Proportional To in LaTeX (\propto)

Where it is used

Says one quantity is proportional to another, equal up to a constant factor.

Physics writes F \propto 1/r^2 for inverse-square laws, and Bayesian statistics relies on it constantly: p(\theta \mid x) \propto p(x \mid \theta)\, p(\theta), dropping the normalizing constant. It is a relation, so spacing is automatic. Do not confuse it with the Greek letter \alpha, which looks similar in some fonts but has no relation spacing. A variant \varpropto has a slightly different shape. For scaling in algorithm analysis, \sim or \Theta are usually clearer. Chain it with a constant only when the constant matters; otherwise the point of \propto is to hide it.

Also listed under: Probability & Statistics

Minimal compilable example

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

\documentclass{article}
\begin{document}
Proportional To: $\propto$

\[ p(\theta \mid x) \propto p(x \mid \theta)\, p(\theta) \]
\end{document}

Related symbols

• Similar To\sim
• Equivalent\equiv
• Congruent\cong
• Approximately Equal\approx
• Subset\subset
• Not Equal\neq

Frequently asked questions

How do I write Proportional To in LaTeX?

Type \propto in math mode, for example $p(\theta \mid x) \propto p(x \mid \theta)\, p(\theta)$. It works in plain LaTeX without loading any package.

Which package do I need for \propto?

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

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

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\propto$ 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).