# Ellipsoid

Calculates ellipsoid and spheroid volume and surface area.

## Scalene ellipsoid

Ellipsoid is a sphere-like surface for which all cross-sections are ellipses.

Equation of standard ellipsoid body in xyz coordinate system is
,
where a - radius along x axis, b - radius along y axis, c - radius along z axis.
The following formula gives the volume of an ellipsoid:
The surface area of a general ellipsoid cannot be expressed exactly by an elementary function. Knud Thomsen from Denmark proposed the following approximate formula: , where p=1.6075

Digits after the decimal point: 5
Volume

Surface area (approx.)

## Spheroids

If any two of the three axes of an ellipsoid are equal, the figure becomes a spheroid (ellipsoid of revolution). There are two kinds of spheroid: oblate spheroid (lens like) and prolate spheroid (сigar like).
Volume of spheroid is calculated by the following formula:

Unlike ellipsoids, exact surface area formulas exist for spheroids:

For oblate spheroid (a = b > c):

where angular eccentricity

For prolate spheroid (a = b < c):

where angular eccentricity

Digits after the decimal point: 5
Volume

Surface area