Case 1
- Semi-axis a (half the width)
- 3
- Semi-axis b (half the depth)
- 4
- Semi-axis c (half the height)
- 5
251.327412
Open with these valuesEllipsoid Volume Calculator
251.327412units³
Result: 251.327412 units³An ellipsoid holds 4⁄3 × π times the product of its three semi-axes. Semi-axes 3, 4 and 5 give 4⁄3 × π × 60 = 80π ≈ 251.327412 cubic units. Enter half-widths measured from the centre, not full diameters — using diameters would overstate the volume eightfold.
The numbers at a glance
Held fixed: Semi-axis a (half the width) 3.000, Semi-axis b (half the depth) 4.000.
| Semi-axis c (half the height) | Result |
|---|---|
| 2.000 | 100.530965 |
| 4.000 | 201.061930 |
| 5.000Your value | 251.327412 |
| 6.000 | 301.592895 |
| 8.000 | 402.123860 |
| 10.000 | 502.654825 |
Worked examples
Case 2
- Semi-axis a (half the width)
- 1
- Semi-axis b (half the depth)
- 1
- Semi-axis c (half the height)
- 1
4.188790
Open with these valuesCase 3
- Semi-axis a (half the width)
- 5
- Semi-axis b (half the depth)
- 3
- Semi-axis c (half the height)
- 2
125.663706
Open with these valuesHow it's calculated
V = 4 ÷ 3 × π × a × b × c
- StepMeasure each axis right through the centre and halve it.
- StepMultiply the three semi-axes together.
- ResultMultiply that product by 4π ÷ 3 ≈ 4.188790.
Reference table
| Semi-axes a, b, c | Exact | Volume |
|---|---|---|
| 1, 1, 1 | 4π ÷ 3 | 4.188790 |
| 2, 2, 2 | 32π ÷ 3 | 33.510322 |
| 10, 1, 1 | 40π ÷ 3 | 41.887902 |
| 5, 3, 2 | 40π | 125.663706 |
| 3, 4, 5 | 80π | 251.327412 |
Questions
How do I calculate the volume of an ellipsoid?
Multiply the three semi-axes together, then by 4π ÷ 3 ≈ 4.188790. For semi-axes 3, 4 and 5 that is 4⁄3 × π × 60 = 80π ≈ 251.327412 cubic units.
What is an ellipsoid?
An ellipsoid is a squashed or stretched sphere: a smooth solid with three perpendicular axes that may each have a different length. Eggs, rugby and American footballs and watermelons are all roughly ellipsoidal. It is described by its three semi-axes a, b and c.
Should I enter the semi-axis or the full diameter?
The semi-axis, meaning half the width along each axis, measured from the centre out to the surface. If you only have full diameters, halve each one first. Entering diameters would overstate the volume by a factor of eight.
How is an ellipsoid related to a sphere?
A sphere is the special case where all three semi-axes are equal. Then a × b × c becomes r³ and the formula collapses to the familiar 4⁄3 × π × r³, which is why the row 1, 1, 1 shows 4π ÷ 3.
Which units does the answer use?
Whatever you entered, cubed. Semi-axes in centimetres give cubic centimetres, in inches cubic inches. All three must use the same unit.
Sources and last check
Information, not professional advice.