Ellipsoid Volume Calculator

Find the volume of an ellipsoid from its three semi-axes a, b, and c, with an approximate surface area too.

Input

Enter the three semi-axes a, b, and c of an ellipsoid to compute its volume and an approximate surface area.

Semi-axis a

Semi-axis b

Semi-axis c

Volume V

37.699112

Surface area (approx.)

57.819012

Semi-axis a

Semi-axis b

Semi-axis c

1.5

The surface area is an estimate from the Thomsen formula with exponent p equals 1.6075, with an error of about one percent.

Lengths use the same unit as the inputs, area is in squared units, and volume is in cubed units.

The volume is V equals four thirds pi a b c, where a, b, and c are the three semi-axes measured from the center to the surface.
When a equals b equals c the ellipsoid becomes a sphere, and the volume matches four thirds pi r cubed.
Surface area has no exact elementary formula, so it is estimated with the Thomsen approximation using the exponent p equals 1.6075. The error is typically around one percent.
Lengths use the same unit as the inputs, while area is in squared units and volume is in cubed units.

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