What is an ellipsoid?

It's the 3D equivalent of an ellipse — like a squashed or stretched sphere with three different axis lengths (or two equal and one different, for a spheroid).

How is ellipsoid volume calculated?

Volume = (4/3) × π × a × b × c, where a, b, and c are the three semi-axis lengths.

Where are ellipsoid shapes seen in nature or engineering?

Planets (like Earth's slightly flattened shape), rugby balls, and some pressure vessel designs approximate ellipsoid or spheroid shapes.

Ellipsoid Calculator - CalculatorLabs.net

Ellipsoid Calculator

Semi-Axis a

Semi-Axis b

Semi-Axis c

Instant Result

Volume -

Approx. Surface Area -

What Is a Ellipsoid Calculator?

An ellipsoid is a 3D shape that looks like a sphere stretched or squashed along one or more directions — the shape of an egg, a rugby ball, or the Earth itself (which bulges slightly at the equator). This calculator uses the three semi-axes (half the length in each of the three directions) to find the volume and an accurate approximate surface area.

How to Use This Ellipsoid Calculator

Measure the three semi-axes: a (left-right half-length), b (front-back half-length), and c (up-down half-length).
Enter all three values into the fields above.
Click Calculate to get the volume and approximate surface area.
If all three semi-axes are equal, the ellipsoid is simply a sphere.

Formula

Volume = (4/3) × π × a × b × c
Surface Area ≈ 4π × [ ((a^p b^p + a^p c^p + b^p c^p) / 3) ]^(1/p), using Knud Thomsen's approximation with p ≈ 1.6075

Worked Example

A rugby ball has semi-axes of 15 cm, 9 cm, and 9 cm. Volume = (4/3)π(15)(9)(9) ≈ 5,089.4 cm³. Using the approximation formula, Surface Area ≈ 923 cm² — accurate to within about 1% of the true value for most ellipsoid shapes.