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 ${\displaystyle f}$ and its definition in terms of the semi-axes ${\displaystyle a}$ and ${\displaystyle b}$ of the resulting ellipse or ellipsoid is

The compression factor is ${\displaystyle b/a}$ in each case; for the ellipse, this is also its aspect ratio.

There are three variants: the flattening ${\displaystyle f,}$ sometimes called the first flattening, as well as two other "flattenings" ${\displaystyle f'}$ and ${\displaystyle n,}$ each sometimes called the second flattening, sometimes only given a symbol, or sometimes called the second flattening and third flattening, respectively.

In the following, ${\displaystyle a}$ is the larger dimension (e.g. semimajor axis), whereas ${\displaystyle b}$ is the smaller (semiminor axis). All flattenings are zero for a circle (a = b).

The flattenings can be related to each-other:

The flattenings are related to other parameters of the ellipse. For example,

where ${\displaystyle e}$ is the eccentricity.