How this calculator works
An ellipsoid is the three-dimensional version of an ellipse. It can be squashed independently along three perpendicular axes, and the semi-axes a, b and c are the distances from the centre to the surface along those axes. For a sphere all three are equal, and the formula reduces to 4/3 πr³. Setting two axes equal gives a spheroid, such as the shape of a rugby ball or a planet flattened by rotation.
Formula
V = (4/3)πabc; a = 3V/(4πbc); b = 3V/(4πac); c = 3V/(4πab).
Worked example
Semi-axes of 3 m, 2 m and 1 m give V = (4/3)π × 6 = 8π ≈ 25.133 m³. If the volume is 8π and axes b and c are 2 m and 1 m, the missing semi-axis a comes back as 3 m.
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Frequently asked questions
What is a semi-axis?
It is half of the full width of the ellipsoid along one of its three axes. A semi-axis of 3 m means the ellipsoid is 6 m wide in that direction, measured through the centre.
Is an ellipsoid the same as an oval?
Only loosely. An oval is an informal word for any rounded elongated shape. An ellipsoid has a precise definition: a sphere stretched or compressed along three perpendicular axes.
What happens if all three semi-axes are equal?
The ellipsoid becomes a sphere of that radius, and the volume formula becomes the familiar 4/3 πr³. Entering 2 m for all three axes gives about 33.510 m³.