Greek Letters and Math Symbols in LaTeX

Greek letters and math symbols are essential for scientific and mathematical writing. LaTeX provides commands for every Greek letter, operator, relation, arrow, and miscellaneous symbol you will ever need. This complete reference covers them all with copy-paste commands you can use immediately.

Lowercase Greek Letters

Lowercase Greek letters are used extensively in mathematics, physics, statistics, and engineering. Each letter is produced by a backslash followed by the letter's English name. All Greek letter commands must be used inside math mode (between $...$ or \[...\]).

Example usage:

% Lowercase Greek letters in equations
$\alpha + \beta = \gamma$

$\epsilon > 0$

$\lambda_1, \lambda_2, \ldots, \lambda_n$    % eigenvalues

$\theta \in [0, 2\pi)$                        % angle range

$\mu = \frac{1}{n} \sum_{i=1}^{n} x_i$       % sample mean

Uppercase Greek Letters

Not every Greek letter has a distinct uppercase form in LaTeX. Letters like Alpha (A) and Beta (B) look identical to their Latin counterparts, so LaTeX does not provide separate commands for them — simply type the Latin letter instead. The letters below have unique uppercase forms.

Example usage:

% Uppercase Greek letters
$\Gamma(n) = (n-1)!$                     % Gamma function

$\Delta x = x_2 - x_1$                   % difference

$\Sigma = \begin{pmatrix}
  \sigma_1^2 & \rho\sigma_1\sigma_2 \\
  \rho\sigma_1\sigma_2 & \sigma_2^2
\end{pmatrix}$                            % covariance matrix

$\Omega = \{1, 2, 3, 4, 5, 6\}$          % sample space

$f(n) = \Theta(n \log n)$                 % algorithm complexity

Binary Operators

Binary operators appear between two operands with appropriate spacing. LaTeX automatically adds the correct spacing around these symbols when used in math mode.

Example usage:

% Binary operators
$3 \times 4 = 12$

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$    % quadratic formula

$\mathbf{a} \cdot \mathbf{b} = |a||b|\cos\theta$   % dot product

$(f \circ g)(x) = f(g(x))$                    % composition

$V = V_1 \oplus V_2$                           % direct sum

Relation Symbols

Relation symbols express relationships between mathematical expressions. LaTeX spaces them differently from binary operators to preserve readability.

Example usage:

% Relation symbols
$x \leq y$                       % less than or equal

$a \neq b$                       % not equal

$\pi \approx 3.14159$             % approximately

$a \equiv b \pmod{n}$             % modular congruence

$X \sim \mathcal{N}(\mu, \sigma^2)$  % normal distribution

$F \propto ma$                    % proportional

$A \subseteq B$                   % subset or equal

$x \in \mathbb{R}$                % element of real numbers

$0 \notin \mathbb{N}$             % not a natural number (by convention)

Arrows

Arrow symbols are used for mappings, implications, limits, and many other mathematical constructs.

Example usage:

% Arrows in practice
$x \rightarrow \infty$             % x tends to infinity

$A \Rightarrow B$                  % A implies B

$P \Leftrightarrow Q$              % P if and only if Q

$f: X \rightarrow Y$               % function from X to Y

$x \mapsto x^2$                    % maps x to x squared

$f: \mathbb{R} \longrightarrow \mathbb{R}$  % long arrow mapping

$\lim_{n \to \infty} a_n = L$      % limit notation (\to is alias for \rightarrow)

Miscellaneous Symbols

These symbols appear frequently in advanced mathematics, physics, and theoretical computer science.

Example usage:

% Miscellaneous symbols in context
$\lim_{x \to \infty} f(x) = 0$           % limit at infinity

$\nabla f = \left( \frac{\partial f}{\partial x},
  \frac{\partial f}{\partial y},
  \frac{\partial f}{\partial z} \right)$  % gradient

$\forall x \in \mathbb{R}, \; x^2 \geq 0$  % universal statement

$\exists n \in \mathbb{N} : n > 100$       % existential statement

$A \cap B = \varnothing$                   % disjoint sets

$E = \frac{p^2}{2m} + V(x)$               % using \hbar: $E = \hbar\omega$

Dots and Ellipses

LaTeX provides several dot commands for different positions and orientations. Choosing the right one improves the visual quality of your equations.

Example usage:

% Dots and ellipses
$x_1, x_2, \ldots, x_n$                    % baseline dots for lists

$x_1 + x_2 + \cdots + x_n$                 % centered dots for operations

% Matrix with dots
$\begin{pmatrix}
  a_{11} & a_{12} & \cdots & a_{1n} \\
  a_{21} & a_{22} & \cdots & a_{2n} \\
  \vdots & \vdots & \ddots & \vdots \\
  a_{m1} & a_{m2} & \cdots & a_{mn}
\end{pmatrix}$

Accents and Decorations

Math accents add marks above or below symbols to denote vectors, estimates, averages, derivatives, and other modifications.

Example usage:

% Accents in practice
$\hat{\theta}$                   % estimated parameter

$\bar{x} = \frac{1}{n}\sum x_i$ % sample mean

$\vec{F} = m\vec{a}$             % Newton's second law

$\dot{x} = \frac{dx}{dt}$        % velocity

$\ddot{x} = \frac{d^2x}{dt^2}$  % acceleration

$\widehat{ABC}$                  % wide hat over angle name

$\tilde{f}(\xi) = \int_{-\infty}^{\infty} f(x) e^{-2\pi i \xi x} \, dx$  % Fourier transform

Using Symbols in Practice

Here is a comprehensive example combining many Greek letters and math symbols in real physics and mathematics equations:

\documentclass{article}
\usepackage{amsmath, amssymb}

\begin{document}

\section{Maxwell's Equations}
\begin{align}
  \nabla \cdot \vec{E} &= \frac{\rho}{\epsilon_0} \\
  \nabla \cdot \vec{B} &= 0 \\
  \nabla \times \vec{E} &= -\frac{\partial \vec{B}}{\partial t} \\
  \nabla \times \vec{B} &= \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}
\end{align}

\section{Schrödinger Equation}
\[
  i\hbar \frac{\partial}{\partial t} \Psi(\vec{r}, t)
  = \left[ -\frac{\hbar^2}{2m} \nabla^2 + V(\vec{r}, t) \right] \Psi(\vec{r}, t)
\]

\section{Euler's Identity}
\[
  e^{i\pi} + 1 = 0
\]

\section{Navier-Stokes Equation}
\[
  \rho \left( \frac{\partial \vec{v}}{\partial t}
  + (\vec{v} \cdot \nabla) \vec{v} \right)
  = -\nabla p + \mu \nabla^2 \vec{v} + \rho \vec{g}
\]

\section{Gaussian Integral}
\[
  \int_{-\infty}^{\infty} e^{-\alpha x^2} \, dx = \sqrt{\frac{\pi}{\alpha}},
  \quad \alpha > 0
\]

\section{Cauchy's Integral Formula}
\[
  f(a) = \frac{1}{2\pi i} \oint_\gamma \frac{f(z)}{z - a} \, dz
\]

\section{Bayes' Theorem}
\[
  P(A \mid B) = \frac{P(B \mid A) \, P(A)}{P(B)},
  \quad P(B) \neq 0
\]

\section{General Relativity — Einstein Field Equations}
\[
  R_{\mu\nu} - \frac{1}{2} R g_{\mu\nu} + \Lambda g_{\mu\nu}
  = \frac{8\pi G}{c^4} T_{\mu\nu}
\]

\end{document}

The amssymb Package

The amssymb package from the American Mathematical Society adds hundreds of extra symbols. Load it with \usepackage{amssymb}. Here are some of the most useful additions:

Example with number sets:

\usepackage{amssymb}

% Number sets
$\mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q}
  \subset \mathbb{R} \subset \mathbb{C}$

% Proof endings
$\therefore x = 5 \quad \blacksquare$

% Non-existence
$\nexists \, x \in \mathbb{R} : x^2 < 0$

Quick Reference Table

The most commonly searched LaTeX symbols in one place. Copy and paste the command directly into your document.

Next Steps

Now that you have a complete reference for Greek letters and math symbols, explore these related topics:

• Mathematical Expressions in LaTeX – Learn how to write inline and display math, fractions, roots, and more
• Subscripts and Superscripts – Master sub/superscript positioning and nesting
• Integrals, Sums, and Limits – Typeset integral signs, summation notation, and limit expressions

Free LaTeX Tools

• LaTeX Symbols Reference – Browse and search every Greek letter and math operator interactively
• LaTeX Preview – Test your symbol commands with live PDF preview
• Math to LaTeX – Convert handwritten equations to LaTeX
• AI LaTeX Generator – Generate LaTeX from text descriptions