Calculations at an ellipsoid. An ellipsoid is a round, three-dimensional shape with different semi-axes and diameters; it is to a sphere as an ellipse is to a circle.
Enter the three semi axes and choose the number of decimal places. Then click Calculate. The surface area is calculated with an approximation formula (by Knud Thomsen), the error is 1.061% at most. The exact calculation would be done with elliptic integrals (Jacobi integrals), whose values can be taken from tables.

Formulas:
A ≈ 4π * ( ((a*b)^{1.6075}+(a*c)^{1.6075}+(b*c)^{1.6075})/3 )^{1/1.6075}
V = 4/3 * π * a * b * c

pi:
π = 3.141592653589793...

The semi axes have the same unit (e.g. meter), the area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit ^{-1}.

If all three semiaxes are different, then it is a triaxial ellipsoid. An ellipsoid in which two of the three semiaxes (the equatorial semiaxes) are the same is a spheroid or ellipsoid of revolution, of which there are two different types: the oblate spheroid with a shorter polar semiaxis and the elongated spheroid with a longer polar semiaxis. In contrast to the ellipsoid, the surface area of spheroids can be calculated algebraically. A spheroid is a mixture of a sphere and an ellipsoid. The oblate spheroid is the simplified form of planets and stars. Two spheroids with the same base but different polar semiaxis make a pretty good egg shape. An ellipsoid divided by an axial plane is a semi-ellipsoid. Any straight section through an ellipsoid always has the shape of an ellipse as long as the section affects more than one point.
The approximate formula for the surface was discovered and published by the Danish geologist Knud Thomsen in 2004.