Triple Integral in LaTeX (\iiint)

Where it is used

Triple integral sign, used to integrate over a three-dimensional solid region.

Volume integrals such as \iiint_V \rho\,dV for total mass, or the left side of the divergence theorem \iiint_V \nabla\cdot\mathbf{F}\,dV, use this symbol. Like \iint, it spaces the three signs closer than \int\int\int would, so the result reads as one operator. The region goes in a single subscript; for explicit iterated bounds on each variable, chain separate \int commands instead. There is also \iiiint for four signs and \idotsint, which draws two signs separated by dots for an n-fold integral. In spherical coordinates, remember the Jacobian: dV = r^2\sin\theta\,dr\,d\theta\,d\phi.

Minimal compilable example

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

\documentclass{article}
\usepackage{amsmath}
\begin{document}
Triple Integral: $\iiint$

\[ \iiint_V \rho(x,y,z)\,dV \]
\end{document}

Related symbols

• Contour Integral\oint
• Double Integral\iint
• Derivative\frac{d}{dx}
• Integral\int_{a}^{b}
• Partial derivative operator\frac{\partial}{\partial x}
• Integral\int

Frequently asked questions

How do I write Triple Integral in LaTeX?

Type \iiint in math mode, for example $\iiint_V \rho(x,y,z)\,dV$. Load amsmath first with \usepackage{amsmath}.

Which package do I need for \iiint?

\iiint needs amsmath: add \usepackage{amsmath} to your preamble before the document starts.

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

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