An ellipsoid is a stretched sphere with three different radii, such as an egg, a rugby ball or a watermelon. Enter the three semi-axes a, b and c to get the exact volume and an accurate approximation of the surface area.
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The semi-axes are half of the full lengths in each direction. If you measured the full length, width and depth, switch to Diameter mode and type those instead. The surface area has no simple exact formula, so it is marked approximate.
This page is the ellipsoid view of the full 3D Shape Calculator, which covers 24 solids. Every shape button is still available, so you can compare solids without leaving the page.
In every formula, r is a radius, h is a height or depth, and all measurements must use the same unit. The result is in that unit cubed for volume and squared for area.
A melon is about 30 cm long and 20 cm across both ways, so its semi-axes are 15, 10 and 10 cm. The volume is (4/3) × π × 15 × 10 × 10 ≈ 6,283 cm³, about 6.28 litres, and the surface area is roughly 1,692 cm².
Ellipsoids model eggs, rugby and American footballs, melons, some tanks and the shape of the Earth and other planets, which are slightly flattened. Packaging and food designers use the volume to compare shapes.
Why is the surface area of an ellipsoid approximate? There is no simple closed formula for it. The exact value needs elliptic integrals, so this calculator uses Knud Thomsen’s formula, which is accurate to about 1%. The volume is exact.
What are semi-axes? Semi-axes are half of the full length of the ellipsoid along each of its three perpendicular directions, just as a radius is half a diameter.
What is a spheroid? A spheroid is an ellipsoid with two equal axes, such as a rugby ball (prolate) or a flattened planet (oblate). Enter two equal values for those axes.
How do I find the volume if I know the full lengths? Divide each length by two to get the semi-axes, or switch the calculator to Diameter mode and type the full lengths.