Volume of Ellipsoid Calculator
Volume = (4/3)πabc (a, b, c are the three semi-axes)
A Sphere That's Been Stretched
Stretch a sphere unevenly along each axis and the result is an ellipsoid — the shape of a rugby ball, an egg, or a planet's actual (slightly flattened) form. Instead of one radius, it takes three semi-axis lengths, one for each direction, and when all three happen to match, the ellipsoid formula collapses back into the ordinary sphere formula.
The Formula
Volume = (4/3)πabc
where a, b, and c are the three semi-axis lengths. Setting a = b = c = r reduces this to (4/3)πr³, the sphere volume formula.
Worked Example
For semi-axes a = 3, b = 4, c = 5:
| a | b | c | Volume |
|---|---|---|---|
| 3 | 4 | 5 | 251.3274 |
Where This Matters
- Geodesy — Earth is modeled as an oblate ellipsoid (slightly flattened at the poles) for precise mapping and GPS calculations.
- Medical imaging — organ or tumor volumes are frequently approximated as ellipsoids from three measured axis lengths.
- Product design — egg-shaped or football-shaped product volumes follow this same formula.
How to Use This Calculator
- Enter Semi-Axis A.
- Enter Semi-Axis B.
- Enter Semi-Axis C.
- Select Calculate to get the volume.
Related Calculations
When all three axes are equal, use the simpler Sphere Volume Calculator.