Square Pyramid Calculator

About this calculator

This calculator finds the volume and total surface area of a right square pyramid from its base edge length a and height h. Volume is V = ⅓ · a² · h — one-third of the base area times height, the same one-third factor that applies to any pyramid or cone. Total surface area adds the square base (a²) to the four triangular lateral faces, each computed from the slant height, l = √(h² + (a/2)²), as ½·a·l per face.

This geometry underlies real structures from ancient monuments like the Great Pyramid of Giza to modern architectural pyramids (the Louvre Pyramid, hotel atriums), and the volume formula is used to estimate material quantities for pyramid-shaped roofs, tents, and packaging.

Geometry students solving solid-shape problems, architects and engineers estimating material for pyramidal structures, and anyone curious about historical pyramid volumes use this calculator by entering the base edge and height.