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Use ( ) for ordinary parentheses, [ ] for square brackets, and \{ \} for curly braces. Use \left ... \right when the bracket should grow with the expression, and use \big, \Big, \bigg, or \Bigg when you want manual control over bracket size.
Quick answer: the most common bracket commands are (), [], \{ \}, \langle \rangle, \left ... \right, and \big( ... \big). If LaTeX complains about unbalanced delimiters, check that every \left has a matching \right.Prerequisites: Basic LaTeX math mode knowledge. See Mathematical Expressions for math mode basics.

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Quick answers

If you need…Use
Ordinary parentheses(a+b)
Square brackets[a,b]
Curly braces in math mode\{x \in A\}
Angle brackets\langle u, v \rangle
Automatically sized brackets\left( \frac{a}{b} \right)
Manually larger brackets\big( ... \big) or \Big( ... \Big)
One visible delimiter only\left. or \right.

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Types of Brackets and Delimiters

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Complete Visual Reference

TypeLaTeX CodeOutputCommon Use
Parentheses( )( )( \, )General grouping
Square brackets[ ][ ][ \, ]Arrays, intervals
Curly braces\{ \}{ }\{ \, \}Sets, systems
Angle brackets\langle \rangle⟨ ⟩\langle \, \rangleInner products
Vertical bars| or \vert∣ ∣\lvert \, \rvertAbsolute value
Double bars|| or \Vert∥ ∥\lVert \, \rVertNorms
Floor\lfloor \rfloor⌊ ⌋\lfloor \, \rfloorFloor function
Ceiling\lceil \rceil⌈ ⌉\lceil \, \rceilCeiling function

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Basic Examples

\documentclass{article}
\usepackage{amsmath}
\begin{document}

% Parentheses
$(a + b)$

% Square brackets  
$[x, y]$

% Curly braces (must be escaped)
$\{z : z > 0\}$

% Angle brackets
$\langle u, v \rangle$

% Absolute value
$|x - y|$

% Norm
$\|v\|$

% Floor and ceiling
$\lfloor x \rfloor$ and $\lceil x \rceil$

\end{document}

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Automatic Delimiter Sizing

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The \left and \right Commands

LaTeX can automatically size delimiters to match their content using \left and \right: 
\documentclass{article}
\usepackage{amsmath}
\begin{document}

% Without automatic sizing
$(\frac{1}{2})$

% With automatic sizing
$\left(\frac{1}{2}\right)$

% Works with any delimiter type
$\left[\frac{x^2}{y}\right]$

$\left\{\sqrt{\frac{a}{b}}\right\}$

$\left|\sum_{i=1}^n x_i\right|$

% Nested fractions
$\left(\frac{\frac{a}{b}}{\frac{c}{d}}\right)$

\end{document}

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Important Rules for \left and \right

Critical: Every \left must have a matching \right in the same math environment. They must be balanced like opening and closing HTML tags.

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Invisible Delimiters

Sometimes you need an invisible delimiter to balance the equation: 
% Using \right. for invisible right delimiter
$\left\{\begin{array}{ll}
x + y = 1 \\
x - y = 0
\end{array}\right.$

% Using \left. for invisible left delimiter
$\left.\frac{dy}{dx}\right|_{x=0}$

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Manual Size Control

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Size Commands

When automatic sizing doesn’t give the desired result, use manual size commands:
Delimiter Size Commands (smallest to largest):
CommandSize
\big50% larger than normal
\Big2× normal size
\bigg2.5× normal size
\Bigg3× normal size

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Size Comparison

\documentclass{article}
\usepackage{amsmath}
\begin{document}

% Normal size
$( \frac{1}{2} )$

% \big
$\big( \frac{1}{2} \big)$

% \Big
$\Big( \frac{1}{2} \Big)$

% \bigg
$\bigg( \frac{1}{2} \bigg)$

% \Bigg
$\Bigg( \frac{1}{2} \Bigg)$

% For opening and closing separately
$\bigl( x \bigr)$  % 'l' for left, 'r' for right

\end{document}

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Left and Right Variants

Use l and r suffixes for proper spacing: \bigl(, \bigr), \Bigl[, \Bigr], etc. This ensures correct spacing around the delimiters.

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Advanced Techniques

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Nested Brackets

\documentclass{article}
\usepackage{amsmath}
\begin{document}

% Poor: all brackets same size
$[1 + [2 + [3 + 4]]]$

% Better: graduated sizes
$\Big[1 + \big[2 + [3 + 4]\big]\Big]$

% Best: automatic sizing
$\left[1 + \left[2 + \left[3 + 4\right]\right]\right]$

% Complex nesting
$\left\{x : \left[a + \left(\frac{b}{c}\right)\right] > 0\right\}$

\end{document}

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Multi-line Equations with Brackets

For equations that span multiple lines, you need special handling: 
\documentclass{article}
\usepackage{amsmath}
\begin{document}

% Using \right. and \left. for invisible delimiters
\begin{align}
f(x) = & \left[ x^2 + 2x \right. \\
       & \left. + 1 \right]
\end{align}

% Alternative using \big commands
\begin{align}
g(x) = & \Big[ x^3 + 3x^2 \\
       & \phantom{\Big[} + 3x + 1 \Big]
\end{align}

% For cases/piecewise functions
\begin{equation}
f(x) = \begin{cases}
x^2 & \text{if } x \geq 0 \\
-x^2 & \text{if } x < 0
\end{cases}
\end{equation}

\end{document}

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Matrix Delimiters

\documentclass{article}
\usepackage{amsmath}
\begin{document}

% Different matrix environments
$\begin{pmatrix}  % parentheses
a & b \\
c & d
\end{pmatrix}$

$\begin{bmatrix}  % brackets
a & b \\
c & d
\end{bmatrix}$

$\begin{Bmatrix}  % braces
a & b \\
c & d
\end{Bmatrix}$

$\begin{vmatrix}  % vertical bars
a & b \\
c & d
\end{vmatrix}$

$\begin{Vmatrix}  % double bars
a & b \\
c & d
\end{Vmatrix}$

\end{document}

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Special Use Cases

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Set Notation

\documentclass{article}
\usepackage{amsmath}
\begin{document}

% Basic set
$A = \{1, 2, 3, 4, 5\}$

% Set builder notation
$B = \{x \in \mathbb{R} : x^2 < 4\}$

% Set with conditions
$C = \left\{x \in \mathbb{Z} : \begin{array}{l}
x > 0 \\
x \text{ is even}
\end{array}\right\}$

% Empty set
$\emptyset = \{\}$

\end{document}

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Interval Notation

\documentclass{article}
\usepackage{amsmath}
\begin{document}

% Open interval
$(a, b)$

% Closed interval
$[a, b]$

% Half-open intervals
$[a, b)$ and $(a, b]$

% Infinite intervals
$(-\infty, a]$ and $[b, \infty)$

% Union of intervals
$[0, 1] \cup [2, 3]$

\end{document}

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Physics and Engineering

\documentclass{article}
\usepackage{amsmath}
\usepackage{physics} % provides \bra, \ket, \braket
\begin{document}

% Quantum mechanics bra-ket notation
$\langle \psi | \phi \rangle$

% With physics package
$\bra{\psi}\ket{\phi}$
$\braket{\psi|\phi}$

% Commutator
$[A, B] = AB - BA$

% Anticommutator  
$\{A, B\} = AB + BA$

% Poisson bracket
$\{f, g\} = \sum_i \left(\frac{\partial f}{\partial q_i}\frac{\partial g}{\partial p_i} - \frac{\partial f}{\partial p_i}\frac{\partial g}{\partial q_i}\right)$

\end{document}

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Common Errors and Solutions

Problem: Every \left needs a matching \right, even across line breaks.Solution: Use \right. for an invisible right delimiter:
\left[ x + y \right.  % End of first line
\left. + z \right]    % Start of second line
Problem: Automatic sizing makes brackets unnecessarily large.Solution: Use manual sizing instead:
% Instead of
$\left( \sum_{i=1}^n x_i \right)$

% Use
$\bigg( \sum_{i=1}^n x_i \bigg)$
Problem: { and } have special meaning in LaTeX.Solution: Escape them with backslash:
$\{ x : x > 0 \}$  % Correct
${ x : x > 0 }$    % Wrong - braces disappear
Problem: Brackets don’t match across aligned lines.Solution: Use phantom brackets:
\begin{align}
f(x) = & \Big[ x^2 + 2x \\
       & \phantom{\Big[} + 1 \Big]
\end{align}

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Best Practices

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1. Choose the Right Delimiter

Good Delimiter Choices:
  • Parentheses: General grouping, function arguments
  • Square brackets: Matrices, commutators, intervals
  • Curly braces: Sets, systems of equations
  • Angle brackets: Inner products, averages
  • Vertical bars: Absolute values, determinants, norms

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2. Sizing Guidelines

  • Use \left...\right for complex expressions with varying heights
  • Use manual sizing (\big, \Big, etc.) for simple expressions
  • Be consistent within the same document
  • Don’t oversize—readability is key

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3. Spacing Considerations

% Good spacing with \bigl and \bigr
$\bigl( x + y \bigr)$

% Poor spacing with just \big
$\big( x + y \big)$

% For better spacing around bars
$\left\lvert x \right\rvert$  % Better than |x|

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4. Semantic Markup

Use meaningful commands when available: 
% Instead of manual brackets
$|| v ||$

% Use semantic commands
$\lVert v \rVert$      % Double bars for norm
$\lvert x \rvert$      % Single bars for absolute value
$\langle u, v \rangle$ % Angle brackets for inner product

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Quick Reference Card

CategoryCommandsResult
Parentheses( )(x)(x)
Square brackets[ ][x][x]
Curly braces\{ \}{x}\{x\}
Angle brackets\langle \rangle⟨x⟩\langle x \rangle
Vertical bars| or \vert∣x∣\lvert x \rvert
Double bars|| or \Vert∥x∥\lVert x \rVert
Floor\lfloor \rfloor⌊x⌋\lfloor x \rfloor
Ceiling\lceil \rceil⌈x⌉\lceil x \rceil
Auto sizing\left( \frac{1}{2} \right)(12)\left(\frac{1}{2}\right)
Manual sizing\Big( x \Big)(x)\Big( x \Big)

Mathematical Expressions

Learn math mode basics and expressions

Matrices Guide

Complete guide to matrices and arrays

Equations

Multi-line and numbered equations

Math Symbols

Comprehensive symbol reference
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