Ellipsoid Volume and Surface Area Calculator

What this tool does

An ellipsoid is a sphere stretched by different amounts along three directions; its volume is simply 4/3 π times the three semi-axes, the half-widths, not the full widths. The surface area is another matter: for three different axes it has no formula with elementary functions, so this calculator uses Knud Thomsen's approximation, which is never off by more than about 1.06 % and is exact for a sphere. Earth itself is a slightly flattened ellipsoid, 21 km shorter from pole to pole than across the equator, and so are eggs, rugby balls, many tanks and the shape doctors use to estimate the volume of an organ from three measurements.

Formula

V = 4/3 π a b c · S ≈ 4π [((ab)^p + (ac)^p + (bc)^p) ÷ 3]^(1/p), p = 1.6075

Variables

Worked example

Limitations

• Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.