Ellipsoid Volume
Replace r³ in the sphere formula with the product of the three semi-axes. All three equal collapses it back to the sphere formula. Handy for estimating eggs, melons and rugby balls.
Your numbers
Volume
251.33cm³
Litres
0.2513L
Radius
3.915cm
Formula
Volume = 4 ÷ 3 × π × Semi-major axis × Semi-minor axis × Third radius
These are radii, not diameters. Entering diameters gives eight times the volume.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Semi-major axis (cm)The longer radius of an ellipse. | 5 | 0 and up |
| Semi-minor axis (cm)The shorter radius of an ellipse. | 4 | 0 and up |
| Third radius (cm)The ellipsoid’s third semi-axis; all three equal gives a sphere. | 3 | 0 and up |
Step by step
Quick reference table
Results when only Semi-major axis (cm) changes and everything else stays put.
| Semi-major axis (cm) | Volume (cm³) | Litres (L) | Radius (cm) |
|---|---|---|---|
| 2.5 | 125.66 | 0.1257 | 3.107 |
| 3.75 | 188.5 | 0.1885 | 3.557 |
| 5 | 251.33 | 0.2513 | 3.915 |
| 7.5 | 376.99 | 0.377 | 4.481 |
| 10 | 502.65 | 0.5027 | 4.932 |
What each result means
| Result | At default values |
|---|---|
| Volume (cm³)The space a solid holds — length cubed. | 251.33 |
| Litres (L)Capacity in litres; one litre is 1,000 cm³. | 0.2513 |
| Radius (cm)Centre to edge — half the diameter. | 3.915 |
Common mistakes
These are radii, not diameters. Entering diameters gives eight times the volume.
Glossary
- Semi-major axis
- The longer radius of an ellipse.
- Semi-minor axis
- The shorter radius of an ellipse.
- Third radius
- The ellipsoid’s third semi-axis; all three equal gives a sphere.
- Volume
- The space a solid holds — length cubed.
- Litres
- Capacity in litres; one litre is 1,000 cm³.
- Radius
- Centre to edge — half the diameter.
Frequently asked questions
Q. How is Ellipsoid Volume calculated?
Volume = 4 ÷ 3 × π × Semi-major axis × Semi-minor axis × Third radius — Replace r³ in the sphere formula with the product of the three semi-axes. All three equal collapses it back to the sphere formula. Handy for estimating eggs, melons and rugby balls.
Q. Can you walk through an example?
With Semi-major axis 5cm, Semi-minor axis 4cm, Third radius 3cm, the answer is Volume 251.33cm³.
Q. What do I need to enter?
Enter Semi-major axis, Semi-minor axis, Third radius. The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only Semi-major axis (cm) moves the answer to Semi-major axis (cm) 2.5 → Volume (cm³) 125.66 and Semi-major axis (cm) 10 → Volume (cm³) 502.65. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
These are radii, not diameters. Entering diameters gives eight times the volume.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.