Ellipsoid Volume Calculator

Built and fact-checked by the DocNectar team — see our editorial standards

Thanks for rating!

Key Features

Instant Calculation

Get accurate results in real time with our optimized algorithm.

Mobile Friendly

Fully responsive design. Works on all devices & screen sizes.

Privacy Focused

Your data stays on your device. We don't store any inputs.

100% Free

No hidden costs. This tool is completely free forever.

An ellipsoid is essentially a sphere that has been stretched or compressed independently along three perpendicular axes, giving it three (possibly different) semi-axis lengths a, b, and c instead of a single radius. Ellipsoids show up throughout science and engineering: the Earth itself is more accurately modeled as an oblate ellipsoid (slightly flattened at the poles) rather than a perfect sphere in geodesy and GPS systems, egg shapes and certain pharmaceutical capsules approximate ellipsoids, and statisticians use ellipsoids to visualize confidence regions in multivariate data.

How it works

Enter the three semi-axes a, b, and c — each measured from the ellipsoid's center to its surface along one of the three perpendicular directions (not the full end-to-end length). The calculator applies V = (4/3)πabc, which is the direct three-variable generalization of the sphere volume formula (4/3)πr³, replacing the single repeated r with three independent semi-axis lengths.

Enter semi-axis a.
Enter semi-axis b.
Enter semi-axis c.
Click Calculate to see your results.

Examples

a = b = c = 3

V = (4/3)π(3)(3)(3) ≈ 113.10, matching the sphere volume formula for radius 3 — as expected, since equal semi-axes make the ellipsoid a perfect sphere.

a = 5, b = 3, c = 2

V = (4/3)π(5)(3)(2) = (4/3)π(30) ≈ 125.66 cubic units — a flattened, egg-like shape rather than a sphere.

Common mistakes to avoid

Entering full axis lengths (diameters, end-to-end) instead of semi-axes (center-to-surface, half-lengths) — this would double each dimension and inflate the volume by a factor of 8.
Assuming the ellipsoid volume formula also gives the correct surface area — that's a much harder calculation with no simple closed form in general.
Mixing up which semi-axis is a, b, or c when the ellipsoid has a specific orientation that matters for your application.

Frequently asked questions

The ellipsoid becomes a perfect sphere, and the formula collapses exactly to the sphere volume formula (4/3)πr³, since abc becomes r×r×r=r³.

It's the distance from the ellipsoid's center to its surface along one of the three principal directions — analogous to a sphere's radius, but an ellipsoid has three of these (possibly different) values instead of just one.

You get a "spheroid" — either oblate (flattened, like a lentil or the Earth) if the unequal axis is shorter, or prolate (elongated, like a rugby ball) if it's longer.

Unlike volume, which has this simple closed formula, an ellipsoid's surface area generally has no elementary closed form (except in the sphere or spheroid special cases) and requires elliptic integrals to compute exactly.

It increases eightfold (2×2×2=8), since volume is directly proportional to the product of all three semi-axes, and doubling each one multiplies the total product by 2³.

Technically that collapses the solid into a flat 2D ellipse with zero volume — a degenerate case rather than a genuine 3D ellipsoid.

No — multiplication is commutative, so V=(4/3)πabc gives the same result no matter which semi-axis is labeled a, b, or c, though the labeling does matter if you're tracking which physical direction each one corresponds to.

Free Ellipsoid Volume Calculator