VolLab

Ellipsoid Volume Calculator

A sphere stretched along up to three different axes.

Semi-axis a

Semi-axis b

Semi-axis c

Volume

251.327

What you entered

Semi-axis a: 5Semi-axis b: 3Semi-axis c: 4

1
Volume = 4/3 × π × a × b × c
(4/3) × π × 5 × 3 × 4= 251.3274

Result

Volume: 251.327

An ellipsoid with semi-axes 5, 3, and 4 has a volume of 251.327. Setting all three semi-axes equal gives the familiar sphere formula.

Ellipsoid volume from three semi-axes

Volume is four thirds pi times the three semi-axes multiplied together - the sphere formula with three different radii.

a	b	c	Volume
3	2	2	50.27
4	3	2	100.53
5	4	3	251.33
6	4	3	301.59
8	5	4	670.21
10	6	5	1256.64

When all three semi-axes are equal the formula collapses to four thirds pi r cubed, the sphere. Two equal axes give a spheroid - the shape of a rugby ball if the third is longer, or a discus if it is shorter. Volume is linear in each axis separately, so doubling any one of them doubles the volume, while doubling all three multiplies it by eight. Use semi-axes measured from the centre, not full widths.

A sphere is a special ellipsoid

Set a = b = c and the ellipsoid volume formula 4/3·π·a·b·c collapses to 4/3·π·r³ — the familiar sphere volume formula. An ellipsoid is a sphere independently stretched along each axis.

Where ellipsoids show up

Rugby balls, planets (which bulge slightly at the equator), and pharmaceutical capsules are all commonly modeled as ellipsoids for volume estimates.

Frequently asked questions

How do I calculate the volume of an ellipsoid?

Volume = (4/3) × π × a × b × c, where a, b, c are the three semi-axes. An ellipsoid with semi-axes 5, 3, 2: V = (4/3) × π × 5 × 3 × 2 = 125.7 cubic units. When a=b=c, it becomes a sphere.

What is a prolate vs oblate ellipsoid?

Prolate: one axis is longer (like a rugby ball or egg) — stretched along the polar axis. Oblate: flattened at the poles (like Earth) — stretched along the equator. Both use the same volume formula.

Is Earth an ellipsoid?

Earth is an oblate ellipsoid — slightly flattened at the poles and bulging at the equator. Equatorial radius ≈ 6,378 km, polar radius ≈ 6,357 km. The difference is only 21 km (0.3%), but it matters for GPS and satellite calculations.