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In LaTeX, \prod typesets the large product operator ∏. Give it a lower bound with _ and an upper bound with ^, for example \prod_{i=1}^{n} a_i. The same command answers the search “prod in LaTeX”: there is no separate prod function, only the \prod symbol command. This guide is for researchers and analysts who need to write products in papers, theses and supplementary material, and covers limit placement, multi-index products and the mistakes that most often break them.
What \prod is used for in research
A product operator multiplies a sequence of terms, the way a sum operator adds them. Typical uses are likelihoods written as a product over independent observations, joint probabilities of independent events, and normalising constants. The Overleaf documentation on integrals, sums and limits (read 2026-11-07) writes products in the form \prod_{lower}^{upper}, for instance the display \[ \prod_{i=a}^{b} f(i) \] and the inline form $\prod_{i=a}^{b} f(i)$.
Do not confuse it with other symbols that look similar or share a name. The vector operations (cross, dot, wedge) are covered in the guide to vector products in LaTeX, and the Greek capital letter Π is a different command (\Pi) covered in Greek symbols in LaTeX. \Pi is a letter, while \prod is a large operator with its own spacing and limit behaviour.
Install or access
No extra package is needed to try the basic examples in this guide in an ordinary LaTeX math environment; the Overleaf examples above use \prod directly. The limit-placement options discussed below belong to the amsmath package, which CTAN lists as part of the LaTeX required distribution (version 2.17z, dated 2025-07-09, LaTeX Project Public License 1.3c) and as contained in TeX Live and MiKTeX (CTAN page read 2026-11-07). Load it with:
\usepackage{amsmath}Step by step: writing a product
- Enter math mode. Use
$...$for inline math or\[ ... \]for a displayed equation. - Write the operator with bounds.
\prod_{i=1}^{n} x_i. By convention, subscripts and superscripts are created with_and^(Overleaf, “Subscripts and superscripts”, read 2026-11-07). - Brace multi-character bounds. A bound longer than one character must be wrapped in braces:
\prod_{i=1}^{n}, not\prod_i=1^n. - Add the term being multiplied. Everything after the bounds, such as
f(i)orx_i, is the factor. Use parentheses when the factor is a longer expression. - Compile and check the placement of the bounds (next sections).
\[ L(\theta) = \prod_{i=1}^{n} f(x_i \mid \theta) \]Inline versus display placement
Per the amsmath user’s guide (amsldoc.pdf on CTAN, read 2026-11-07), the default package option sumlimits places the subscripts and superscripts of summation-type symbols above and below the symbol in displayed equations. It also affects other symbols of the same type, but not integrals. If you want the bounds beside the symbol even in display, load the package with:
\usepackage[nosumlimits]{amsmath}The guide describes nosumlimits as always placing the scripts to the side, even in displayed equations. Limit notation for the lim operator is explained in limit notation in LaTeX, and the integral equivalents in integrals in LaTeX.
Products over several indices
amsmath provides \substack for a multiline subscript. The user’s guide gives a sum example with two index conditions stacked under the operator, and the same construction can be written with \prod:
\prod_{\substack{1\le i\le m \\ 1\le j\le n}} a_{ij}The same guide documents \sideset, which places symbols at the corners of a large operator (for example a prime after a sum), and states it is not designed to be applied to anything other than sum-class symbols. Treat it as a tool for sums, and check the compiled output before relying on it with a product.
Output and how to read it
In display style you get a large ∏ with the index condition centred below and the upper limit centred above. Inline, you get a smaller ∏ with the bounds as a subscript and superscript to its right. Both mean the same: multiply the factor over every integer from the lower bound to the upper bound. For the sum counterpart, the Overleaf page shows \sum_{n=1}^{\infty} 2^{-n} = 1; an infinite product is written the same way with \prod and \infty as the upper bound.
Troubleshooting
| Symptom | Likely cause | Fix |
|---|---|---|
| Only the first character of a bound is subscripted | Missing braces on a multi-character bound | Write _{i=1} and ^{n}; the Overleaf documentation notes braces are needed for multi-character scripts. |
| Bounds sit beside the symbol in display math when you want them above and below | nosumlimits loaded |
Remove the package option; the default sumlimits places them above and below in display. |
| A capital Greek letter appears instead of an operator | \Pi used instead of \prod |
Use \prod for the product operator. |
Free alternatives and where to run it
| Option | What this guide’s sources say |
|---|---|
| Overleaf | Its documentation (read 2026-11-07) provides the \prod examples used above. See Overleaf alternatives for collaborative LaTeX writing for collaboration limits. |
| TeX Live or MiKTeX on your own machine | CTAN lists amsmath as contained in both, so the limit options above are available locally (CTAN, read 2026-11-07). |
| MathJax for web pages | See the CASRAI guide to MathJax LaTeX setup for configuring delimiters for web display. |
FAQ
How do you write prod in LaTeX?
Type \prod_{i=1}^{n} followed by the factor, inside math mode. _ sets the lower bound and ^ sets the upper bound.
Is \prod part of amsmath?
The sources read for this guide show \prod in ordinary math examples without mention of a package. The limit-placement options (sumlimits, nosumlimits) and \substack are documented in the amsmath user’s guide.
How do I put the limits beside the product in a displayed equation?
Load \usepackage[nosumlimits]{amsmath}; the amsmath guide says this always places scripts to the side, even in display.
What is the difference between \prod and \Pi?
\prod is the large operator for products. \Pi is the capital Greek letter; see Greek symbols in LaTeX.
Sources
- Overleaf, “Integrals, sums and limits”: https://www.overleaf.com/learn/latex/Integrals,_sums_and_limits (read 2026-11-07)
- Overleaf, “Subscripts and superscripts”: https://www.overleaf.com/learn/latex/Subscripts_and_superscripts (read 2026-11-07)
- amsmath user’s guide (amsldoc.pdf), CTAN: https://mirrors.ctan.org/macros/latex/required/amsmath/amsldoc.pdf (read 2026-11-07)
- CTAN, amsmath package page: https://ctan.org/pkg/amsmath (read 2026-11-07)
