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. Other terms used are ellipticity, or oblateness. The usual notation for flattening is f and its definition in terms of the semi-axes a and b of the resulting ellipse or ellipsoid is The compression factor is b/a in each case; for the ellipse, this is also its aspect ratio.

Definitions

There are three variants: the flattening f, sometimes called the first flattening, as well as two other "flattenings" f' and n, each sometimes called the second flattening, sometimes only given a symbol, or sometimes called the second flattening and third flattening, respectively. In the following, a is the larger dimension (e.g. semimajor axis), whereas b is the smaller (semiminor axis). All flattenings are zero for a circle ( ). ! style="padding-left: 0.5em" scope="row" | (First) flattening ! style="padding-left: 0.5em" scope="row" | Second flattening ! style="padding-left: 0.5em" scope="row" | Third flattening 

Identities

The flattenings can be related to each-other: The flattenings are related to other parameters of the ellipse. For example, where e is the eccentricity.