Composition in LaTeX (\circ)

Where it is used

Small circle operator, standard for function composition and also used for degrees.

(f \circ g)(x) = f(g(x)) is the main use. As a superscript, 90^\circ gives degrees, though a dedicated degree symbol from a text-companion font may look better, and A^\circ often means interior or the polar set. Some authors use \circ for the Hadamard product, where \odot is the clearer alternative. \circ is a binary operator, so it gets medium space; \bigcirc is a larger circle and \cdot a filled dot. Avoid using the letter o for composition.

Also listed under: Geometry

Minimal compilable example

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

\documentclass{article}
\begin{document}
Composition: $\circ$

\[ (f \circ g)(x) = f(g(x)) \]
\end{document}

Related symbols

• Bullet\bullet
• Asterisk\ast
• Diamond\diamond
• Star\star
• Big Circle\bigcirc
• Circle Slash\oslash

Frequently asked questions

How do I write Composition in LaTeX?

Type \circ in math mode, for example $(f \circ g)(x) = f(g(x))$. It works in plain LaTeX without loading any package.

Which package do I need for \circ?

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

Can I use \circ in text mode, or only in math mode?

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\circ$ in running text. If you only need the glyph in text, paste the Unicode character ∘ instead (with XeLaTeX or LuaLaTeX and a font that has it).