Sigma in LaTeX (\sigma)

Where it is used

Lowercase Greek sigma, the standard deviation, activation functions, and the sigma-algebra.

Statistics writes the standard deviation as \sigma and variance as \sigma^2. Machine learning uses \sigma(x) = 1/(1 + e^{-x}) for the logistic sigmoid and \sigma for a generic activation function. Measure theory talks of \sigma-algebras, physics uses \sigma for cross-sections, conductivity, and Pauli matrices \sigma_x, and linear algebra uses \sigma_i for singular values. The final-sigma variant \varsigma resembles a Latin s and is rarely used in math. Do not use the capital \Sigma for summation; that is \sum.

Also listed under: Probability & Statistics, Machine Learning & AI

Minimal compilable example

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

\documentclass{article}
\begin{document}
Sigma: $\sigma$

\[ \sigma(x) = \frac{1}{1 + e^{-x}} \]
\end{document}

Related symbols

• Sigma (Upper)\Sigma
• Rho\rho
• Tau\tau
• Pi (Upper)\Pi
• Upsilon\upsilon
• Pi\pi

Frequently asked questions

How do I write Sigma in LaTeX?

Type \sigma in math mode, for example $\sigma(x) = \frac{1}{1 + e^{-x}}$. It works in plain LaTeX without loading any package.

Which package do I need for \sigma?

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

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

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