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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Volume/Capacity Ratio (V/C)
Calculate the volume/capacity ratio (degree of saturation), X = V ÷ C, dividing the traffic volume V by the capacity C of the road or intersection. The dimensionless result measures the road's utilization: X near 0 indicates a free road; X = 1 means the road operating exactly at capacity; X > 1 indicates demand above capacity, with growing queues and congestion. The V/C ratio is the main indicator to classify the level of service (LOS A to F) and identify bottlenecks. Values above 0.85–0.90 already indicate near-saturation operation. Enter the volume and the capacity.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.