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How is Earth’s flattening calculated from its equatorial and polar radii?

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Diagram showing the deflection of the vertical from the geoid to the ellipsoid or spheroid, with labeled lines for geoid, spheroid, rock surface, ocean, and geoid height in a geology context. — geoid Deflection of the vertical from the geoid to the spheroid.

Earth’s flattening, denoted by the symbol $f$ , is a parameter used to describe the degree to which the planet deviates from a perfect sphere into an oblate spheroid.

It is calculated by determining the difference between the semimajor axis ( $a$ ), which represents the equatorial radius, and the semiminor axis ( $b$ ), which represents the polar radius, and then dividing that difference by the semimajor axis. The formula is expressed as follows:

$f = \frac{a - b}{a}$

In this context, the semimajor axis ( $a$ ) and semiminor axis ( $b$ ) for Earth differ by approximately 21 kilometres (13 miles), resulting in a flattening value of roughly 1 part in 300. This reference ellipsoid serves as a simplified geometric model for geodesy, providing a more accurate representation of the planet's shape than a sphere for scientific and navigational calculations.12