Pyramid Volume Calculator

A pyramid is a three-dimensional solid with a polygon base and triangular faces that meet at one apex. Its volume is one third of the base area multiplied by the perpendicular height. Written symbolically, V = B times h divided by 3, where B is base area and h is the shortest distance from the apex to the plane containing the base. This calculator applies that universal formula to square, rectangular, and triangular bases. For a square pyramid, base area is side length squared. A square base measuring 6 units on each side has area 36 square units; with a perpendicular height of 10 units, its volume is 36 times 10 divided by 3, or 120 cubic units. For a rectangular pyramid, multiply base length by base width before applying the one-third factor. An 8 by 3 base with height 9 therefore has volume 72 cubic units. A triangular base requires one additional step. Its area is one half of the triangle base times the corresponding triangle height. That triangle height lies in the base plane and must be perpendicular to the selected triangle base. It is not the height of the pyramid. Once the triangular area is known, multiply it by the separate perpendicular pyramid height and divide by three. Keeping these two heights distinct prevents the most common mistake with triangular pyramids. The one-third factor is not an approximation. Three pyramids with the same base area and perpendicular height occupy the same volume as a corresponding prism, a fact established by geometric dissection and calculus. The apex does not need to sit directly above the base center for the volume formula to work; an oblique pyramid still has volume B h / 3 as long as h is measured perpendicular to the base plane. Slant height and lateral edge length are not substitutes for perpendicular height. Use one consistent length unit for every dimension. If all entries are centimeters, the answer is cubic centimeters; if they are feet, the answer is cubic feet. The interface reports generic cubic units because it does not assume a measurement system. Convert dimensions before calculating if they use mixed units. The tool is suitable for geometry study, container capacity estimates, architectural models, material planning, and checking manual calculations. For irregular polygon bases, calculate the base area separately and apply the same one-third formula.