Right Square Pyramid Calculator
Find the volume, slant height, lateral surface area, and total surface area of a right square pyramid from base side length and height.
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 all pyramids — one-third of base area times 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 2.58 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 (apex to base corner) is √(h² + a²/2 × √2)… actually it is √(h² + (a√2/2)²) = √(h² + a²/2). That is always longer than the slant height. The surface area formula uses slant height, not edge length.