Mathematics, Equations & Symbols
Complete guide to typeset elegant mathematical formulas, multiline aligned equations, matrices, piecewise functions, physics notation, and SI units.
Typeset single equations, multiline aligned systems (align), grouped subequations (1a, 1b, 1c), piecewise cases, long split equations, and matrix delimiters (pmatrix, bmatrix, vmatrix).
Math Modes & Formulas
Comprehensive syntax, arguments, options, and copyable snippets for math modes & formulas.
$ ... $
Inline math mode
The energy is $E=mc^2$.
\( ... \)
Inline math mode (alternative)
The energy is \(E=mc^2\).
$$ ... $$
Display math mode (plain TeX style)
$$E = mc^2$$
\[ ... \]
Display math mode (LaTeX style)
\[E = mc^2\]
\frac{num}{den}
Fraction
Fraction: Typesets fraction. In display math use \dfrac for full size, in inline text use \tfrac for compact size.
$\frac{1}{2}$
\dfrac{num}{den}
Display-style fraction (amsmath)
$\dfrac{1}{2}$
\tfrac{num}{den}
Text-style fraction (amsmath)
$\tfrac{1}{2}$
\sqrt{x}
Square root
$\sqrt{2}$
\sqrt[n]{x}
nth root
Radical / N-th Root: Computes radical symbol. Optional [n] specifies root degree.
$\sqrt[3]{8}$
\sum
Summation symbol
$\sum_{i=1}^{n} i$
\prod
Product symbol
$\prod_{i=1}^{n} i$
\int
Integral symbol
$\int_0^1 x^2\,dx$
\iint
Double integral (amsmath)
$\iint_D f(x,y)\,dA$
\iiint
Triple integral (amsmath)
$\iiint_V f\,dV$
\oint
Contour integral
$\oint_C \vec{F}\cdot d\vec{r}$
\lim
Limit operator
$\lim_{x\to 0} \frac{\sin x}{x}$
\limsup
Limit superior
$\limsup_{n\to\infty} a_n$
\liminf
Limit inferior
$\liminf_{n\to\infty} a_n$
\sup
Supremum operator
$\sup_{x \in S} f(x)$
\inf
Infimum operator
$\inf_{x \in S} f(x)$
\max
Maximum operator
$\max(a,b)$
\min
Minimum operator
$\min(a,b)$
\log
Logarithm operator
$\log_{10} x$
\ln
Natural logarithm operator
$\ln x$
\exp
Exponential operator
$\exp(x)$
\sin
Sine function
$\sin\theta$
\cos
Cosine function
$\cos\theta$
\tan
Tangent function
$\tan\theta$
\cot
Cotangent function
$\cot\theta$
\sec
Secant function
$\sec\theta$
\csc
Cosecant function
$\csc\theta$
\arcsin
Arcsine function
$\arcsin x$
\arccos
Arccosine function
$\arccos x$
\arctan
Arctangent function
$\arctan x$
\sinh
Hyperbolic sine
$\sinh x$
\cosh
Hyperbolic cosine
$\cosh x$
\tanh
Hyperbolic tangent
$\tanh x$
\det
Determinant operator
$\det(A)$
\dim
Dimension operator
$\dim(V)$
\gcd
Greatest common divisor operator
$\gcd(a,b)$
\deg
Degree operator
$\deg(p)$
\hom
Hom operator
$\hom(A,B)$
\ker
Kernel operator
$\ker(T)$
\Pr
Probability operator (amsmath)
$\Pr(X > 0)$
x^{a}
Superscript
$x^{2}$
x_{a}
Subscript
$x_{i}$
\overline{x}
Overline
$\overline{x}$
\underline{x}
Underline (math mode)
$\underline{x}$
\overbrace{x}
Overbrace
$\overbrace{a+b+c}^{\text{sum}}$
\underbrace{x}
Underbrace
$\underbrace{a+b+c}_{\text{sum}}$
\overrightarrow{x}
Right arrow over text (vectors)
$\overrightarrow{AB}$
\overleftarrow{x}
Left arrow over text
$\overleftarrow{AB}$
\hat{x}
Hat accent
$\hat{x}$
\widehat{x}
Wide hat accent
$\widehat{xyz}$
\bar{x}
Bar accent
$\bar{x}$
\vec{x}
Vector arrow accent
$\vec{v}$
\dot{x}
Dot accent (derivative)
$\dot{x}$
\ddot{x}
Double dot accent (second derivative)
$\ddot{x}$
\tilde{x}
Tilde accent
$\tilde{x}$
\widetilde{x}
Wide tilde accent
$\widetilde{xyz}$
\mathbb{X}
Blackboard bold (amssymb)
$\mathbb{R}$
\mathcal{X}
Calligraphic letters
$\mathcal{L}$
\mathfrak{X}
Fraktur letters (amssymb)
$\mathfrak{g}$
\mathrm{x}
Roman (upright) math text
$\mathrm{d}x$
\mathbf{x}
Bold math text
$\mathbf{v}$
\mathit{x}
Italic math text
$\mathit{abc}$
\mathsf{x}
Sans-serif math text
$\mathsf{abc}$
\mathtt{x}
Typewriter math text
$\mathtt{abc}$
\boldsymbol{x}
Bold math symbol (amsmath/bm)
$\boldsymbol{\alpha}$
\text{text}
Text inside math mode (amsmath)
$x = 5 \text{ meters}$
\left(
Auto-sized left parenthesis
$\left(\frac{a}{b}\right)$
\right)
Auto-sized right parenthesis
$\left(\frac{a}{b}\right)$
\left[
Auto-sized left bracket
$\left[\frac{a}{b}\right]$
\right]
Auto-sized right bracket
$\left[\frac{a}{b}\right]$
\left\{
Auto-sized left brace
$\left\{\frac{a}{b}\right\}$
\right\}
Auto-sized right brace
$\left\{\frac{a}{b}\right\}$
\left|
Auto-sized left vertical bar
$\left|\frac{a}{b}\right|$
\right|
Auto-sized right vertical bar
$\left|\frac{a}{b}\right|$
\big(
Manually sized parenthesis (big)
$\big(x\big)$
\Big(
Manually sized parenthesis (Big)
$\Big(x\Big)$
\bigg(
Manually sized parenthesis (bigg)
$\bigg(x\bigg)$
\Bigg(
Manually sized parenthesis (Bigg)
$\Bigg(x\Bigg)$
\nonumber
Suppresses equation numbering on a line
\begin{align}
x &= y \nonumber
\end{align}
\notag
Suppresses equation numbering (amsmath)
\begin{align}
x &= y \notag
\end{align}
\label{key}
Assigns a label for cross-referencing
Label Anchor Placement: Must be placed after (or inside) \caption{...} for figures and tables, or inside an equation, so \ref{key} retrieves the correct counter.
\label{eq:energy}
\tag{text}
Custom equation tag (amsmath)
\begin{equation}
E=mc^2 \tag{A}
\end{equation}
Advanced AMS-LaTeX Equations
Comprehensive syntax, arguments, options, and copyable snippets for advanced ams-latex equations.
\begin{split}...\end{split}
Splits a single equation across lines while keeping one equation number (amsmath, used inside equation)
\begin{equation}
\begin{split}
f(x) &= (x+1)^2 \\
&= x^2 + 2x + 1
\end{split}
\end{equation}
\begin{subequations}...\end{subequations}
Groups several equations under one main number with letter suffixes (amsmath)
Sub-Equation Numbering (1a, 1b, 1c): Encloses an equation environment (such as align). The system shares a main equation index while individual equations are labeled alphabetically (e.g. \eqref{eq:1a}).
\begin{subequations}
\begin{align}
a &= b \\
c &= d
\end{align}
\end{subequations}
\begin{alignat}{n}...\end{alignat}
Aligns multiple columns of equations with tighter spacing than align (amsmath)
\begin{alignat}{2}
x &= y &\quad a &= b \\
u &= v &\quad c &= d
\end{alignat}
\begin{flalign}...\end{flalign}
Flush left/right aligned equations spanning full line width (amsmath)
\begin{flalign}
x &= y &
\end{flalign}
\begin{smallmatrix}...\end{smallmatrix}
Compact inline-sized matrix (amsmath)
$\bigl(\begin{smallmatrix}a&b\\c&d\end{smallmatrix}\bigr)$
\boxed{expr}
Draws a box around a math expression (amsmath)
\boxed{E=mc^2}
\DeclareMathOperator{\op}{name}
Defines a new math operator like \sin or \log (amsmath)
\DeclareMathOperator{\Tr}{Tr}
\DeclareMathOperator*{\op}{name}
Defines a new math operator with limits placed above/below, like \lim (amsmath)
\DeclareMathOperator*{\argmax}{arg\,max}
\substack{line1 \\ line2}
Stacks multiple lines of subscript/superscript text (amsmath)
$\sum_{\substack{0 \le i \le n \\ i \ne j}} a_i$
\allowdisplaybreaks
Allows page breaks within long align/gather blocks (amsmath)
\allowdisplaybreaks
\intertext{text}
Inserts a line of ordinary text between aligned equation lines without breaking the alignment (amsmath)
\begin{align}
x &= y \\
\intertext{Substituting gives}
y &= z
\end{align}
Greek Letters & Symbols
Comprehensive syntax, arguments, options, and copyable snippets for greek letters & symbols.
\alpha
Lowercase alpha
$\alpha$
\beta
Lowercase beta
$\beta$
\gamma
Lowercase gamma
$\gamma$
\delta
Lowercase delta
$\delta$
\epsilon
Lowercase epsilon (variant)
$\epsilon$
\varepsilon
Lowercase epsilon (alternate form)
$\varepsilon$
\zeta
Lowercase zeta
$\zeta$
\eta
Lowercase eta
$\eta$
\theta
Lowercase theta
$\theta$
\vartheta
Lowercase theta (alternate form)
$\vartheta$
\iota
Lowercase iota
$\iota$
\kappa
Lowercase kappa
$\kappa$
\lambda
Lowercase lambda
$\lambda$
\mu
Lowercase mu
$\mu$
\nu
Lowercase nu
$\nu$
\xi
Lowercase xi
$\xi$
\pi
Lowercase pi
$\pi$
\varpi
Lowercase pi (alternate form)
$\varpi$
\rho
Lowercase rho
$\rho$
\varrho
Lowercase rho (alternate form)
$\varrho$
\sigma
Lowercase sigma
$\sigma$
\varsigma
Lowercase sigma (alternate form)
$\varsigma$
\tau
Lowercase tau
$\tau$
\upsilon
Lowercase upsilon
$\upsilon$
\phi
Lowercase phi
$\phi$
\varphi
Lowercase phi (alternate form)
$\varphi$
\chi
Lowercase chi
$\chi$
\psi
Lowercase psi
$\psi$
\omega
Lowercase omega
$\omega$
\Gamma
Uppercase gamma
$\Gamma$
\Delta
Uppercase delta
$\Delta$
\Theta
Uppercase theta
$\Theta$
\Lambda
Uppercase lambda
$\Lambda$
\Xi
Uppercase xi
$\Xi$
\Pi
Uppercase pi
$\Pi$
\Sigma
Uppercase sigma
$\Sigma$
\Upsilon
Uppercase upsilon
$\Upsilon$
\Phi
Uppercase phi
$\Phi$
\Psi
Uppercase psi
$\Psi$
\Omega
Uppercase omega
$\Omega$
Math Operators & Delimiters
Comprehensive syntax, arguments, options, and copyable snippets for math operators & delimiters.
\pm
Plus-minus sign
$5 \pm 2$
\mp
Minus-plus sign
$5 \mp 2$
\times
Multiplication sign
$3 \times 4$
\div
Division sign
$10 \div 2$
\cdot
Centered dot (multiplication)
$a \cdot b$
\ast
Asterisk operator
$a \ast b$
\star
Star operator
$a \star b$
\circ
Small circle operator
$f \circ g$
\bullet
Bullet operator
$a \bullet b$
\oplus
Circled plus
$a \oplus b$
\ominus
Circled minus
$a \ominus b$
\otimes
Circled times
$a \otimes b$
\oslash
Circled slash
$a \oslash b$
\odot
Circled dot
$a \odot b$
\leq
Less than or equal to
$x \leq 5$
\geq
Greater than or equal to
$x \geq 5$
\neq
Not equal to
$x \neq y$
\approx
Approximately equal to
$\pi \approx 3.14$
\equiv
Equivalent to
$a \equiv b \pmod{n}$
\sim
Similar to (tilde relation)
$f(x) \sim g(x)$
\simeq
Similar or equal to
$a \simeq b$
\cong
Congruent to
$\triangle ABC \cong \triangle DEF$
\propto
Proportional to
$y \propto x$
\ll
Much less than
$a \ll b$
\gg
Much greater than
$a \gg b$
\subset
Proper subset
$A \subset B$
\subseteq
Subset or equal
$A \subseteq B$
\supset
Proper superset
$A \supset B$
\supseteq
Superset or equal
$A \supseteq B$
\in
Element of
$x \in A$
\notin
Not an element of
$x \notin A$
\ni
Contains as member
$A \ni x$
\cup
Set union
$A \cup B$
\cap
Set intersection
$A \cap B$
\setminus
Set difference
$A \setminus B$
\emptyset
Empty set symbol
$A = \emptyset$
\varnothing
Empty set symbol (alternate, amssymb)
$A = \varnothing$
\forall
Universal quantifier
$\forall x \in \mathbb{R}$
\exists
Existential quantifier
$\exists x \in A$
\nexists
Negated existential quantifier (amssymb)
$\nexists x$
\neg
Logical negation
$\neg p$
\land
Logical AND
$p \land q$
\lor
Logical OR
$p \lor q$
\implies
Implication arrow (amssymb)
$p \implies q$
\iff
If and only if (amsmath)
$p \iff q$
\rightarrow
Right arrow
$A \rightarrow B$
\to
Right arrow (shorthand)
$f: A \to B$
\leftarrow
Left arrow
$A \leftarrow B$
\leftrightarrow
Left-right arrow
$A \leftrightarrow B$
\Rightarrow
Double right arrow
$p \Rightarrow q$
\Leftarrow
Double left arrow
$p \Leftarrow q$
\Leftrightarrow
Double left-right arrow
$p \Leftrightarrow q$
\mapsto
Maps-to arrow
$x \mapsto x^2$
\longrightarrow
Long right arrow
$A \longrightarrow B$
\longleftarrow
Long left arrow
$A \longleftarrow B$
\uparrow
Up arrow
$x \uparrow y$
\downarrow
Down arrow
$x \downarrow y$
\nabla
Nabla / del operator
$\nabla f$
\partial
Partial derivative symbol
$\frac{\partial f}{\partial x}$
\infty
Infinity symbol
$\lim_{x \to \infty} f(x)$
\aleph
Aleph symbol
$\aleph_0$
\hbar
Reduced Planck's constant symbol
$E = \hbar \omega$
\ell
Script lowercase l
$\ell^2$ space
\Re
Real part symbol
$\Re(z)$
\Im
Imaginary part symbol
$\Im(z)$
\angle
Angle symbol
$\angle ABC$
\perp
Perpendicular symbol
$AB \perp CD$
\parallel
Parallel symbol
$AB \parallel CD$
\wedge
Wedge (logical AND / cross product)
$\vec{a} \wedge \vec{b}$
\vee
Vee (logical OR)
$p \vee q$
\dagger
Dagger symbol
$A^\dagger$
\ddagger
Double dagger symbol
$x^\ddagger$
\ldots
Horizontal ellipsis (low dots)
$a_1, a_2, \ldots, a_n$
\cdots
Horizontal ellipsis (centered dots)
$a_1 + a_2 + \cdots + a_n$
\vdots
Vertical ellipsis
$\vdots$
\ddots
Diagonal ellipsis
$\ddots$
\prime
Prime symbol
$f\prime(x)$
\backslash
Backslash symbol
$A \backslash B$
SI Units & Numbers (siunitx)
Comprehensive syntax, arguments, options, and copyable snippets for si units & numbers (siunitx).
\si{unit}
Typesets a physical unit correctly formatted (siunitx package)
\si{\meter\per\second}
\SI{value}{unit}
Typesets a numeric value with its unit (siunitx package)
\SI{9.8}{\meter\per\second\squared}
\num{value}
Typesets a number with consistent formatting, e.g. scientific notation (siunitx)
\num{6.022e23}
\ang{value}
Typesets an angle value (siunitx package)
\ang{45}
Chemistry & Physics (mhchem, physics)
Comprehensive syntax, arguments, options, and copyable snippets for chemistry & physics (mhchem, physics).
\ce{formula}
Typesets a chemical formula or reaction (mhchem package)
\ce{H2O + CO2 -> H2CO3}
\bra{x}
Typesets a quantum bra vector (physics package)
$\bra{\psi}$
\ket{x}
Typesets a quantum ket vector (physics package)
$\ket{\psi}$
\braket{x}{y}
Typesets a quantum bra-ket inner product (physics package)
$\braket{\phi}{\psi}$
\dv{f}{x}
Typesets a total derivative (physics package)
$\dv{f}{x}$
\pdv{f}{x}
Typesets a partial derivative (physics package)
$\pdv{f}{x}$
\vb{x}
Typesets a bold vector symbol (physics package)
$\vb{F} = m\vb{a}$