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In mathematics (particularly multivariable calculus), a **volume integral** (∭) is an integral over a 3-dimensional domain; that is, it is a special case of multiple integrals. Volume integrals are especially important in physics for many applications, for example, to calculate flux densities, or to calculate mass from a corresponding density function.

It can also mean a triple integral within a region of a function and is usually written as:

A volume integral in cylindrical coordinates is

Integrating the equation over a unit cube yields the following result:

So the volume of the unit cube is 1 as expected. This is rather trivial however, and a volume integral is far more powerful. For instance if we have a scalar density function on the unit cube then the volume integral will give the total mass of the cube. For example for density function:

- "Multiple integral",
*Encyclopedia of Mathematics*, EMS Press, 2001 [1994] - Weisstein, Eric W. "Volume integral".
*MathWorld*.