Prismoidal Volume Calculator

About this calculator

Civil engineers computing earthwork — cut-and-fill volumes for roads, dams and excavations — often need the volume of a solid between two parallel cross-sections that aren't uniform in shape. The prismoidal formula, V = (L/6)(A1 + 4·Am + A2), estimates that volume from the two end areas (A1, A2), the area at the exact midpoint (Am), and the distance L between the ends.

The formula is a direct application of Simpson's rule for numerical integration, and it is exact for any solid whose cross-sectional area varies as a quadratic (or lower-order) function of position — which covers prisms, pyramids, cones, wedges and most graded roadway sections. Because it uses a middle sample instead of just averaging the two ends, it is noticeably more accurate than the simpler average-end-area method commonly used for quick grading estimates.