Ellipsoid Calculator

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Calculate the volume and surface area of an ellipsoid with three distinct axes.

Ellipsoid Dimensions

Semi-axis X (a)

Semi-axis Y (b)

Semi-axis Z (c)

Ellipsoid Metrics

2010.62

Volume (V)

The three-dimensional volume and surface area of the ellipsoid.

Surface Area (SA)798.01

About this calculator

What is an Ellipsoid?

An ellipsoid is a three-dimensional surface that is the analog of an ellipse in two dimensions. It is essentially a 'squashed' sphere. Every plane section of an ellipsoid is an ellipse. If all three axes are equal, the ellipsoid becomes a perfect sphere.

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Pro Tips

V = (4/3)πabc: Volume is easy to calculate exactly.
SA ≈ 4π((aᵖbᵖ + aᵖcᵖ + bᵖcᵖ)/3)¹/ᵖ: Surface area is much harder and usually requires the Knud Thomsen approximation.
An oblate ellipsoid (like Earth) has a shorter Z-axis, while a prolate ellipsoid (like a rugby ball) has a longer Z-axis.

Fun Facts

"The Earth is not a sphere, but an 'Oblate Spheroid' (a type of ellipsoid) due to its rotation, bulging at the equator."
"Rugby balls and American footballs are prolate spheroids."
"Melted chocolate drops in 'M&M's' are oblate spheroids."

Formula: V = (4/3)πabc