Right Square Pyramid Calculator

A right square pyramid has a square base and an apex directly above the center. The four triangular sides are congruent isosceles triangles. The base side length is a, and h is the vertical height.

Volume follows the same rule as every pyramid and every cone: one-third of the base area times the height.

Volume = (1/3) × a² × h

The slant height l is the distance from the apex to the midpoint of a base edge, not to a corner. That midpoint sits a/2 away from the center of the base, so:

Slant height l = √(h² + (a/2)²)

Each triangular face has base a and height l. Four faces give:

Lateral SA = 4 × (1/2 × a × l) = 2al Total SA = 2al + a²

The Great Pyramid of Giza has a base side of 230.33 m and an original height of about 146.5 m. Plugging those in gives a volume of roughly 2.59 million cubic meters, consistent with the 2.3 million stone blocks the ancient Egyptians used.

People commonly confuse slant height with edge length. The lateral edge runs from the apex to a base corner, and a corner is further from the center than an edge midpoint is, so:

Lateral edge = √(h² + (a√2/2)²) = √(h² + a²/2)

That is always the longer of the two. The surface area formulas use the slant height, never the edge length, and putting the edge in by mistake overstates the lateral area by the ratio between them. The calculator prints both so you can see the gap. On the Great Pyramid the slant height is 186.3 m and the lateral edge is 219.1 m, a difference of nearly 33 metres.