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How does the geoid differ from an oblate spheroid?

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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.

The geoid and the oblate spheroid are both models used to represent the figure of Earth, but they differ significantly in their mathematical precision and physical basis.

An oblate spheroid (or ellipsoid of revolution) is a simple geometric model that approximates Earth as a sphere flattened at the poles due to its rotation. It is defined by two parameters: the equatorial radius and the polar radius (or the degree of flattening). Because it is a smooth, regular mathematical surface, it is frequently used as a reference figure for geodetic calculations.12

In contrast, the geoid is a more complex, irregular model that represents an equipotential surface of Earth's gravitational field. It coincides with mean sea level over the oceans and extends as an imaginary surface through continental areas. Unlike the oblate spheroid, the geoid accounts for local variations in Earth's mass and density, which cause the surface to warp and undulate. Consequently, the geoid is not a simple mathematical form and serves as a vital reference for measuring precise elevations.13