Flattening

Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution (spheroid) respectively.

The usual notation for flattening is

and its definition in terms of the semi-axes

of the resulting ellipse or ellipsoid is The compression factor is

in each case; for the ellipse, this is also its aspect ratio.

is the larger dimension (e.g. semimajor axis), whereas

is the smaller (semiminor axis).

The flattenings can be related to each-other: The flattenings are related to other parameters of the ellipse.

A circle of radius a compressed to an ellipse.
A sphere of radius a compressed to an oblate ellipsoid of revolution.