Prismatoid Volume Calculator

About this calculator

The prismoidal formula, V = h⁄6 × (A₁ + 4Aₘ + A₂), computes the volume of a prismatoid — any solid whose cross-sectional area varies smoothly between two parallel end faces — from the area of the bottom face A₁, the area of the cross-section exactly at mid-height Aₘ, the area of the top face A₂, and the perpendicular height h between the two ends.

Because it's essentially Simpson's Rule applied to volume, this single formula gives the exact volume for a remarkable range of shapes — prisms, pyramids, cones, frustums, wedges, spheres and even cylinders — as long as the cross-sectional area varies as a polynomial of degree three or less along the height. Civil engineers use it constantly for earthwork and excavation volumes, and it appears in surveying, mining and construction estimating wherever an irregular but smoothly-tapering solid needs a precise volume.