Angle Brackets in LaTeX (\langle x \rangle)

Where it is used

Encloses an expression in angle brackets, for averages, inner products or the span of generators.

This pairing is used for expectation values in physics, \langle E \rangle, for inner products \langle x, y \rangle, and for the subgroup or ideal generated by elements, \langle a \rangle. For tall arguments switch to \left\langle \frac{a}{b} \right\rangle. If you write inner products often, define a macro, for instance with a paired-delimiter tool, so sizing is consistent. In Dirac notation, many prefer a dedicated bra-ket macro set because spacing around the vertical bar inside \langle \phi | \psi \rangle can be uneven; \mid adds relation spacing, while | adds none.

Minimal compilable example

Paste this into an empty .tex file and compile it with pdfLaTeX, XeLaTeX or LuaLaTeX.

\documentclass{article}
\begin{document}
Angle Brackets: $\langle x \rangle$

\[ \langle x \rangle = \int x\, p(x)\, dx \]
\end{document}

Related symbols

• Ceiling Left\lceil
• Angle Bracket Right\rangle
• Ceiling Right\rceil
• Angle Bracket Left\langle
• Ceiling\lceil x \rceil
• Floor Left\lfloor

Frequently asked questions

How do I write Angle Brackets in LaTeX?

Type \langle x \rangle in math mode, for example $\langle x \rangle = \int x\, p(x)\, dx$. It works in plain LaTeX without loading any package.

Which package do I need for \langle x \rangle?

None. \langle x \rangle is part of standard LaTeX, so it compiles with nothing in the preamble but the document class.

Can I use \langle x \rangle in text mode, or only in math mode?

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\langle x \rangle$ in running text.