Similar To in LaTeX (\sim)

Where it is used

Tilde relation for distributed as, asymptotically equal, similar, or equivalent under a relation.

In probability X \sim \mathcal{N}(0, 1) reads X is distributed as a standard normal. In asymptotics f \sim g means f/g \to 1, as in Stirling's formula. Algebra uses x \sim y for an equivalence relation, and geometry uses it for similar triangles. As a relation it has spacing on both sides; for a tilde accent on a letter use \tilde{x}. Close cousins are \simeq (asymptotically equal or homotopy equivalent), \approx (approximately), and \thicksim, a bolder version. As a prefix meaning approximately, as in \sim 10^3, the spacing can look odd; write {\sim}10^3.

Also listed under: Probability & Statistics, Geometry

Minimal compilable example

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

\documentclass{article}
\begin{document}
Similar To: $\sim$

\[ n! \sim \sqrt{2\pi n} \left( \frac{n}{e} \right)^{n} \]
\end{document}

Related symbols

• Congruent\cong
• Proportional To\propto
• Subset\subset
• Equivalent\equiv
• Subset or Equal\subseteq
• Approximately Equal\approx

Frequently asked questions

How do I write Similar To in LaTeX?

Type \sim in math mode, for example $n! \sim \sqrt{2\pi n} \left( \frac{n}{e} \right)^{n}$. It works in plain LaTeX without loading any package.

Which package do I need for \sim?

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

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

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