Ellipsoid Volume Calculator
The volume of an ellipsoid — a sphere stretched along three axes, the shape of an egg, a rugby ball or a planet.
An ellipsoid is a sphere scaled by a different factor along each axis, so its volume is ⁴⁄₃πabc where a, b and c are the semi-axes.
How the ellipsoid volume calculator works
An ellipsoid is a sphere scaled by a different factor along each axis, so its volume is ⁴⁄₃πabc where a, b and c are the semi-axes. When all three are equal it collapses to the sphere's ⁴⁄₃πr³. Real planets are close to this shape: spin flattens them slightly at the poles, making an oblate spheroid where two axes match and the third is shorter.
Formula: cone ⅓πr²h; pyramid ⅓lwh; torus 2π²Rr²; hemisphere ⅔πr³; ellipsoid ⁴⁄₃πabc
Worked examples
| Inputs | Volume | Note |
|---|---|---|
| Semi-axes 6, 4 and 3 | 301.5929 | 301.6 |
| A rugby ball, 14 by 9 by 9 cm | 4,750.0881 | 4,750 cm³ |
| Equal axes — a sphere | 523.5988 | 523.6 |
FAQFrequently asked questions
What is the volume of an ellipsoid?
⁴⁄₃πabc, where a, b and c are the three semi-axes.
What is a semi-axis?
Half the full width across that direction, measured from the centre.
Is a sphere an ellipsoid?
Yes — the case where all three semi-axes are equal.
What is an oblate spheroid?
An ellipsoid with two equal axes and a shorter third — the shape spinning planets settle into, Earth included.
How do I measure an egg?
Take the length and the width, halve each; use the width for both of the shorter axes.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Australian Curriculum (ACARA) — Mathematics — the terms and methods taught in Australian schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.