Calculate ellipsoid volume and Knud Thomsen surface area from the three semi-axes.
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Result
Volume
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Surface area (approx.)
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Equivalent sphere radius
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Shape
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How to use this tool
1
Enter the three semi-axesEnter a, b and c.
2
Choose the unitPick the length unit.
3
Read volumeRead the exact volume.
4
Read surface and shapeRead approximate surface area, equivalent radius and shape.
Formula & worked example
Volume = 4/3 πabc. Surface ≈ 4π(( (ab)^p + (ac)^p + (bc)^p )/3)^(1/p), p = 1.6075.
An ellipsoid with semi-axes 3, 2 and 1 cm has volume 25.1327 cm³.
Limitations — read this before you rely on it
Volume exact; surface area is Knud Thomsen’s approximation. Axes must be semi-axes.
Frequently asked questions
A 3D analogue of an ellipse, with three semi-axes a, b and c; a sphere is the special case a = b = c.
No: it uses Knud Thomsen’s approximation, accurate to about 1.2%.
An ellipsoid with two equal axes, like a rugby ball (prolate) or a squashed sphere (oblate).
Yes: half-lengths from the centre, not full diameters.
The radius of a sphere with the same volume, (abc)^(1/3).