Ellipsoid Volume Calculator
From three semi-axes, get the volume — the single number that tells you how much space an ellipsoid encloses.
Three semi-axes in, volume out
Enter the three semi-axes a, b, and c and the calculator returns the volume (4/3)·π·a·b·c straight away.
Use semi-axes, not full axes
Each input is half the width along that axis (centre to surface), not the full diameter — and all three must share one length unit, so don't mix centimetres with inches.
What is an ellipsoid volume calculator?
Three half-widths in, volume out
An ellipsoid is a squashed or stretched sphere — a smooth, egg-like solid whose three principal axes can each have a different length. It is fully described by its three semi-axes a, b, and c, the half-widths from the centre out to the surface along each axis. This calculator turns those three numbers into the volume, the space the ellipsoid encloses. It is the tool for estimating the volume of an egg, a rugby or American football, a watermelon, a planet's slightly flattened shape, or a tumour or organ in medical imaging. A sphere is just the special case where a = b = c.
Enter the three semi-axes in any single length unit to get the ellipsoid's volume instantly.
One short formula, built from the three semi-axes and the constant π (about 3.14159).
volume = (4/3) × π × a × b × cThe formula generalises the familiar sphere volume (4/3)·π·r³: a sphere is an ellipsoid whose three semi-axes are all equal to the radius r, so a·b·c becomes r³. Multiplying the three different half-widths together replaces that cube and accounts for the stretch or squash along each axis.
Suppose you have an ellipsoid with semi-axes a = 3, b = 4, and c = 5.
Multiply the semi-axes
3 × 4 × 5 = 60 — the product of the three half-widths.
Apply the constant factor
(4/3) × π ≈ 4.188790 — the fixed factor shared by every ellipsoid.
Volume
4.188790 × 60 = 251.327412 cubic units — the space inside.
The volume (about 251.327412 cubic units for a = 3, b = 4, c = 5) is how much the ellipsoid holds. The single most useful insight is that volume scales linearly with each semi-axis: double just one of them and the volume doubles; double all three and the volume grows eightfold (2 × 2 × 2). That makes the formula easy to reason about when you stretch or shrink a shape along one direction. It also explains why a sphere is the most "efficient" ellipsoid: for a fixed total of the three semi-axes, the volume is largest when they are all equal, which is the a = b = c sphere case — anything more elongated encloses less. In practice this is why egg- and football-shaped objects feel smaller than a ball whose widest measurement looks the same: the narrower axes pull the volume down. Always double-check you entered semi-axes (half-widths), not full diameters — using diameters would overstate the volume by a factor of eight.
The formula is exact, but a couple of practical points are worth keeping in mind.
Semi-axes, true ellipsoids, and consistent units
This formula describes a true ellipsoid — a smooth surface with three perpendicular axes. A real egg or football is only approximately an ellipsoid, so a measured object's volume will differ slightly from the computed value. Each input must be a semi-axis (half the width, centre to surface), not the full diameter. The semi-axes are also unit-agnostic, so the answer is only meaningful if you keep one unit throughout: semi-axes in centimetres give a volume in cubic centimetres, never a mix.