Triple Integral Calculator

About this calculator

A triple integral extends the idea of an integral to three dimensions, summing a function’s values over a solid region — commonly a rectangular box defined by bounds [x0, x1] × [y0, y1] × [z0, z1]. When the integrand is a constant k rather than a function of x, y, and z, the integral simplifies dramatically: it equals k times the volume of the box, i.e. k × (x1−x0) × (y1−y0) × (z1−z0).

This special case shows up constantly in multivariable calculus courses as a stepping stone before tackling variable integrands, and in physics and engineering it directly computes quantities like the mass of a uniform-density block (density × volume) or a constant charge density’s total charge. This calculator takes your constant k and the six box bounds and evaluates the triple integral.