Angle Brackets ⟨ ⟩: Symbol, Copy and Paste, and LaTeX

Angle brackets ⟨ ⟩, also called angular brackets, are the paired delimiters mathematicians use for inner products like ⟨u, v⟩ and physicists use for bra-ket notation like ⟨φ|ψ⟩. They look a lot like the less-than and greater-than signs < > and like the chevron quotation marks ‹ ›, but all three are different characters with different codes, and mixing them up is one of the most common typesetting mistakes in math documents.

Below: the characters to copy, the codes for every platform, what angle brackets are used for, and how to write them in LaTeX.

Angle Brackets ⟨ ⟩: Copy and Paste

Copy the brackets from the box below (use the copy button), or take the code you need from the table:

1⟨ ⟩
Copy

Avoid the older look-alikes U+2329 and U+232A: Unicode treats them as the wide CJK brackets 〈 〉 and no longer recommends them for math. HTML5 maps ⟨ to U+27E8, the mathematical bracket.

Why < and > Are Wrong for Angle Brackets

The keyboard signs < and > are relations: "less than" and "greater than", and typesetting systems treat them that way. In LaTeX math mode, $<u, v>$ puts the wide spacing of a relation around each sign, so an inner product reads like two inequalities, and the signs are wider and flatter than real brackets. In text mode with LaTeX's old default OT1 font encoding, a bare < even prints as an inverted exclamation mark ¡ and > as ¿.

Use \langle and \rangle instead. They are true delimiters: tight spacing, the correct shape, and they grow with \left and \right. In HTML the problem runs the other way: < and > start and end tags, so you write < and > to show them as text, and ⟨ ⟩ when you want the math brackets. For the inequality signs themselves, see greater than and less than symbols.

How to Type Angle Brackets

• Windows: ⟨ and ⟩ have no Alt code, because Alt codes only cover the old 256-character code pages. In Word, type 27E8 and press Alt + X (27E9 for the closing bracket). The chevrons do have codes: Alt + 0139 for ‹ and Alt + 0155 for ›.
• Mac: open the Character Viewer with Control + Command + Space and search "angle bracket". With the Unicode Hex Input source enabled, hold Option and type 27E8. Option + Shift + 3 and Option + Shift + 4 type the chevrons ‹ ›.
• Word Insert Symbol: Insert → Symbol → More Symbols, set "from" to Unicode (hex), choose the subset Miscellaneous Mathematical Symbols-A and pick ⟨ (character code 27E8). In a Word equation, typing \langle or \rangle followed by a space also works.
• HTML: ⟨ and ⟩, or the numeric references ⟨ and ⟩.
• iPhone and Android: no phone keyboard has them. Copy them from this page, or save them as a text replacement shortcut.

Uses of Angle Brackets

• Inner products: the inner product of two vectors is written ⟨u, v⟩; for real vectors it is the dot product u₁v₁ + … + uₙvₙ. Angle brackets also mark the span or subgroup generated by a set, as in ⟨S⟩, and an average in physics, as in ⟨x⟩.
• Bra-ket notation: Dirac notation writes a quantum state as a ket |ψ⟩, its dual as a bra ⟨ψ|, an inner product as ⟨φ|ψ⟩ and an expectation value as ⟨A⟩ = ⟨ψ|A|ψ⟩.
• HTML and XML tags: tags such as <p> and <div> use the plain less-than and greater-than signs, as do generics in code (List<String>). People often call these "angle brackets" too, but they are U+003C and U+003E, not ⟨ ⟩.
• Placeholders: in documentation and command syntax, <name> or <file> marks a value you replace. Linguists use ⟨ ⟩ to mark spellings, as in "⟨ph⟩ spells /f/".
• Chevrons in French quotes: French and many other languages quote with guillemets « » (U+00AB and U+00BB; Alt + 0171 and Alt + 0187; Option + \ and Option + Shift + \ on a Mac), with a space inside: « Bonjour ». The single chevrons ‹ › serve as quotes within quotes.

Angle Brackets in LaTeX

In math mode, write \langle and \rangle. This example shows the plain brackets, auto-sized brackets, bra-ket notation and the text-mode version:

1\documentclass{article}
2\usepackage{amsmath}
3\usepackage{braket}   % \bra, \ket, \braket
4\begin{document}
5The inner product is $\langle u, v \rangle$.
6
7Brackets that grow with their content:
8\[
9  \left\langle \frac{\partial f}{\partial x}, \frac{\partial g}{\partial x} \right\rangle
10\]
11
12Dirac notation: $\bra{\phi}$, $\ket{\psi}$, $\braket{\phi | \psi}$.
13
14In text: \textlangle tag\textrangle.
15\end{document}
Copy

• \left\langle ... \right\rangle sizes the pair to its content. For fixed sizes use \big\langle, \Big\langle, \bigg\langle and \Bigg\langle.
• The braket package gives \bra{\phi}, \ket{\psi} and \braket{\phi | \psi} (bar inside one argument). The physics package uses two arguments, \braket{\phi}{\psi}, and adds \expval{A} for ⟨A⟩. Load one or the other: both define \bra and \ket.
• \textlangle and \textrangle give angle brackets in running text (from textcomp, built into LaTeX since 2020).
• For an inner product you write often, mathtools lets you define \DeclarePairedDelimiter{\ip}{\langle}{\rangle}, then write \ip{u, v}, or \ip*{...} to auto-size.
• With XeLaTeX or LuaLaTeX and the unicode-math package, you can type ⟨ ⟩ directly inside math.

For every other delimiter, including floor, ceiling and double bars, see the LaTeX brackets lesson. For round, square and curly brackets outside LaTeX, see parentheses and the types of brackets.

Related symbols and guides

• Angle Brackets 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
• Parentheses and types of brackets
• Greater than and less than (> <)

Angle Brackets FAQ

What are angular brackets?

Angular brackets and angle brackets are the same thing: the pair ⟨ ⟩, Unicode U+27E8 and U+27E9. In everyday use, especially in HTML and programming, people also call the less-than and greater-than signs < > angle brackets.

What is the difference between ⟨ ⟩ and < >?

⟨ ⟩ are delimiters with a narrow, tall shape used to enclose something, such as an inner product. < and > are the less-than and greater-than relation signs; they are wider, sit with relation spacing in math, and are the characters HTML uses for tags.

How do I type angle brackets in LaTeX?

In math mode use \langle and \rangle, for example $\langle u, v \rangle$. Use \left\langle and \right\rangle around tall content, the braket or physics package for bra-ket notation, and \textlangle and \textrangle in text mode.

What is the HTML code for angle brackets?

Use ⟨ for ⟨ and ⟩ for ⟩, or the numeric references ⟨ and ⟩. For the less-than and greater-than signs use < and >, and for the chevrons ‹ › use ‹ and ›.

Is there an Alt code for ⟨ and ⟩?

No. Windows Alt codes only reach the characters of the old code pages, and ⟨ ⟩ are not among them. In Word, type 27E8 or 27E9 and press Alt + X, use Insert → Symbol, or copy the characters from this page. The chevrons ‹ › do have Alt codes: Alt + 0139 and Alt + 0155.