Math Commands and Symbols

It can be a little hard to remember all the math symbols and commands. Here is a quick reference guide to help you out.

For practice, I recommend the texnique website which turns LaTeX equations in to a game.

Note

This page uses a lot of MathJax, so some symbols may take a second to render.

Greek Letters

Lowercase Command	Symbol	Uppercase Command	Symbol
\alpha	$\alpha$	A	$A$
\beta	$\beta$	B	$B$
\gamma	$\gamma$	\Gamma	$\mathrm{\Gamma }$
\delta	$\delta$	\Delta	$\mathrm{\Delta }$
\epsilon	$ϵ$	E	$E$
\zeta	$\zeta$	Z	$Z$
\eta	$\eta$	H	$H$
\theta	$\theta$	\Theta	$\mathrm{\Theta }$
\iota	$\iota$	I	$I$
\kappa	$\kappa$	K	$K$
\lambda	$\lambda$	\Lambda	$\mathrm{\Lambda }$
\mu	$\mu$	M	$M$
\nu	$\nu$	N	$N$
\xi	$\xi$	\Xi	$\mathrm{\Xi }$
\omicron	$o$	O	$O$
\pi	$\pi$	\Pi	$\mathrm{\Pi }$
\rho	$\rho$	P	$P$
\sigma	$\sigma$	\Sigma	$\mathrm{\Sigma }$
\tau	$\tau$	T	$T$
\upsilon	$\upsilon$	\Upsilon	$\mathrm{{\rm Y}}$
\phi	$\varphi$	\Phi	$\mathrm{\Phi }$
\chi	$\chi$	X	$X$
\psi	$\psi$	\Psi	$\mathrm{\Psi }$
\omega	$\omega$	\Omega	$\mathrm{\Omega }$

In addition to the standard Greek letters, there are also some variant forms:

Command	Symbol
\varepsilon	$\epsilon$
\vartheta	$\vartheta$
\varkappa	$\varkappa$
\varpi	$\varpi$
\varrho	$\varrho$
\varsigma	$\varsigma$
\varphi	$\phi$

Delimiters

Command	Symbol	Command	Symbol
\left(	$($	\right)	$)$
\left[	$[$	\right]	$]$
\left\{	$\{$	\right\}	$\}$
\left\langle	$⟨$	\right\rangle	$⟩$
\left\lfloor	$\lfloor$	\right\rfloor	$\rfloor$
\left\lceil	$\lceil$	\right\rceil	$\rceil$
\left\|	$|$	\right\|	$|$
\left\\|	$\Vert$	\right\\|	$\Vert$
\left.	$.$	\right.	$.$
\left/	$/$	\right/	$/$
\left\backslash	$\mathrm{\setminus }$	\right\backslash	$\mathrm{\setminus }$

Arrows

Command	Symbol	Command	Symbol
\leftarrow	$\leftarrow$	\longleftarrow	$⟵$
\uparrow	$\uparrow$	\Uparrow	$\Uparrow$
\rightarrow	$\to$	\longrightarrow	$⟶$
\downarrow	$\downarrow$	\Downarrow	$\Downarrow$
\leftrightarrow	$\leftrightarrow$	\longleftrightarrow	$⟷$
\updownarrow	$\updownarrow$	\Updownarrow	$\Updownarrow$
\mapsto	$\mapsto$	\longmapsto	$⟼$
\hookleftarrow	$\hookleftarrow$	\hookrightarrow	$\hookrightarrow$
\leftharpoonup	$\leftharpoonup$	\rightharpoonup	$\rightharpoonup$
\leftharpoondown	$\leftharpoondown$	\rightharpoondown	$\rightharpoondown$
\rightleftharpoons	$\rightleftharpoons$	\leftrightharpoons	$\leftrightharpoons$
\nearrow	$\nearrow$	\searrow	$\searrow$
\swarrow	$\swarrow$	\nwarrow	$\nwarrow$
\leadsto	$⇝$	\rightsquigarrow	$⇝$
\curvearrowleft	$\curvearrowleft$	\curvearrowright	$\curvearrowright$
\circlearrowleft	$\circlearrowleft$	\circlearrowright	$\circlearrowright$
\Leftrightarrow	$\iff$	\Longleftrightarrow	$⟺$
\Leftarrow	$\Leftarrow$	\Longleftarrow	$⟸$
\Rightarrow	$\Rightarrow$	\Longrightarrow	$⟹$
\iff	$⟺$	\implies	$⟹$

Binary Operators

Command	Symbol	Command	Symbol
\pm	$\pm$	\mp	$\mp$
\times	$\times$	\div	$÷$
\cdot	$\cdot$	\ast	$\ast$
\star	$\star$	\dagger	$†$
\ddagger	$‡$	\amalg	$⨿$
\cap	$\cap$	\cup	$\cup$
\uplus	$\uplus$	\sqcap	$\sqcap$
\sqcup	$\bigsqcup$	\vee	$\vee$
\wedge	$\wedge$	\setminus	$\setminus$
\wr	$\wr$	\diamond	$\diamond$
\bigtriangleup	$△$	\bigtriangledown	$▽$
\triangleleft	$◃$	\triangleright	$▹$
\lhd	$⊲$	\rhd	$⊳$
\unlhd	$⊴$	\unrhd	$⊵$
\oplus	$\oplus$	\otimes	$\otimes$
\odot	$\odot$	\oslash	$\oslash$
\circledcirc	$⊚$	\circledast	$⊛$
\circleddash	$⊝$	\boxplus	$⊞$
\boxtimes	$⊠$	\boxdot	$⊡$
\bigcirc	$◯$	\bigodot	$⨀$
\bigotimes	$⨂$	\bigoplus	$⨁$
\biguplus	$⨄$	\bigsqcup	$⨆$
\bigvee	$\bigvee$	\bigwedge	$\bigwedge$
\coprod	$\coprod$
\bigcap	$\bigcap$	\bigcup	$\bigcup$
\prod	$\prod$	\sum	$\sum$
\int	$\int$	\oint	$\oint$
\iiint	$\iiint$	\iiiint	$⨌$
\idotsint	$\int \cdots \int$
\therefore	$\therefore$	\because	$\because$
\dotplus	$\dotplus$	\centerdot	$\cdot$
\ltimes	$⋉$	\rtimes	$⋊$
\leftthreetimes	$⋋$	\rightthreetimes	$⋌$
\curlywedge	$⋏$	\curlyvee	$⋎$
\boxminus	$\boxminus$
\boxdot	$⊡$	\divideontimes	$\divideontimes$

Trigonometry

Command	Symbol	Command	Symbol
\sin	$\sin$	\cos	$\cos$
\tan	$\tan$	\cot	$\cot$
\sec	$\sec$	\csc	$\csc$
\arcsin	$\arcsin$	\arccos	$\arccos$
\arctan	$\arctan$	\sinh	$\sinh$
\cosh	$\cosh$	\tanh	$\tanh$
\coth	$\coth$

Logarithms

Command	Symbol	Command	Symbol
\log	$\log$	\ln	$\ln$
\lg	$\lg$	\exp	$\exp$
\lim	$lim$	\liminf	$lim inf$
\limsup	$lim sup$	\sup	$sup$
\inf	$inf$	\max	$max$
\min	$min$	\arg	$\arg$
\deg	$\mathrm{deg}$	\det	$det$
\dim	$\dim$	\hom	$\mathrm{hom}$
\ker	$\ker$	\Pr	$Pr$
\gcd	$gcd$	\varliminf	$\underset{―}{\lim }$
\varlimsup	$\bar{\lim }$	\varinjlim	$\underrightarrow{\lim }$
\varprojlim	$\underleftarrow{\lim }$

Relations

Command	Symbol	Command	Symbol
<	$<$	>	$>$
\leq	$\le$	\geq	$\ge$
\ll	$\ll$	\gg	$\gg$
\equiv	$\equiv$	\sim	$\sim$
\subset	$\subset$	\supset	$\supset$
\approx	$\approx$	\cong	$\cong$
\subseteq	$\subseteq$	\supseteq	$\supseteq$
\propto	$\propto$	\neq	$\ne$
\in	$\in$	\ni	$\ni$
\notin	$\notin$	\subsetneq	$⊊$
\supsetneq	$⊋$	\nsubseteq	$⊈$
\nsupseteq	$⊉$	\parallel	$\parallel$
\nparallel	$\nparallel$	\perp	$\perp$
\mid	$\mid$	\nmid	$\nmid$
\asymp	$\asymp$	\doteq	$\doteq$
\bowtie	$\bowtie$	\models	$\models$
\smile	$⌣$	\frown	$⌢$
\vdash	$⊢$	\dashv	$⊣$
\infty	$\mathrm{\infty }$	\aleph	$\mathrm{\aleph }$
\forall	$\mathrm{\forall }$	\exists	$\mathrm{\exists }$
\nexists	$\nexists$	\emptyset	$\mathrm{\varnothing }$
\varnothing	$\varnothing$	\neg	$\mathrm{\neg }$
\top	$\mathrm{\top }$	\bot	$\mathrm{\perp }$
\angle	$\mathrm{\angle }$	\measuredangle	$\measuredangle$
\sphericalangle	$\sphericalangle$	\triangle	$\mathrm{△}$
\nabla	$\mathrm{\nabla }$	\partial	$\partial$
\hbar	$\hslash$	\imath	$ı$
\jmath	$ȷ$	\ell	$\ell$
\wp	$\mathrm{\wp }$	\Re	$\mathrm{\Re }$
\Im	$\mathrm{\Im }$	\mho	$\mho$
\eth	$\mathrm{ð}$	\Finv	$Ⅎ$
\Game	$⅁$	\Bbbk	$\mathbb{k}$
\circ	$\circ$	\bullet	$\bullet$
\wr	$\wr$	\diamond	$\diamond$
\bigtriangleup	$△$	\bigtriangledown	$▽$
\triangleleft	$◃$	\triangleright	$▹$

Accents

Command	Symbol	Command	Symbol
\hat{a}	$\hat{a}$	\check{a}	$\check{a}$
\breve{a}	$\breve{a}$	\acute{a}	$\acute{a}$
\grave{a}	$\stackrel{`}{a}$	\tilde{a}	$\tilde{a}$
\bar{a}	$\overline{a}$	\vec{a}	$\overrightarrow{a}$
\dot{a}	$\dot{a}$	\ddot{a}	$\ddot{a}$
\mathring{a}	$\mathring{a}$	\widehat{a}	$\hat{a}$
\widetilde{a}	$\tilde{a}$	\overline{a}	$\bar{a}$
\underline{a}	$\underset{―}{a}$	\overbrace{a}	$\overbrace{a}$
\underbrace{a}	$\underbrace{a}$	\overleftarrow{a}	$\overleftarrow{a}$
\overrightarrow{a}	$\overrightarrow{a}$	\overleftrightarrow{a}	$\overleftrightarrow{a}$

Environments

LaTeX has some built in environments and some common packages like amsmath and mathtools provide additional environments.

LaTeX Environments

Type	Inline	Display	Numbered	Description	Command
equation	No	Yes	Yes	Standard equation environment	\begin{equation} ... \end{equation}
Inline	Yes	No	No	Inline equation environment	$ ... $
Inline (alt)	Yes	No	No	Inline equation environment	\(...\)
Display	No	Yes	No	Display equation environment	$$ ... $$
Display (alt)	No	Yes	No	Display equation environment	\[ ... \]

The different inline and display environments extend from the difference in TeX and LaTeX. TeX uses $ ... $ for inline math and $$ ... $$ for display math. LaTeX uses \[ ... \] for display math and \(...\) for inline math. The results will be the same, and choice is personal preference. However, the LaTeX environments is considered better practice.

amsmath Environments

Type	Inline	Display	Numbered	Description	Command
equation*	No	Yes	No	Standard equation environment	\begin{equation*} ... \end{equation*}
align	No	Yes	Yes	Align multiple equations	\begin{align} ... \end{align}
align*	No	Yes	No	Align multiple equations	\begin{align*} ... \end{align*}
gather	No	Yes	Yes	Center multiple equations	\begin{gather} ... \end{gather}
gather*	No	Yes	No	Center multiple equations	\begin{gather*} ... \end{gather*}
multline	No	Yes	Yes	Multi-line equations	\begin{multline} ... \end{multline}
multline*	No	Yes	No	Multi-line equations	\begin{multline*} ... \end{multline*}
split	No	Yes	No	Multi-line equations	\begin{split} ... \end{split}
aligned	No	Yes	No	Multi-line equations	\begin{aligned} ... \end{aligned}
cases	No	Yes	No	Multi-line equations	\begin{cases} ... \end{cases}
matrix	No	Yes	No	Matrix equations	\begin{matrix} ... \end{matrix}
pmatrix	No	Yes	No	Matrix equations	\begin{pmatrix} ... \end{pmatrix}
bmatrix	No	Yes	No	Matrix equations	\begin{bmatrix} ... \end{bmatrix}
Bmatrix	No	Yes	No	Matrix equations	\begin{Bmatrix} ... \end{Bmatrix}
vmatrix	No	Yes	No	Matrix equations	\begin{vmatrix} ... \end{vmatrix}
Vmatrix	No	Yes	No	Matrix equations	\begin{Vmatrix} ... \end{Vmatrix}

mathtools Environments

Type	Inline	Display	Numbered	Description	Command
dcases	No	Yes	No	Multi-line equations	\begin{dcases} ... \end{dcases}

Fonts

Command	Symbol	Command	Symbol
\mathbb{A}	$\mathbb{A}$	\mathcal{A}	$\mathcal{A}$
\mathfrak{A}	$\mathfrak{A}$	\mathsf{A}	$\mathsf{A}$
\mathscr{A}	$\mathcal{A}$	\mathbf{A}	$\mathbf{A}$
\mathit{A}	$\mathit{A}$	\mathrm{A}	$\mathrm{A}$
\mathnormal{A}	$A$	\mathsf{A}	$\mathsf{A}$
\mathbf{A}	$\mathbf{A}$