Ellipsoid Calculator
Semi-axis a
Semi-axis b
Semi-axis c
An ellipsoid is a 3D surface where all cross-sections are ellipses. It is the generalisation of a sphere — a sphere is a special case where all three semi-axes are equal. Ellipsoids model the shape of the Earth, planets, and many biological structures.
- 1Volume = (4/3) × π × a × b × c, where a, b, c are the three semi-axes
- 2Surface area has no closed-form exact formula — Knud Thomsen's approximation is used:
- 3SA ≈ 4π × ((aᵖbᵖ + aᵖcᵖ + bᵖcᵖ) / 3)^(1/p), where p ≈ 1.6075
- 4Accuracy of Thomsen's formula: within 1.061% for all ellipsoids
a=3, b=2, c=1=Volume = 25.13 units³(4/3)π × 3 × 2 × 1 = 8π ≈ 25.13
a=b=c=5 (sphere)=Volume = 523.6 units³(4/3)π × 5³ — confirms formula works for spheres
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