An ellipsoid volume calculator computes the space inside a 3D oval shape defined by three semi-axes. Enter a, b, and c for instant results in any volume unit.
An ellipsoid is a 3D shape where every cross-section is an ellipse or circle. It is defined by three semi-axes: a (longest), b (middle), c (shortest). When a = b = c, the ellipsoid becomes a sphere.
The Earth is an oblate spheroid (a special ellipsoid where a = b > c) — slightly flattened at the poles and bulging at the equator.
Ellipsoid volume = (4/3) × π × a × b × c.
Where a, b, c are the three semi-axes. This is a generalization of the sphere formula (where all three equal r).
Example: Semi-axes 6, 4, 3 cm: V = (4/3) × π × 6 × 4 × 3 = 301.59 cm³.
Semi-axes ~2.8, 2.1, 2.1 cm: V = (4/3)π×2.8×2.1×2.1 ≈ 51.7 cm³ ≈ 52 mL.
Semi-axes 14.4, 8.5, 8.5 cm: V = (4/3)π×14.4×8.5×8.5 ≈ 4,366 cm³ = 4.37 L.
Semi-axes 6378.1, 6378.1, 6356.8 km: V ≈ 1.083 × 10¹² km³.
Semi-axes 0.9, 0.35, 0.35 cm: V ≈ 0.462 cm³ = 0.462 mL.
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Answers to common questions about the ellipsoid volume calculator.
V = (4/3)πabc where a, b, c are the three semi-axes. Each semi-axis is half the full diameter in that direction.
A sphere has all three axes equal (a = b = c = r). An ellipsoid has at least two different axes. The sphere formula V = (4/3)πr³ is a special case of the ellipsoid formula.
An oblate spheroid is an ellipsoid where a = b > c — flattened at the poles like the Earth. A prolate spheroid has a = b < c — stretched like a rugby ball.
Measure the full diameter (widest distance) in each direction and divide by 2. For an egg: measure length, width at widest point, and depth (usually same as width).
There is no simple exact formula. An approximation: SA ≈ 4π[(aᵖbᵖ + aᵖcᵖ + bᵖcᵖ)/3]^(1/p) where p ≈ 1.6075.