Pyramid Volume Calculator
The volume of a square pyramid from its base side and height.
Result
Volume
108.00
How it works
A square-based pyramid's volume is one third of the box that would contain it: V = (1/3) × base² × height. A pyramid with a 6 m base and 9 m height holds (1/3) × 36 × 9 = 108 m³. The factor of one third is not arbitrary — three identical pyramids fit exactly inside a cube of the same base and height. That relationship holds for every pyramid and cone, whatever the base shape, which is why the same one-third appears in the cone volume formula. Careful with the height: it is the vertical distance from the base to the apex, not the slanted edge or the slant height of a face. On the Great Pyramid of Giza (base ≈ 230 m, height ≈ 147 m), the formula gives roughly 2.6 million cubic metres of stone.
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Frequently asked questions
Why divide by three?
A pyramid is exactly one third of a prism with the same base and height.
Does this cover all pyramids?
This is for a square base; other bases replace base² with that base’s area.
Should I use the vertical height or the slant height?
The vertical height — the perpendicular distance from the base to the apex. The slant height runs along a face and is longer; using it would overestimate the volume.
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