Pyramid Volume Calculator
Compute volume of a regular pyramid (square base): V = (base area × height) / 3. Also shows lateral and total area.
Pyramid volume
The volume of any pyramid is V = (1/3)·A_base·h, where A_base is the base area and h is the perpendicular height from base to apex. Works for square, rectangular, triangular, hexagonal or arbitrary polygonal bases. For a square pyramid: V = a²·h/3. The formula comes from Cavalieri's principle (Democritus ~440 BC, formalised by Euclid). The Great Pyramid of Giza has base 230 m and h ≈ 147 m, giving V ≈ 2.6 million m³ across about 2.3 million stone blocks.
Applications
Civil construction (Egyptian pyramids, pyramidal roofs, modern atriums), packaging (TetraPak cartons are tetrahedra), decor and architecture, 3D modelling and CAD/CAM, geological volume estimates of conical-pyramidal deposits.
FAQ
Does the formula work for any base? Yes, as long as you compute the correct base area: square (a²), rectangle (b·c), triangle (b·h_base/2), regular hexagon (3√3·a²/2).
What is the difference between a regular and an oblique pyramid? A regular pyramid has its apex over the centre of the base; an oblique one does not — but the volume formula stays the same.
Why the factor of 1/3? It comes from integration (Cavalieri): a pyramid fills exactly one-third of the prism with the same base and height.
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