Flattening

Definition

Let $E$ be an ellipse with semi-major axis $a > 0$ and semi-minor axis $b$ , where $0 \le b \le a$ . The flattening of $E$ is $f = \frac{a - b}{a}.$ The flattening of an ellipsoid of revolution is the flattening of its meridian ellipse, the section by a plane through the axis.

Remarks

Example: the ellipse $x^2/25 + y^2/16 = 1$ has $a = 5$ , $b = 4$ , so $f = 1/5$ . Non-example: the formula is not used with $a < b$ ; for a prolate ellipse one first names the longer semi-axis $a$ . One always has $0 \le f \le 1$ , with $f = 0$ exactly for a circle. The flattening and the eccentricity $e = \sqrt{1 - b^2/a^2}$ are related by $e^2 = f(2 - f)$ . Geodesists often give the inverse flattening $1/f$ , for example $1/f = 298.257223563$ for the WGS 84 ellipsoid.

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Eccentricity concept
Ellipse concept
Flattening definition

Tag	`25RG9WKN36`
URI	`m2://25RG9WKN36`
Kind	definition
Writing	W0 stub
MSC	86A30, 51N20
Defines	Flattening
Uses	Ellipse, Eccentricity
Changed	3 November 2026

Flattening

Definition

Remarks

Reading path

Further reading

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