underlinesegment{AB} \underlinesegment{AB}
\widehat{ac} \widehat{ac} \widecheck{ac} \widecheck{ac}

Accent functions inside \text{…}
\text{\'{a}} \'{a} \text{\~{a}} \~{a} \text{\.{a}} \.{a} \text{\H{a}} \H{a}
\text{\`{a}} \｀{a}|\text{\={a}} \={a}|\text{\"{a}} \"{a}|\text{\v{a}} \v{a}
\text{\^{a}} \^{a} \text{\u{a}} \u{a} \text{\r{a}} \r{a}

See also letters

Delimiters
(~) ( ) \lparen~\rparen \lparen~~~~\rparen ⌈~⌉ ⌈ ⌉ \lceil~\rceil \lceil~~~~~\rceil \uparrow \uparrow
[~] [ ] \lbrack~\rbrack \lbrack~~~~\rbrack ⌊~⌋ ⌊ ⌋ \lfloor~\rfloor \lfloor~~~~~\rfloor \downarrow \downarrow
\{ \} \{ \} \lbrace \rbrace \lbrace~~~~\rbrace ⎰⎱ ⎰⎱ \lmoustache \rmoustache \lmoustache~~~~\rmoustache \updownarrow \updownarrow
⟨~⟩ ⟨ ⟩ \langle~\rangle \langle~~~~\rangle ⟮~⟯ ⟮ ⟯ \lgroup~\rgroup \lgroup~~~~~\rgroup \Uparrow \Uparrow
\vert | \vert \vert ┌ ┐ ┌ ┐ \ulcorner \urcorner \ulcorner~~~~\urcorner \Downarrow \Downarrow
\Vert \| \Vert \Vert └ ┘ └ ┘ \llcorner \lrcorner \llcorner~~~~\lrcorner \Updownarrow \Updownarrow
\lvert~\rvert \lvert~~~~\rvert \lVert~\rVert \lVert~~~~~\rVert \left. \right. \backslash \backslash
\lang~\rang \lang~~~~\rang \lt~\gt \lt \gt ⟦~⟧ ⟦ ⟧ \llbracket~\rrbracket \llbracket~~~~\rrbracket \lBrace~\rBrace \lBrace \rBrace

Delimiter Sizing

$( \big( \Big( \bigg( \Bigg($ `( \big( \Big( \bigg( \Bigg(` |||||| |:--------|:------|:--------|:-------|:------| |`\left` |`\big` |`\bigl` |`\bigm` |`\bigr` |`\middle`|`\Big` |`\Bigl` |`\Bigm` | `\Bigr` |`\right` |`\bigg`|`\biggl` |`\biggm`|`\biggr` | |`\Bigg`|`\Biggl` |`\Biggm`|`\Biggr` ## Environments ||||| |:---------------------|:---------------------|:---------------------|:-------- |$\begin{matrix} a & b \\ c & d \end{matrix}$ | `\begin{matrix}`&nbsp;&nbsp;&nbsp;`a & b \\`&nbsp;&nbsp;&nbsp;`c & d` `\end{matrix}` |$\begin{array}{cc}a & b\\c & d\end{array}$ | `\begin{array}{cc}`&nbsp;&nbsp;&nbsp;`a & b \\`&nbsp;&nbsp;&nbsp;`c & d` `\end{array}` |$\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ |`\begin{pmatrix}`&nbsp;&nbsp;&nbsp;`a & b \\`&nbsp;&nbsp;&nbsp;`c & d` `\end{pmatrix}` |$\begin{bmatrix} a & b \\ c & d \end{bmatrix}$ | `\begin{bmatrix}`&nbsp;&nbsp;&nbsp;`a & b \\`&nbsp;&nbsp;&nbsp;`c & d` `\end{bmatrix}` |$\begin{vmatrix} a & b \\ c & d \end{vmatrix}$ |`\begin{vmatrix}`&nbsp;&nbsp;&nbsp;`a & b \\`&nbsp;&nbsp;&nbsp;`c & d` `\end{vmatrix}` |$\begin{Vmatrix} a & b \\ c & d \end{Vmatrix}$ |`\begin{Vmatrix}`&nbsp;&nbsp;&nbsp;`a & b \\`&nbsp;&nbsp;&nbsp;`c & d` `\end{Vmatrix}` |$\begin{Bmatrix} a & b \\ c & d \end{Bmatrix}$ |`\begin{Bmatrix}`&nbsp;&nbsp;&nbsp;`a & b \\`&nbsp;&nbsp;&nbsp;`c & d` `\end{Bmatrix}`|$\def\arraystretch{1.5}\begin{array}{c:c:c} a & b & c \\ \hline d & e & f \\ \hdashline g & h & i \end{array}$|`\def\arraystretch{1.5}`&nbsp;&nbsp;&nbsp;`\begin{array}{c:c:c}`&nbsp;&nbsp;&nbsp;`a & b & c \\ \hline`&nbsp;&nbsp;&nbsp;`d & e & f \\`&nbsp;&nbsp;&nbsp;`\hdashline`&nbsp;&nbsp;&nbsp;`g & h & i` `\end{array}` |$\begin{aligned} a&=b+c \\ d+e&=f \end{aligned}$ |`\begin{aligned}`&nbsp;&nbsp;&nbsp;`a&=b+c \\`&nbsp;&nbsp;&nbsp;`d+e&=f` `\end{aligned}`|$\begin{alignedat}{2}10&x+&3&y=2\\3&x+&13&y=4\end{alignedat}$ |`\begin{alignedat}{2}`&nbsp;&nbsp;&nbsp;`10&x+ &3&y = 2 \\`&nbsp;&nbsp;&nbsp;` 3&x+&13&y = 4` `\end{alignedat}` |$\begin{gathered} a=b \\ e=b+c \end{gathered}$ |`\begin{gathered}`&nbsp;&nbsp;&nbsp;`a=b \\ `&nbsp;&nbsp;&nbsp;`e=b+c` `\end{gathered}`|$x = \begin{cases} a &\text{if } b \\ c &\text{if } d \end{cases}$ |`x = \begin{cases}`&nbsp;&nbsp;&nbsp;`a &\text{if } b \\`&nbsp;&nbsp;&nbsp;`c &\text{if } d` `\end{cases}` |$\begin{smallmatrix} a & b \\ c & d \end{smallmatrix}$ | `\begin{smallmatrix}`&nbsp;&nbsp;&nbsp;`a & b \\`&nbsp;&nbsp;&nbsp;`c & d` `\end{smallmatrix}` |$\begin{rcases} a &\text{if } b \\ c &\text{if } d \end{rcases}⇒…$ |`\begin{rcases}`&nbsp;&nbsp;&nbsp;`a &\text{if } b \\`&nbsp;&nbsp;&nbsp;`c &\text{if } d` `\end{rcases}⇒…`| KaTeX also supports `darray`, `dcases`, and `drcases`. Acceptable line separators include: `\\`, `\cr`, `\\[distance]`, and `\cr[distance]`. *Distance* can be written with any of the [KaTeX units](#units). The `{array}` environment supports `|` and `:` vertical separators. The `{array}` environment does not yet support `\cline` or `\multicolumn`. ## HTML The following "raw HTML" features are potentially dangerous for untrusted inputs, so they are disabled by default, and attempting to use them produces the command names in red (which you can configure via the `errorColor` [option](https://github.com/KaTeX/KaTeX/blob/v0.11.1/website/versioned_docs/version-0.11.0/options.md)). To fully trust your LaTeX input, you need to pass an option of `trust: true`; you can also enable just some of the commands or for just some URLs via the `trust` [option](https://github.com/KaTeX/KaTeX/blob/v0.11.1/website/versioned_docs/version-0.11.0/options.md). ||| |:----------------|:-------------------| | $\href{https://katex.org/}{\KaTeX}$ | `\href{https://katex.org/}{\KaTeX}` | | $\url{https://katex.org/}$ | `\url{https://katex.org/}` | | $\includegraphics[height=0.8em, totalheight=0.9em, width=0.9em, alt=KA logo]{https://katex.org/img/khan-academy.png}$ | `\includegraphics[height=0.8em, totalheight=0.9em, width=0.9em, alt=KA logo]{https://katex.org/img/khan-academy.png}` | | $\htmlId{bar}{x}$ `…<span id="bar" class="enclosing">…x…</span>…` | `\htmlId{bar}{x}` | | $\htmlClass{foo}{x}$ `…<span class="enclosing foo">…x…</span>…` | `\htmlClass{foo}{x}` | | $\htmlStyle{color: red;}{x}$ `…<span style="color: red;" class="enclosing">…x…</span>…` | `\htmlStyle{color: red;}{x}` | | $\htmlData{foo=a, bar=b}{x}$ `…<span data-foo="a" data-bar="b" class="enclosing">…x…</span>…` | `\htmlData{foo=a, bar=b}{x}` | `\includegraphics` supports `height`, `width`, `totalheight`, and `alt` in its first argument. `height` is required. HTML extension (`\html`-prefixed) commands are non-standard, so loosening `strict` option for `htmlExtension` is required. ## Letters and Unicode **Greek Letters** Direct Input: $Α Β Γ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω α β γ δ ϵ ζ η θ ι κ λ μ ν ξ o π ρ σ τ υ ϕ χ ψ ω ε ϑ ϖ ϱ ς φ ϝ
\Alpha \Alpha \Beta \Beta \Gamma \Gamma \Delta \Delta
\Epsilon \Epsilon \Zeta \Zeta \Eta \Eta \Theta \Theta
\Iota \Iota \Kappa \Kappa \Lambda \Lambda \Mu \Mu
\Nu \Nu \Xi \Xi \Omicron \Omicron \Pi \Pi
\Rho \Rho \Sigma \Sigma \Tau \Tau \Upsilon \Upsilon
\Phi \Phi \Chi \Chi \Psi \Psi \Omega \Omega
\varGamma \varGamma \varDelta \varDelta \varTheta \varTheta \varLambda \varLambda
\varXi \varXi \varPi \varPi \varSigma \varSigma \varUpsilon \varUpsilon
\varPhi \varPhi \varPsi \varPsi \varOmega \varOmega
\alpha \alpha \beta \beta \gamma \gamma \delta \delta
\epsilon \epsilon \zeta \zeta \eta \eta \theta \theta
\iota \iota \kappa \kappa \lambda \lambda \mu \mu
\nu \nu \xi \xi \omicron \omicron \pi \pi
\rho \rho \sigma \sigma \tau \tau \upsilon \upsilon
\phi \phi \chi \chi \psi \psi \omega \omega
\varepsilon \varepsilon \varkappa \varkappa \vartheta \vartheta \thetasym \thetasym
\varpi \varpi \varrho \varrho \varsigma \varsigma \varphi \varphi
\digamma \digamma

Other Letters
\imath \imath \nabla \nabla \Im \Im \Reals \Reals \text{\OE} \text{\OE}
\jmath \jmath \partial \partial \image \image \wp \wp \text{\o} \text{\o}
\aleph \aleph \Game \Game \Bbbk \Bbbk \weierp \weierp \text{\O} \text{\O}
\alef \alef \Finv \Finv \N \N \Z \Z \text{\ss} \text{\ss}
\alefsym \alefsym \cnums \cnums \natnums \natnums \text{\aa} \text{\aa} \text{\i} \text{\i}
\beth \beth \Complex \Complex \R \R \text{\AA} \text{\AA} \text{\j} \text{\j}
\gimel \gimel \ell \ell \Re \Re \text{\ae} \text{\ae}
\daleth \daleth \hbar \hbar \real \real \text{\AE} \text{\AE}
\eth \eth \hslash \hslash \reals \reals \text{\oe} \text{\oe}

Direct Input: ∂ ∇ ℑ Ⅎ ℵ ℶ ℷ ℸ ⅁ ℏ ð ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖÙÚÛÜÝÞßàáâãäåçèéêëìíîïðñòóôöùúûüýþÿ

Unicode Mathematical Alphanumeric Symbols

（这段本来炸成了一串问号，修了一下，将就着看。）

（Upd：专栏里又炸了，懒得修。）

Item Range Item Range
Bold \text{&#119808;-&#119833; &#119834;-&#119859; &#120782;-&#120791;} Double-struck \text{&#120120;-}ℤ\ &#120156;
Italic \text{&#119860;-&#119885; &#119886;-&#119911;} Sans serif \text{&#120224;-&#120249; &#120250;-&#120275; &#120802;-&#120811;}
Bold Italic \text{&#119912;-&#119937; &#119938;-&#119963;} Sans serif bold \text{&#120276;-&#120301; &#120302;-&#120327; &#120812;-&#120821;}
Script \text{&#119964;-&#119989;} Sans serif italic \text{&#120328;-&#120353; &#120354;-&#120379;}
Fractur \text{&#120068;-}ℨ\text{ &#120094;-&#120119;} Monospace \text{&#120432;-&#120457; &#120458;-&#120483; &#120822;-&#120831;}

Unicode

The letters listed above will render properly in any KaTeX rendering mode.

In addition, Brahmic, Georgian, Chinese, Japanese, and Korean glyphs are always accepted in text mode. However, these glyphs will be rendered from system fonts (not KaTeX-supplied fonts) so their typography may clash. You can provide rules for CSS classes .latin-fallback, .cyrillic-fallback, .brahmic-fallback, .georgian-fallback, .cjk-fallback, and .hangul-fallback to provide fallback fonts for these languages. Use of these glyphs may cause small vertical alignment issues: KaTeX has detailed metrics for listed symbols and most Latin, Greek, and Cyrillic letters, but other accepted glyphs are treated as if they are each as tall as the letter M in the current KaTeX font.

If the KaTeX rendering mode is set to strict: false or strict: "warn" (default), then KaTeX will accept all Unicode letters in both text and math mode. All unrecognized characters will be treated as if they appeared in text mode, and are subject to the same issues of using system fonts and possibly using incorrect vertical alignment.

For Persian composite characters, a user-supplied plug-in is under development.

Layout

Annotation
\cancel{5} \cancel{5} \overbrace{a+b+c}^{\text{note}} \overbrace{a+b+c}^{\text{note}}
\bcancel{5} \bcancel{5} \underbrace{a+b+c}_{\text{note}} \underbrace{a+b+c}_{\text{note}}
\xcancel{ABC} \xcancel{ABC} \not = \not =
\sout{abc} \sout{abc} \boxed{\pi=\frac c d} \boxed{\pi=\frac c d}

\tag{hi} x+y^{2x}

\tag{hi} x+y^{2x}

\tag*{hi} x+y^{2x}

\tag*{hi} x+y^{2x}

Line Breaks

KaTeX 0.10.0+ will insert automatic line breaks in inline math after relations or binary operators such as “=” or “+”. These can be suppressed by \nobreak or by placing math inside a pair of braces, as in {F=ma}. \allowbreak will allow automatic line breaks at locations other than relations or operators.

Hard line breaks are \\ and \newline.

In display math, KaTeX does not insert automatic line breaks. It ignores display math hard line breaks when rendering option strict: true.

Vertical Layout
x_n x_n \stackrel{!}{=} \stackrel{!}{=} a \atop b a \atop b
e^x e^x \overset{!}{=} \overset{!}{=} a\raisebox{0.25em}{b}c a\raisebox{0.25em}{b}c
_u^o _u^o \underset{!}{=} \underset{!}{=} \sum_{\substack{0<i<m\\0<j<n}} \sum_{\substack{0<i<m\\0<j<n}}

The second argument of \raisebox can contain math if it is nested within $…$ delimiters, as in \raisebox{0.25em}{$\frac a b$}

Overlap and Spacing
{=}\mathllap{/\,} {=}\mathllap{/\,} \left(x^{\smash{2}}\right) \left(x^{\smash{2}}\right)
\mathrlap{\,/}{=} \mathrlap{\,/}{=} \sqrt{\smash[b]{y}} \sqrt{\smash[b]{y}}
KaTeX also supports `\llap`, `\rlap`, and `\clap`, but they will take only text, not math, as arguments. **Spacing** | Function | Produces | Function | Produces| |:----------------|:-------------------|:---------------------|:--------------------------------------| | `\,` | ³∕₁₈ em space | `\kern{distance}` | space, width = *distance* | `\thinspace` | ³∕₁₈ em space | `\mkern{distance}` | space, width = *distance* | `\>` | ⁴∕₁₈ em space | `\mskip{distance}` | space, width = *distance* | `\:` | ⁴∕₁₈ em space | `\hskip{distance}` | space, width = *distance* | `\medspace` | ⁴∕₁₈ em space | `\hspace{distance}` | space, width = *distance* | `\;` | ⁵∕₁₈ em space | `\hspace*{distance}` | space, width = *distance* | `\thickspace` | ⁵∕₁₈ em space | `\phantom{content}` | space the width and height of content | `\enspace` | ½ em space | `\hphantom{content}` | space the width of content | `\quad` | 1 em space | `\vphantom{content}` | a strut the height of content | `\qquad` | 2 em space | `\!` | – ³∕₁₈ em space | `~` | non-breaking space | `\negthinspace` | – ³∕₁₈ em space | `\<space>` | space | `\negmedspace` | – ⁴∕₁₈ em space | `\nobreakspace` | non-breaking space | `\negthickspace` | – ⁵∕₁₈ em space | `\space` | space | **Notes:** `distance` will accept any of the [KaTeX units](#units). `\kern`, `\mkern`, `\mskip`, and `\hspace` accept unbraced distances, as in: `\kern1em`. `\mkern` and `\mskip` will not work in text mode and both will write a console warning for any unit except `mu`. ## Logic and Set Theory ||||| |:--------------------|:--------------------------|:----------------------------|:----- |$\forall$ `\forall` |$\complement$ `\complement`|$\therefore$ `\therefore` |$\emptyset$ `\emptyset` |$\exists$ `\exists` |$\subset$ `\subset` |$\because$ `\because` |$\empty$ `\empty` |$\exist$ `\exist` |$\supset$ `\supset` |$\mapsto$ `\mapsto` |$\varnothing$ `\varnothing` |$\nexists$ `\nexists`|$\mid$ `\mid` |$\to$ `\to` |$\implies$ `\implies` |$\in$ `\in` |$\land$ `\land` |$\gets$ `\gets` |$\impliedby$ `\impliedby` |$\isin$ `\isin` |$\lor$ `\lor` |$\leftrightarrow$ `\leftrightarrow`|$\iff$ `\iff` |$\notin$ `\notin` |$\ni$ `\ni` |$\notni$ `\notni` |$\neg$ `\neg` or `\lnot` Direct Input: $∀ ∴ ∁ ∵ ∃ ∣ ∈ ∉ ∋ ⊂ ⊃ ∧ ∨ ↦ → ← ↔ ¬$ ℂ ℍ ℕ ℙ ℚ ℝ ## Macros ||| |:-------------------------------------|:------ |$\def\foo{x^2} \foo + \foo$ | `\def\foo{x^2} \foo + \foo` |$\gdef\bar#1{#1^2} \bar{y} + \bar{y}$ | `\gdef\bar#1{#1^2} \bar{y} + \bar{y}` | | `\edef\macroname#1#2…{definition to be expanded}` | | `\xdef\macroname#1#2…{definition to be expanded}` | | `\let\foo=\bar` | | `\futurelet\foo\bar x` | | `\global\def\macroname#1#2…{definition}` | | `\newcommand\macroname[numargs]{definition}` | | `\renewcommand\macroname[numargs]{definition}` | | `\providecommand\macroname[numargs]{definition}` Macros can also be defined in the KaTeX [rendering options](https://github.com/KaTeX/KaTeX/blob/v0.11.1/website/versioned_docs/version-0.11.0/options.md). Macros accept up to nine arguments: #1, #2, etc. Delimiters (such as `\def\add#1+#2{#1\oplus#2}`) are not currently supported. `\gdef`, `\xdef`, `\global\def`, `\global\edef`, `\global\let`, and `\global\futurelet` will persist between math expressions. KaTeX has no `\par`, so all macros are long by default and `\long` will be ignored. Available functions include: `\char` `\mathchoice` `\TextOrMath` `\@ifstar` `\@ifnextchar` `\@firstoftwo` `\@secondoftwo` `\relax` `\expandafter` `\noexpand` @ is a valid character for commands, as if `\makeatletter` were in effect. ## Operators ### Big Operators ||||| |------------------|-------------------------|--------------------------|--------------| | $\sum$ `\sum` | $\prod$ `\prod` | $\bigotimes$ `\bigotimes`| $\bigvee$ `\bigvee` | $\int$ `\int` | $\coprod$ `\coprod` | $\bigoplus$ `\bigoplus` | $\bigwedge$ `\bigwedge` | $\iint$ `\iint` | $\intop$ `\intop` | $\bigodot$ `\bigodot` | $\bigcap$ `\bigcap` | $\iiint$ `\iiint`| $\smallint$ `\smallint` | $\biguplus$ `\biguplus` | $\bigcup$ `\bigcup` | $\oint$ `\oint` | $\oiint$ `\oiint` | $\oiiint$ `\oiiint` | $\bigsqcup$ `\bigsqcup` Direct Input: $∫ ∬ ∭ ∮ ∏ ∐ ∑ ⋀ ⋁ ⋂ ⋃ ⨀ ⨁ ⨂ ⨄ ⨆

Binary Operators
+ + \cdot \cdot \gtrdot \gtrdot x \pmod a x \pmod a
- - \cdotp \cdotp \intercal \intercal x \pod a x \pod a
/ / \centerdot \centerdot \land \land \rhd \rhd
* * \circ \circ \leftthreetimes \leftthreetimes \rightthreetimes \rightthreetimes
\amalg \amalg \circledast \circledast \ldotp \ldotp \rtimes \rtimes
\And \And \circledcirc \circledcirc \lor \lor \setminus \setminus
\ast \ast \circleddash \circleddash \lessdot \lessdot \smallsetminus \smallsetminus
\barwedge \barwedge \Cup \Cup \lhd \lhd \sqcap \sqcap
\bigcirc \bigcirc \cup \cup \ltimes \ltimes \sqcup \sqcup
\bmod \bmod \curlyvee \curlyvee x \mod a x\mod a \times \times
\boxdot \boxdot \curlywedge \curlywedge \mp \mp \unlhd \unlhd
\boxminus \boxminus \div \div \odot \odot \unrhd \unrhd
\boxplus \boxplus \divideontimes \divideontimes \ominus \ominus \uplus \uplus
\boxtimes \boxtimes \dotplus \dotplus \oplus \oplus \vee \vee
\bullet \bullet \doublebarwedge \doublebarwedge \otimes \otimes \veebar \veebar
\Cap \Cap \doublecap \doublecap \oslash \oslash \wedge \wedge
\cap \cap \doublecup \doublecup \pm \pm or \plusmn \wr \wr

Direct Input: + - / * ⋅ ± × ÷ ∓ ∔ ∧ ∨ ∩ ∪ ≀ ⊎ ⊓ ⊔ ⊕ ⊖ ⊗ ⊘ ⊙ ⊚ ⊛ ⊝

Fractions and Binomials
\frac{a}{b} \frac{a}{b} \tfrac{a}{b} \tfrac{a}{b} \genfrac ( ] {2pt}{1}a{a+1} \genfrac ( ] {2pt}{1}a{a+1}
{a \over b} {a \over b} \dfrac{a}{b} \dfrac{a}{b} {a \above{2pt} b+1} {a \above{2pt} b+1}
a/b a/b \cfrac{a}{1 + \cfrac{1}{b}} \cfrac{a}{1 + \cfrac{1}{b}}
\binom{n}{k} \binom{n}{k} \dbinom{n}{k} \dbinom{n}{k} {n\brace k} {n\brace k}
{n \choose k} {n \choose k} \tbinom{n}{k} \tbinom{n}{k} {n\brack k} {n\brack k}

Math Operators
\arcsin \arcsin \cotg \cotg \ln \ln \det \det
\arccos \arccos \coth \coth \log \log \gcd \gcd
\arctan \arctan \csc \csc \sec \sec \inf \inf
\arctg \arctg \ctg \ctg \sin \sin \lim \lim
\arcctg \arcctg \cth \cth \sinh \sinh \liminf \liminf
\arg \arg \deg \deg \sh \sh \limsup \limsup
\ch \ch \dim \dim \tan \tan \max \max
\cos \cos \exp \exp \tanh \tanh \min \min
\cosec \cosec \hom \hom \tg \tg \Pr \Pr
\cosh \cosh \ker \ker \th \th \sup \sup
\cot \cot \lg \lg \argmax \argmax \argmin \argmin
\plim \plim \operatorname{f} \operatorname{f} \operatorname*{f} \operatorname*{f}

Functions on the right column of this table can take \limits.

\sqrt

$\sqrt[3]{x}$ `\sqrt[3]{x}` ## Relations $\stackrel{!}{=}$ `\stackrel{!}{=}` ||||| |:----------------------------|:--------------------------------|:--------------------------------|:----- |$=$ `=` |$\eqcirc$ `\eqcirc` |$\lesseqgtr$ `\lesseqgtr` |$\sqsupset$ `\sqsupset` |$<$ `<` |$\eqcolon$ `\eqcolon`|$\lesseqqgtr$ `\lesseqqgtr`|$\sqsupseteq$ `\sqsupseteq` |$>$ `>` |$\Eqcolon$ `\Eqcolon`|$\lessgtr$ `\lessgtr`|$\Subset$ `\Subset` |$:$ `:` |$\eqqcolon$ `\eqqcolon` |$\lesssim$ `\lesssim`|$\subset$ `\subset` or `\sub` |$\approx$ `\approx` |$\Eqqcolon$ `\Eqqcolon` |$\ll$ `\ll` |$\subseteq$ `\subseteq` or `\sube` |$\approxeq$ `\approxeq`|$\eqsim$ `\eqsim` |$\lll$ `\lll` |$\subseteqq$ `\subseteqq` |$\asymp$ `\asymp`|$\eqslantgtr$ `\eqslantgtr`|$\llless$ `\llless` |$\succ$ `\succ` |$\backepsilon$ `\backepsilon`|$\eqslantless$ `\eqslantless` |$\lt$ `\lt` |$\succapprox$ `\succapprox` |$\backsim$ `\backsim` |$\equiv$ `\equiv` |$\mid$ `\mid` |$\succcurlyeq$ `\succcurlyeq` |$\backsimeq$ `\backsimeq` |$\fallingdotseq$ `\fallingdotseq`|$\models$ `\models` |$\succeq$ `\succeq` |$\between$ `\between` |$\frown$ `\frown` |$\multimap$ `\multimap` |$\succsim$ `\succsim` |$\bowtie$ `\bowtie` |$\ge$ `\ge` |$\owns$ `\owns`|$\Supset$ `\Supset` |$\bumpeq$ `\bumpeq` |$\geq$ `\geq` |$\parallel$ `\parallel` |$\supset$ `\supset` |$\Bumpeq$ `\Bumpeq` |$\geqq$ `\geqq`|$\perp$ `\perp`|$\supseteq$ `\supseteq` or `\supe` |$\circeq$ `\circeq` |$\geqslant$ `\geqslant` |$\pitchfork$ `\pitchfork` |$\supseteqq$ `\supseteqq` |$\colonapprox$ `\colonapprox`|$\gg$ `\gg` |$\prec$ `\prec`|$\thickapprox$ `\thickapprox` |$\Colonapprox$ `\Colonapprox`|$\ggg$ `\ggg` |$\precapprox$ `\precapprox`|$\thicksim$ `\thicksim` |$\coloneq$ `\coloneq` |$\gggtr$ `\gggtr` |$\preccurlyeq$ `\preccurlyeq` |$\trianglelefteq$ `\trianglelefteq` |$\Coloneq$ `\Coloneq` |$\gt$ `\gt` |$\preceq$ `\preceq` |$\triangleq$ `\triangleq` |$\coloneqq$ `\coloneqq`|$\gtrapprox$ `\gtrapprox` |$\precsim$ `\precsim`|$\trianglerighteq$ `\trianglerighteq` |$\Coloneqq$ `\Coloneqq`|$\gtreqless$ `\gtreqless` |$\propto$ `\propto` |$\varpropto$ `\varpropto` |$\colonsim$ `\colonsim`|$\gtreqqless$ `\gtreqqless`|$\risingdotseq$ `\risingdotseq` |$\vartriangle$ `\vartriangle` |$\Colonsim$ `\Colonsim`|$\gtrless$ `\gtrless`|$\shortmid$ `\shortmid` |$\vartriangleleft$ `\vartriangleleft` |$\cong$ `\cong` |$\gtrsim$ `\gtrsim` |$\shortparallel$ `\shortparallel`|$\vartriangleright$ `\vartriangleright` |$\curlyeqprec$ `\curlyeqprec`|$\in$ `\in` or `\isin` |$\sim$ `\sim` |$\vcentcolon$ `\vcentcolon` |$\curlyeqsucc$ `\curlyeqsucc`|$\Join$ `\Join`|$\simeq$ `\simeq` |$\vdash$ `\vdash` |$\dashv$ `\dashv`|$\le$ `\le` |$\smallfrown$ `\smallfrown`|$\vDash$ `\vDash` |$\dblcolon$ `\dblcolon`|$\leq$ `\leq` |$\smallsmile$ `\smallsmile`|$\Vdash$ `\Vdash` |$\doteq$ `\doteq`|$\leqq$ `\leqq`|$\smile$ `\smile` |$\Vvdash$ `\Vvdash` |$\Doteq$ `\Doteq`|$\leqslant$ `\leqslant` |$\sqsubset$ `\sqsubset` | |$\doteqdot$ `\doteqdot`|$\lessapprox$ `\lessapprox`|$\sqsubseteq$ `\sqsubseteq`| Direct Input: $= < > : ∈ ∋ ∝ ∼ ∽ ≂ ≃ ≅ ≈ ≊ ≍ ≎ ≏ ≐ ≑ ≒ ≓ ≖ ≗ ≜ ≡ ≤ ≥ ≦ ≧ ≫ ≬ ≳ ≷ ≺ ≻ ≼ ≽ ≾ ≿ ⊂ ⊃ ⊆ ⊇ ⊏ ⊐ ⊑ ⊒ ⊢ ⊣ ⊩ ⊪ ⊸ ⋈ ⋍ ⋐ ⋑ ⋔ ⋙ ⋛ ⋞ ⋟ ⌢ ⌣ ⩾ ⪆ ⪌ ⪕ ⪖ ⪯ ⪰ ⪷ ⪸ ⫅ ⫆ ≲ ⩽ ⪅ ≶ ⋚ ⪋ ⟂ ⊨$ `≔ ≕ ⩴` ### Negated Relations $\not =$ `\not =` ||||| |--------------|-------------------|---------------------|------------------| | $\gnapprox$ `\gnapprox` | $\ngeqslant$ `\ngeqslant`| $\nsubseteq$ `\nsubseteq` | $\precneqq$ `\precneqq`| | $\gneq$ `\gneq`| $\ngtr$ `\ngtr` | $\nsubseteqq$ `\nsubseteqq` | $\precnsim$ `\precnsim`| | $\gneqq$ `\gneqq` | $\nleq$ `\nleq` | $\nsucc$ `\nsucc`| $\subsetneq$ `\subsetneq` | | $\gnsim$ `\gnsim` | $\nleqq$ `\nleqq` | $\nsucceq$ `\nsucceq` | $\subsetneqq$ `\subsetneqq` | | $\gvertneqq$ `\gvertneqq` | $\nleqslant$ `\nleqslant`| $\nsupseteq$ `\nsupseteq` | $\succnapprox$ `\succnapprox`| | $\lnapprox$ `\lnapprox` | $\nless$ `\nless` | $\nsupseteqq$ `\nsupseteqq` | $\succneqq$ `\succneqq`| | $\lneq$ `\lneq`| $\nmid$ `\nmid` | $\ntriangleleft$ `\ntriangleleft` | $\succnsim$ `\succnsim`| | $\lneqq$ `\lneqq` | $\notin$ `\notin` | $\ntrianglelefteq$ `\ntrianglelefteq` | $\supsetneq$ `\supsetneq` | | $\lnsim$ `\lnsim` | $\notni$ `\notni` | $\ntriangleright$ `\ntriangleright`| $\supsetneqq$ `\supsetneqq` | | $\lvertneqq$ `\lvertneqq` | $\nparallel$ `\nparallel`| $\ntrianglerighteq$ `\ntrianglerighteq` | $\varsubsetneq$ `\varsubsetneq` | | $\ncong$ `\ncong` | $\nprec$ `\nprec` | $\nvdash$ `\nvdash` | $\varsubsetneqq$ `\varsubsetneqq` | | $\ne$ `\ne` | $\npreceq$ `\npreceq` | $\nvDash$ `\nvDash` | $\varsupsetneq$ `\varsupsetneq` | | $\neq$ `\neq` | $\nshortmid$ `\nshortmid`| $\nVDash$ `\nVDash` | $\varsupsetneqq$ `\varsupsetneqq` | | $\ngeq$ `\ngeq`| $\nshortparallel$ `\nshortparallel` | $\nVdash$ `\nVdash` | | $\ngeqq$ `\ngeqq` | $\nsim$ `\nsim` | $\precnapprox$ `\precnapprox`| Direct Input: $∉ ∌ ∤ ∦ ≁ ≆ ≠ ≨ ≩ ≮ ≯ ≰ ≱ ⊀ ⊁ ⊈ ⊉ ⊊ ⊋ ⊬ ⊭ ⊮ ⊯ ⋠ ⋡ ⋦ ⋧ ⋨ ⋩ ⋬ ⋭ ⪇ ⪈ ⪉ ⪊ ⪵ ⪶ ⪹ ⪺ ⫋ ⫌

Arrows
\circlearrowleft \circlearrowleft \leftharpoonup \leftharpoonup \rArr \rArr
\circlearrowright \circlearrowright \leftleftarrows \leftleftarrows \rarr \rarr
\curvearrowleft \curvearrowleft \leftrightarrow \leftrightarrow \restriction \restriction
\curvearrowright \curvearrowright \Leftrightarrow \Leftrightarrow \rightarrow \rightarrow
\Darr \Darr \leftrightarrows \leftrightarrows \Rightarrow \Rightarrow
\dArr \dArr \leftrightharpoons \leftrightharpoons \rightarrowtail \rightarrowtail
\darr \darr \leftrightsquigarrow \leftrightsquigarrow \rightharpoondown \rightharpoondown
\dashleftarrow \dashleftarrow \Lleftarrow \Lleftarrow \rightharpoonup \rightharpoonup
\dashrightarrow \dashrightarrow \longleftarrow \longleftarrow \rightleftarrows \rightleftarrows
\downarrow \downarrow \Longleftarrow \Longleftarrow \rightleftharpoons \rightleftharpoons
\Downarrow \Downarrow \longleftrightarrow \longleftrightarrow \rightrightarrows \rightrightarrows
\downdownarrows \downdownarrows \Longleftrightarrow \Longleftrightarrow \rightsquigarrow \rightsquigarrow
\downharpoonleft \downharpoonleft \longmapsto \longmapsto \Rrightarrow \Rrightarrow
\downharpoonright \downharpoonright \longrightarrow \longrightarrow \Rsh \Rsh
\gets \gets \Longrightarrow \Longrightarrow \searrow \searrow
\Harr \Harr \looparrowleft \looparrowleft \swarrow \swarrow
\hArr \hArr \looparrowright \looparrowright \to \to
\harr \harr \Lrarr \Lrarr \twoheadleftarrow \twoheadleftarrow
\hookleftarrow \hookleftarrow \lrArr \lrArr \twoheadrightarrow \twoheadrightarrow
\hookrightarrow \hookrightarrow \lrarr \lrarr \Uarr \Uarr
\iff \iff \Lsh \Lsh \uArr \uArr
\impliedby \impliedby \mapsto \mapsto \uarr \uarr
\implies \implies \nearrow \nearrow \uparrow \uparrow
\Larr \Larr \nleftarrow \nleftarrow \Uparrow \Uparrow
\lArr \lArr \nLeftarrow \nLeftarrow \updownarrow \updownarrow
\larr \larr \nleftrightarrow \nleftrightarrow \Updownarrow \Updownarrow
\leadsto \leadsto \nLeftrightarrow \nLeftrightarrow \upharpoonleft \upharpoonleft
\leftarrow \leftarrow \nrightarrow \nrightarrow \upharpoonright \upharpoonright
\Leftarrow \Leftarrow \nRightarrow \nRightarrow \upuparrows \upuparrows
\leftarrowtail \leftarrowtail \nwarrow \nwarrow
\leftharpoondown \leftharpoondown \Rarr \Rarr

Direct Input: ← ↑ → ↓ ↔ ↕ ↖ ↗ ↘ ↙ ↚ ↛ ↞ ↠ ↢ ↣ ↦ ↩ ↪ ↫ ↬ ↭ ↮ ↰ ↱↶ ↷ ↺ ↻ ↼ ↽ ↾ ↾ ↿ ⇀ ⇁ ⇂ ⇃ ⇄ ⇆ ⇇ ⇈ ⇉ ⇊ ⇋ ⇌⇍ ⇎ ⇏ ⇐ ⇑ ⇒ ⇓ ⇔ ⇕ ⇚ ⇛ ⇝ ⇠ ⇢ ⟵ ⟶ ⟷ ⟸ ⟹ ⟺ ⟼ ↽

Extensible Arrows
\xleftarrow{abc} \xleftarrow{abc} \xrightarrow[under]{over} \xrightarrow[under]{over}
\xLeftarrow{abc} \xLeftarrow{abc} \xRightarrow{abc} \xRightarrow{abc}
\xleftrightarrow{abc} \xleftrightarrow{abc} \xLeftrightarrow{abc} \xLeftrightarrow{abc}
\xhookleftarrow{abc} \xhookleftarrow{abc} \xhookrightarrow{abc} \xhookrightarrow{abc}
\xtwoheadleftarrow{abc} \xtwoheadleftarrow{abc} \xtwoheadrightarrow{abc} \xtwoheadrightarrow{abc}
\xleftharpoonup{abc} \xleftharpoonup{abc} \xrightharpoonup{abc} \xrightharpoonup{abc}
\xleftharpoondown{abc} \xleftharpoondown{abc} \xrightharpoondown{abc} \xrightharpoondown{abc}
\xleftrightharpoons{abc} \xleftrightharpoons{abc} \xrightleftharpoons{abc} \xrightleftharpoons{abc}
\xtofrom{abc} \xtofrom{abc} \xmapsto{abc} \xmapsto{abc}
\xlongequal{abc} \xlongequal{abc}

Extensible arrows all can take an optional argument in the same manner as \xrightarrow[under]{over}.

Special Notation

Bra-ket Notation
\bra{\phi} \bra{\phi} \ket{\psi} \ket{\psi} \braket{\phi\vert\psi} \braket{\phi\vert\psi}
\Bra{\phi} \Bra{\phi} \Ket{\psi} \Ket{\psi}

Style, Color, Size, and Font

Class Assignment

\mathbin \mathclose \mathinner \mathop
\mathopen \mathord \mathpunct \mathrel

Color

Note that KaTeX `\color` acts like a switch. This aligns with LaTeX and differs from MathJax. Other KaTeX color functions expect the content to be a function argument: $\textcolor{blue}{F=ma}$ `\textcolor{blue}{F=ma}` $\textcolor{#228B22}{F=ma}$ `\textcolor{#228B22}{F=ma}` $\colorbox{aqua}{$F=ma$}$ `\colorbox{aqua}{$F=ma$}` $\fcolorbox{red}{aqua}{$F=ma$}$ `\fcolorbox{red}{aqua}{$F=ma$}` Note that, as in LaTeX, `\colorbox` & `\fcolorbox` renders its third argument as text, so you may want to switch back to math mode with `＄` as in the examples above. For color definition, KaTeX color functions will accept the standard HTML [predefined color names](https://developer.mozilla.org/en-US/docs/Web/CSS/color_value#Color_keywords). They will also accept an RGB argument in CSS hexa­decimal style. The "#" is optional before a six-digit specification. （注：所有可使用的预定义颜色可在 [MDN](https://developer.mozilla.org/zh-CN/docs/Web/CSS/named-color) 找到，但注意，支持程度取决于你使用的浏览器。） **Font** |||| |:------------------------------|:------------------------------|:----- |$\mathrm{Ab0}$ `\mathrm{Ab0}` |$\mathbf{Ab0}$ `\mathbf{Ab0}` |$\mathit{Ab0}$ `\mathit{Ab0}` |$\mathnormal{Ab0}$ `\mathnormal{Ab0}`|$\textbf{Ab0}$ `\textbf{Ab0}` |$\textit{Ab0}$ `\textit{Ab0}` |$\textrm{Ab0}$ `\textrm{Ab0}` |$\bf Ab0$ `\bf Ab0` |$\it Ab0$ `\it Ab0` |$\rm Ab0$ `\rm Ab0` |$\bold{Ab0}$ `\bold{Ab0}` |$\textup{Ab0}$ `\textup{Ab0}` |$\textnormal{Ab0}$ `\textnormal{Ab0}`|$\boldsymbol{Ab0}$ `\boldsymbol{Ab}`|$\Bbb{AB}$ `\Bbb{AB}` |$\text{Ab0}$ `\text{Ab0}` |$\bm{Ab0}$ `\bm{Ab0}` |$\mathbb{AB}$ `\mathbb{AB}` |$\mathsf{Ab0}$ `\mathsf{Ab0}` |$\textmd{Ab0}$ `\textmd{Ab0}` |$\frak{Ab0}$ `\frak{Ab0}` |$\textsf{Ab0}$ `\textsf{Ab0}` |$\mathtt{Ab0}$ `\mathtt{Ab0}` |$\mathfrak{Ab0}$ `\mathfrak{Ab0}` |$\sf Ab0$ `\sf Ab0` |$\texttt{Ab0}$ `\texttt{Ab0}` |$\mathcal{AB0}$ `\mathcal{AB0}` | |$\tt Ab0$ `\tt Ab0` |$\cal AB0$ `\cal AB0` | | |$\mathscr{AB}$ `\mathscr{AB}` One can stack font family, font weight, and font shape by using the `\textXX` versions of the font functions. So `\textsf{\textbf{H}}` will produce $\textsf{\textbf{H}}$. The other versions do not stack, e.g., `\mathsf{\mathbf{H}}` will produce $\mathsf{\mathbf{H}}$. In cases where KaTeX fonts do not have a bold glyph, `\pmb` can simulate one. For example, `\pmb{\mu}` renders as : $\pmb{\mu}

Size
\Huge AB \Huge AB \normalsize AB \normalsize AB
\huge AB \huge AB \small AB \small AB
\LARGE AB \LARGE AB \footnotesize AB \footnotesize AB
\Large AB \Large AB \scriptsize AB \scriptsize AB
\large AB \large AB \tiny AB \tiny AB

Style
\displaystyle\sum_{i=1}^n \displaystyle\sum_{i=1}^n
\textstyle\sum_{i=1}^n \textstyle\sum_{i=1}^n
\scriptstyle x \scriptstyle x         (The size of a first sub/superscript)
\scriptscriptstyle x \scriptscriptstyle x (The size of subsequent sub/superscripts)
\lim\limits_x \lim\limits_x
\lim\nolimits_x \lim\nolimits_x
\verb!x^2! \verb!x^2!

\text{…} will accept nested $…$ fragments and render them in math mode.

Symbols and Punctuation
% comment \dots \dots \KaTeX \KaTeX
\% \% \cdots \cdots \LaTeX \LaTeX
\# \# \ddots \ddots \TeX \TeX
\& \& \ldots \ldots \nabla \nabla
\_ \_ \vdots \vdots \infty \infty
\text{\textunderscore} \text{\textunderscore} \dotsb \dotsb \infin \infin
\text{--} \text{--} \dotsc \dotsc \checkmark \checkmark
\text{\textendash} \text{\textendash} \dotsi \dotsi \dag \dag
\text{---} \text{---} \dotsm \dotsm \dagger \dagger
\text{\textemdash} \text{\textemdash} \dotso \dotso \text{\textdagger} \text{\textdagger}
\text{\textasciitilde} \text{\textasciitilde} \sdot \sdot \ddag \ddag
\text{\textasciicircum} \text{\textasciicircum} \mathellipsis \mathellipsis \ddagger \ddagger
`%` ｀ \text{\textellipsis} \text{\textellipsis} \text{\textdaggerdbl} \text{\textdaggerdbl}
\text{\textquoteleft} text{\textquoteleft} \Box \Box \Dagger \Dagger
\lq \lq \square \square \angle \angle
\text{\textquoteright} \text{\textquoteright} \blacksquare \blacksquare \measuredangle \measuredangle
\rq \rq \triangle \triangle \sphericalangle \sphericalangle
\text{\textquotedblleft} \text{\textquotedblleft} \triangledown \triangledown \top \top
" " \triangleleft \triangleleft \bot \bot
\text{\textquotedblright} \text{\textquotedblright} \triangleright \triangleright \$ \$
\colon \colon \bigtriangledown \bigtriangledown \text{\textdollar} \text{\textdollar}
\backprime \backprime \bigtriangleup \bigtriangleup \pounds \pounds
\prime \prime \blacktriangle \blacktriangle \mathsterling \mathsterling
\text{\textless} \text{\textless} \blacktriangledown \blacktriangledown \text{\textsterling} \text{\textsterling}
\text{\textgreater} \text{\textgreater} \blacktriangleleft \blacktriangleleft \yen \yen
\text{\textbar} \text{\textbar} \blacktriangleright \blacktriangleright \surd \surd
\text{\textbardbl} \text{\textbardbl} \diamond \diamond \degree \degree
\text{\textbraceleft} \text{\textbraceleft} \Diamond \Diamond \text{\textdegree} \text{\textdegree}
\text{\textbraceright} \text{\textbraceright} \lozenge \lozenge \mho \mho
\text{\textbackslash} \text{\textbackslash} \blacklozenge \blacklozenge \diagdown \diagdown
\text{\P} \text{\P} \star \star \diagup \diagup
\text{\S} \text{\S} \bigstar \bigstar \flat \flat
\text{\sect} \text{\sect} \clubsuit \clubsuit \natural \natural
\copyright \copyright \clubs \clubs \sharp \sharp
\circledR \circledR \diamondsuit \diamondsuit \heartsuit \heartsuit
\text{\textregistered} \text{\textregistered} \diamonds \diamonds \hearts \hearts
\circledS \circledS \spadesuit \spadesuit \spades \spades
\text{\textcircled a} \text{\textcircled a} \maltese \maltese \minuso \minuso

Direct Input: £ ¥ ∇ ∞ · ∠ ∡ ∢ ♠ ♡ ♢ ♣ ♭ ♮ ♯ ✓ … ⋮ ⋯ ⋱ ! ‼ ⦵

Units

In KaTeX, units are proportioned as they are in TeX. KaTeX units are different than CSS units.

KaTeX Unit Value KaTeX Unit Value
em CSS em bp 1/72​ inch × F × G
ex CSS ex pc 12 KaTeX pt
mu 1/18 CSS em dd 1238/1157​ KaTeX pt
pt 1/72.27 inch × F × G cc 14856/1157 KaTeX pt
mm 1 mm × F × G nd 685/642 KaTeX pt
cm 1 cm × F × G nc 1370/107​ KaTeX pt
in 1 inch × F × G sp 1/65536 KaTeX pt

where:

F = (font size of surrounding HTML text)/(10 pt)

G = 1.21 by default, because KaTeX font-size is normally 1.21 × the surrounding font size. This value can be overridden by the CSS of an HTML page.

The effect of style and size:

Unit textstyle scriptscript huge
em or ex \rule{1em}{1em} \scriptscriptstyle\rule{1em}{1em} \huge\rule{1em}{1em}
mu \rule{18mu}{18mu} \scriptscriptstyle\rule{18mu}{18mu} \huge\rule{18mu}{18mu}
others \rule{10pt}{10pt} \scriptscriptstyle\rule{10pt}{10pt} \huge\rule{10pt}{10pt}