Product in LaTeX (\prod)

Where it is used

Capital-pi product operator, multiplying the terms of a sequence.

Bounds work as for \sum: n! = \prod_{k=1}^{n} k, and the likelihood L(\theta) = \prod_{i=1}^{n} f(x_i \mid \theta) in statistics. It is larger than the letter \Pi and positions limits above and below in display style, so do not substitute the Greek letter. Taking logarithms turns a product into a sum, \log\prod_i a_i = \sum_i \log a_i, a step in nearly every maximum-likelihood derivation. Cartesian products of sets, \prod_{i \in I} X_i, use the same command. Its upside-down counterpart \coprod denotes coproducts.

Minimal compilable example

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

\documentclass{article}
\begin{document}
Product: $\prod$

\[ L(\theta) = \prod_{i=1}^{n} f(x_i \mid \theta) \]
\end{document}

Related symbols

• Product\prod_{i=1}^{n}
• Summation to Infinity\sum_{n=0}^{\infty}
• Coproduct\coprod
• Summation\sum_{i=1}^{n}
• Big Union\bigcup
• Summation\sum

Frequently asked questions

How do I write Product in LaTeX?

Type \prod in math mode, for example $L(\theta) = \prod_{i=1}^{n} f(x_i \mid \theta)$. It works in plain LaTeX without loading any package.

Which package do I need for \prod?

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

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

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