Pyramid Volume Calculator

V = (1/3) × base area × height. For square / rectangular / triangular bases.

Inputs

Result

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How to use this calculator

  • Pick base shape.
  • Enter base dimensions and pyramid height (perpendicular).
  • Read volume.

About this calculator

A pyramid has a polygonal base and triangular faces meeting at an apex. Volume = (1/3) × base area × height. The (1/3) factor is the same as for cones (Cavalieri's principle). Examples: square base = traditional Egyptian pyramid; triangular base = tetrahedron variant. The Great Pyramid of Giza has ~230 m sides × 147 m height → ~2.6 million m³.

Frequently asked

Why (1/3) factor?+
Same reason as cones: a pyramid on the same base and height has 1/3 the volume of the corresponding prism. Geometric proof via Cavalieri.
Height = perpendicular?+
Yes — height is the perpendicular distance from apex to base. Not the slant edge or face.
Tetrahedron volume?+
A regular tetrahedron with edge a: V = a³ / (6√2) ≈ 0.118 a³. All four triangle faces are equilateral.
Egyptian pyramids?+
Khufu (Great Pyramid): square base 230.4 m, height 146.6 m → ~2.6 million m³. Made of ~2.3 million blocks.
Frustum of pyramid?+
Pyramid with top cut off. V = (1/3)h(A₁ + A₂ + √(A₁A₂)) where A₁, A₂ are base areas.

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