Ellipsoid Volume Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/10/2026
The volume of an ellipsoid is calculated with V = (4/3) × π × a × b × c, where a, b, and c are its three semi-axes. For an ellipsoid with semi-axes 3, 4, and 5 cm, the volume is about 251.33 cm³.
Explanation
An ellipsoid is the generalization of a sphere stretched or flattened along three independent perpendicular directions: instead of a single radius common to all directions, it has three distinct semi-axes, one for each dimension of space. Its volume formula directly generalizes that of our sphere volume calculator: when the three semi-axes are equal (a = b = c = r), the formula (4/3)πabc reduces exactly to (4/3)πr³, the usual formula for the volume of a sphere — a property verified directly by this calculator's second test case, where three semi-axes equal to 3 cm give exactly the same volume as a sphere of radius 3 cm. The ellipsoid appears frequently in practice to model naturally elongated or flattened shapes: the approximate shape of the Earth itself (slightly flattened at the poles, an ellipsoid of revolution rather than a perfect sphere), a rugby ball, or certain egg-shaped biological organs.
Example: ellipsoid with semi-axes 3, 4, and 5 cm
Inputs
Semi-axis a: 3 cm. Semi-axis b: 4 cm. Semi-axis c: 5 cm.
Calculation
V = (4/3) × π × 3 × 4 × 5 = (4/3) × π × 60 = 80π ≈ 251.33 cm³.
Result
The volume of this ellipsoid is about 251.33 cm³.
Frequently asked questions
What is the difference between an ellipsoid and an ellipse?
An ellipse is a plane figure, in two dimensions (calculated by our ellipse area and perimeter calculator); an ellipsoid is its three-dimensional equivalent, a solid rather than a closed curve. An ellipsoid can be seen as the result of an ellipse rotated or stretched into a third direction of space.
What happens if only two of the three semi-axes are equal?
In that case, the ellipsoid is called a "spheroid" (or ellipsoid of revolution): it has a rotational axis of symmetry. If the two equal semi-axes are larger than the third, the shape is flattened (an oblate spheroid, like a lens); if they are smaller, the shape is elongated (a prolate spheroid, like a rugby ball). The volume formula stays the same in both cases, only the visual shape changes.
Does this formula apply to the real shape of the Earth?
Approximately yes: the Earth is slightly flattened at the poles because of its rotation, which makes it an oblate spheroid rather than a perfect sphere, with an equatorial radius slightly larger than the polar radius. This ellipsoid formula therefore gives a much better approximation of the Earth's actual volume than a simple sphere formula, even though the difference between the two remains small (Earth's flattening is about 0.3%).