How to Make Big Angle Brackets in LaTeX

If you mean how to make angle brackets large enough to enclose a mathematical expression, use LaTeX’s angle-bracket commands \langle and \rangle. To have them resize automatically, pair them with \left and \right.

The basic commands

Type \langle for the opening bracket and \rangle for the closing bracket. Put them in math mode, for example:

$\langle x,y\rangle$

For a fraction or other tall expression, use scalable delimiters:

\[
\left\langle \frac{x}{y}, z \right\rangle
\]

The \left and \right commands size the delimiters according to the material between them. Always pair them within the same math expression. They can also be used with other delimiters, such as parentheses and square brackets.

Choose the size manually

Automatic sizing can make brackets larger than you want, especially in a display equation. In that case, choose a fixed size. Use matching opening and closing commands:

Opening command	Closing command
\bigl\langle	\bigr\rangle
\Bigl\langle	\Bigr\rangle
\biggl\langle	\biggr\rangle
\Biggl\langle	\Biggr\rangle

For example:

\[
\biggl\langle \sum_{k=1}^{n} x_k, y \biggr\rangle
\]

The lowercase l and r in \bigl and \bigr make the delimiters behave as opening and closing punctuation. This generally gives more appropriate spacing than using \big on both sides.

Complete compilable example

This example uses standard LaTeX commands and includes the amsmath package; \middle is a TeX primitive, not a command provided by that package:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

Inline: $\langle x,y\rangle$.

\[
\left\langle \frac{x}{y} \middle| z \right\rangle
\qquad
\bigl\langle \sum_{k=1}^{n} x_k, y \bigr\rangle
\]

\end{document}

Here \left\langle and \right\rangle resize around the fraction and the separator. The \middle| sizes the vertical bar relative to those delimiters. The second expression uses manually sized brackets instead.

Common mistakes

• Using < and > instead of angle-bracket commands. In math mode, these characters are normally treated as comparison symbols. Write \langle and \rangle when you need angle-shaped delimiters.
• Leaving out math mode. Commands such as \langle belong inside $...$, \(...\), or a displayed equation environment.
• Using \left without \right. LaTeX requires a matching pair. If one side should be invisible, use a period as the delimiter, as in \left. expression \right\rangle.
• Making delimiters automatically large when a smaller size would read better. Try a fixed pair such as \bigl\langle ... \bigr\rangle if \left and \right look oversized.