How this calculator works
A pyramid has one third of the volume of a prism with the same base and height. That factor of one third comes from the shape narrowing steadily to a point. For a rectangular base, multiply the base length by the base width to get the floor area, multiply by the height, then divide by three. A square pyramid is the special case where the length and width are equal, and the same volume formula applies.
Formula
V = (length × width × height)/3; length = 3V/(width × height); width = 3V/(length × height); height = 3V/(length × width).
Worked example
A pyramid with a 6 m by 4 m base and a height of 3 m has a base area of 24 m² and a volume of 6 × 4 × 3 / 3 = 24 m³. A square pyramid with a 4 m base and a 3 m height has a base area of 16 m² and a volume of 16 m³.
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Frequently asked questions
Why divide by three?
A prism with the same base and height holds exactly three times the volume of the pyramid. You can see the factor of one third in the general cone and pyramid volume formula, V = Bh/3, where B is the base area.
Does the apex have to be above the centre?
The volume formula holds for any pyramid with a flat base and a single apex, even if the apex is not centred. The slant heights change, but the height and base area are all the volume needs.
How do I use a square base?
Enter the same number as both the base length and the base width. The two dimensions are separate so the same calculator also handles rectangular bases.