Pyramid Surface Area Calculator

About this calculator

For a square pyramid, total surface area is the base square plus four congruent triangular faces. The tricky part is that the triangles’ height isn’t the pyramid’s vertical height — it’s the slant height, the distance from the apex down the middle of a triangular face, found with the Pythagorean theorem as l = √(h² + (s/2)²), where h is the vertical height and s is the base edge.

Once you have the slant height, the lateral surface area (the four triangular faces only, excluding the base) is 2 × s × l, and the total surface area adds the base: s² + 2sl. Architects, engineers and construction estimators use these formulas when calculating material for pyramid-shaped roofs, tent structures, or packaging, and they’re a staple of solid-geometry coursework. This calculator takes the base edge and vertical height of a square pyramid and returns the slant height along with the lateral and total surface areas.