Square Pyramid Calculator

About this calculator

A square pyramid has a square base and four triangular faces meeting at an apex directly above the base's center. Its volume is V = (1/3)a²h, where a is the base edge and h is the vertical height — the same one-third factor that appears in every pyramid and cone volume formula, reflecting the fact that a pyramid holds exactly one-third the volume of the prism with the same base and height. Its slant height (the distance from the apex to the midpoint of a base edge, along a triangular face) is found with the Pythagorean theorem as l = √(h² + (a/2)²), and that slant height in turn feeds into the lateral and total surface area formulas.

These formulas aren't just textbook exercises — architects and structural engineers use them when designing pyramidal roofs, skylights, and monuments; the ancient Egyptian pyramids themselves are the most famous real-world application of exactly this geometry; and in construction, the volume formula determines how much concrete, fill, or roofing material a pyramidal structure requires.

This calculator takes the base edge length and height and returns the complete geometry of the pyramid — volume, slant height, lateral surface area and total surface area — in one step.