Pyramid Frustum Volume Calculator

About this calculator

A frustum is what remains of a pyramid after its top is sliced off by a plane parallel to the base — a shape with two similar parallel faces (typically squares) of different sizes joined by trapezoidal sides. Its volume is given by V = (h/3)(A₁ + A₂ + √(A₁·A₂)), where A₁ and A₂ are the areas of the top and bottom faces and h is the perpendicular height between them; for a square frustum this reduces to a formula using just the two edge lengths and the height.

This is actually one of the oldest surviving pieces of applied mathematics: the Moscow Mathematical Papyrus (c. 1850 BCE) contains the earliest known correct calculation of a frustum’s volume, likely developed for estimating grain storage or building materials in ancient Egypt. Today the same formula shows up wherever a truncated-pyramid shape is built for real: architects use it for hip-roof and tapered-tower volumes, engineers use it to size hoppers and grain silos, and manufacturers use it to compute material volume for truncated-pyramid molds and packaging.