Parentheses Symbol ( ): Types of Brackets and How to Use Them

The parentheses symbol ( ) is the round bracket pair: an opening parenthesis ( and a closing parenthesis ). It is one of four bracket types in everyday use, along with square brackets [ ], curly braces { } and angle brackets ⟨ ⟩, and each has its own job in math, writing and code. The names also change between American and British English, which is the source of most of the confusion.

This guide lists every bracket with its Unicode, HTML and Alt codes, explains what each one means in math, shows how to write them in LaTeX, and covers the punctuation rules for parentheses in writing.

Parentheses and Brackets: Copy and Paste

Copy the brackets from the box below (use the copy button), or find the name and code you need in the table:

1( ) [ ] { } ⟨ ⟩
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Windows Alt codes (hold Alt and type on the numeric keypad): ( is Alt + 40, ) Alt + 41, [ Alt + 91, ] Alt + 93, { Alt + 123 and } Alt + 125. All of these are on a standard keyboard anyway, on Windows and Mac alike. The mathematical angle brackets ⟨ ⟩ are the exception: they have no Alt code and no key, so copy them or see how to type angle brackets. The < > signs are relations, not brackets, even though they are often called angle brackets in HTML and code.

Parentheses in Math

Order of operations

Parentheses come first in PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). In the UK and many other countries the same rule is taught as BODMAS or BIDMAS, where the B stands for Brackets. So 2 × (3 + 4) = 14, but 2 × 3 + 4 = 10, and (−3)² = 9 while −3² = −9. When groups nest, textbooks often alternate the shapes so each pair is easy to match: {2 × [3 + (4 − 1)]} = 12, worked from the inside out.

Intervals

A parenthesis means the endpoint is excluded and a square bracket means it is included. (a, b) is the open interval a < x < b, [a, b] is the closed interval a ≤ x ≤ b, and (a, b] is half-open: it includes b but not a, so (2, 5] means 2 < x ≤ 5. Infinity always takes a parenthesis, as in [0, ∞). Some European texts write the open end with a reversed bracket, ]a, b].

Functions, points and sets

Parentheses also hold function arguments, f(x), and ordered pairs and coordinates, (3, 4), so (a, b) can mean a point or an interval depending on context. Curly braces enclose sets, as in {1, 2, 3} or {x | x > 0}, and square brackets appear in commutators, [A, B] = AB − BA.

Matrices

A matrix is written inside either large parentheses or large square brackets; both are standard, so pick one and use it throughout. Vertical bars |A| mean the determinant, not the matrix. See matrices in LaTeX for every matrix environment.

Brackets in LaTeX

Parentheses and square brackets can be typed directly. Curly braces are LaTeX's grouping characters, so to print them you write \{ and \} (or \lbrace and \rbrace). Plain brackets keep their normal size, so a fraction inside ( ) looks cramped; \left and \right size the pair to fit:

1\documentclass{article}
2\usepackage{amsmath, amssymb}
3\begin{document}
4Plain: $f(x) = 2(x + 1)$, interval $(a, b]$, set $\{1, 2, 3\}$.
5
6Auto-sized:
7\[
8  \left( \frac{a}{b} \right)^2 \quad
9  \left[ \int_0^1 f(x)\,dx \right] \quad
10  \left\{ x \in \mathbb{R} : x > 0 \right\}
11\]
12
13Manual sizes: $\Bigg( \bigg( \Big( \big( x \big) \Big) \bigg) \Bigg)$
14
15Matrices:
16\[
17  \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \quad
18  \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}
19\]
20\end{document}
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• \left( must be matched by a \right in the same formula. Use \left. or \right. for an invisible side, for example to close a one-sided brace.
• \big, \Big, \bigg and \Bigg give four fixed sizes. They often look better than \left and \right around sums and nested groups, where automatic sizing can come out too large.
• amsmath matrix environments choose the bracket for you: pmatrix ( ), bmatrix [ ], Bmatrix { } and vmatrix | | for determinants.
• A line that starts with [ right after \\ is read as an optional spacing argument. Write \\ {[}a, b] to keep the bracket.

The LaTeX brackets lesson covers every delimiter, including floor, ceiling, norms and angle brackets.

Parentheses in Writing

• Period inside or outside: if the parenthetical is part of a larger sentence, the period goes outside: "The test passed (on the second try)." If it is a complete sentence on its own, the period goes inside: "The test passed. (It took two tries.)"
• Commas: never put a comma before an opening parenthesis. Any comma the sentence needs goes after the closing one: "After the update (version 2.1), the bug was gone."
• Square brackets in quotations: they mark words the writer added or changed inside a quote, as in "She [the editor] approved it," and [sic] flags an error that was in the original.
• Nested brackets: US style guides such as Chicago and APA switch to square brackets for a parenthetical inside parentheses: (see the appendix [Table 3] for details).
• Abbreviations and lists: parentheses introduce an abbreviation the first time you use it, as in "the World Health Organization (WHO)", and enclose list numbers inside a sentence: (1), (2), (3).

Related symbols and guides

• Parentheses symbol page — copy the symbol and its LaTeX command
• Bracket and delimiter symbols reference — every symbol in the category with its LaTeX command
• Brackets and parentheses in LaTeX — how to typeset these symbols in a document
• Angle brackets (⟨ ⟩)
• Set symbols (∪ ∩ ⊆ ∈)

Parentheses and Brackets FAQ

What is the difference between parentheses and brackets?

Parentheses are the round pair ( ). In US English "brackets" means the square pair [ ]; in British English "brackets" means the round pair, and [ ] are called square brackets. In math and writing they do different jobs: parentheses group and add asides, while square brackets mark closed interval endpoints, nested groups and editorial insertions in quotes.

What are the four types of brackets?

Parentheses or round brackets ( ), square brackets [ ], curly braces or curly brackets { }, and angle brackets ⟨ ⟩. The less-than and greater-than signs < > are sometimes called angle brackets in HTML and programming, but they are a separate pair of characters.

Does the period go inside or outside parentheses?

Outside when the parenthetical is part of a sentence, as in "It worked (mostly)." Inside when the parenthetical is a full sentence of its own, as in "It worked. (Mostly.)"

What does (a, b] mean in math?

It is a half-open interval: every number greater than a and less than or equal to b. The parenthesis excludes the endpoint a and the square bracket includes the endpoint b. (a, b) excludes both and [a, b] includes both.

How do I make big parentheses in LaTeX?

Wrap the content in \left( and \right) to size the parentheses automatically, or use \big(, \Big(, \bigg( and \Bigg( for fixed sizes. For curly braces write \left\{ and \right\}, and for a matrix use the pmatrix or bmatrix environment.