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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

InputDefaultAccepted range
Semi-major axis (cm)The longer radius of an ellipse.50 and up
Semi-minor axis (cm)The shorter radius of an ellipse.40 and up
Third radius (cm)The ellipsoid’s third semi-axis; all three equal gives a sphere.30 and up

Step by step

FormulaVolume = 4 ÷ 3 × π × Semi-major axis × Semi-minor axis × Third radius
With the default numbersVolume = 4 ÷ 3 × π × 5 × 4 × 3
AnswerVolume = 251.33 cm³

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)
2.5125.660.12573.107
3.75188.50.18853.557
5251.330.25133.915
7.5376.990.3774.481
10502.650.50274.932

What each result means

ResultAt 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.