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.
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This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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