Brackets and Parentheses in LaTeX - Complete Guide

Master all types of brackets and parentheses in LaTeX. Learn automatic sizing, manual control, and advanced techniques for mathematical expressions.

Master all types of brackets and parentheses in LaTeX mathematical expressions. This comprehensive guide covers everything from basic parentheses to advanced delimiter sizing techniques, with visual examples for every concept.

Quick start: LaTeX provides various bracket types and automatic sizing with \left and \right. For basic parentheses use (), for square brackets [], and for curly braces \{\}.

Prerequisites: Basic LaTeX math mode knowledge. See Mathematical Expressions for math mode basics.

What You’ll Learn

• ✅ All bracket and delimiter types in LaTeX
• ✅ Automatic sizing with \left and \right
• ✅ Manual size control for fine-tuning
• ✅ Multi-line equations with balanced delimiters
• ✅ Special cases and advanced techniques
• ✅ Common errors and how to fix them
• ✅ Best practices for readable mathematics

Types of Brackets and Delimiters

Complete Visual Reference

All LaTeX Bracket Types

Type	LaTeX Code	Output	Common Use
Parentheses	( )	( )	General grouping
Square brackets	[ ]	[ ]	Arrays, intervals
Curly braces	{ }	Sets, systems
Angle brackets	\langle \rangle	⟨ ⟩	Inner products
Vertical bars	| | or \vert \vert	| |	Absolute value
Double bars	| | or \Vert \Vert	‖ ‖	Norms
Floor	\lfloor \rfloor	⌊ ⌋	Floor function
Ceiling	\lceil \rceil	⌈ ⌉	Ceiling function

Basic Examples

basic-brackets.tex

\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}

Rendered output:

(a + b)

[x, y]

{z : z > 0}

⟨u, v⟩

|x − y|

‖v‖

⌊x⌋ and ⌈x⌉

Automatic Delimiter Sizing

The \left and \right Commands

LaTeX can automatically size delimiters to match their content using \left and \right:

auto-sizing.tex

\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}

Rendered output:

Without sizing:(12)

With sizing:(12)

[x²y]

{√ab}

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.

Invisible Delimiters

Sometimes you need an invisible delimiter to balance the equation:

invisible-delimiters.tex

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

Rendered output:

{

x + y = 1

x − y = 0

dydx|_x=0

Manual Size Control

Size Commands

When automatic sizing doesn’t give the desired result, use manual size commands:

Delimiter Size Commands (smallest to largest)

\big	50% larger than normal
\Big	2x normal size
\bigg	2.5x normal size
\Bigg	3x normal size

Size Comparison

size-comparison.tex

\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}

Rendered output:

Normal

( 1 2 )

\big

( 1 2 )

\Big

( 1 2 )

\bigg

( 1 2 )

\Bigg

( 1 2 )

Left and Right Variants

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

Advanced Techniques

Nested Brackets

nested-brackets.tex

\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}

Rendered output:

Poor: [1 + [2 + [3 + 4]]]

Better: [1 + [2 + [3 + 4]]]

Best: [1 + [2 + [3 + 4]]]

Multi-line Equations with Brackets

For equations that span multiple lines, you need special handling:

multiline-brackets.tex

\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}

Rendered output:

f(x) = [ x² + 2x

+ 1 ]

g(x) = [ x³ + 3x²

[ + 3x + 1 ]

f(x) = {

x² if x ≥ 0

−x² if x < 0

Matrix Delimiters

matrix-delimiters.tex

\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}

Rendered output:

pmatrix

(

a	b
c	d

)

bmatrix

[

a	b
c	d

]

Bmatrix

{

a	b
c	d

}

vmatrix

|

a	b
c	d

|

Vmatrix

‖

a	b
c	d

‖

Special Use Cases

Set Notation

set-notation.tex

\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}

Rendered output:

A = {1, 2, 3, 4, 5}

B = {x ∈ ℝ : x² < 4}

C = {x ∈ ℤ :

x > 0

x is even

}

∅ = {}

Interval Notation

intervals.tex

\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}

Physics and Engineering

physics-brackets.tex

\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}

Common Errors and Solutions

Error: Missing \right. inserted

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

Brackets too large with \left...\right

Problem: Automatic sizing makes brackets unnecessarily large.

Solution: Use manual sizing instead:

% Instead of
$\left( \sum_{i=1}^n x_i \right)$

% Use
$\bigg( \sum_{i=1}^n x_i \bigg)$

Curly braces not showing

Problem: { and } have special meaning in LaTeX.

Solution: Escape them with backslash:

$\{ x : x > 0 \}$  % Correct
${ x : x > 0 }$    % Wrong - braces disappear

Mismatched bracket sizes in aligned equations

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}

Best Practices

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

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

3. Spacing Considerations

spacing-examples.tex

% 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|

4. Semantic Markup

Use meaningful commands when available:

semantic-markup.tex

% 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

Quick Reference Card

Brackets Quick Reference

Basic Delimiters

( ) [ ] { }\langle \rangle| | | |\lfloor \rfloor\lceil \rceil

Automatic Sizing

\left( … \right)\left. … \right|\left{ … \right.

Manual Sizes

\big \Big \bigg \Bigg\bigl( \bigr)\Bigl[ \Bigr]

Matrix Environments

pmatrix ()bmatrix []Bmatrix vmatrix ||

Related Topics

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

LaTeX Cloud Studio automatically handles package loading! The amsmath package is pre-loaded, so all bracket commands work immediately without manual package management.