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Why do geodesists use a reference ellipsoid instead of the geoid for many calculations?

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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.

Geodesists use a reference ellipsoid instead of the geoid for many calculations primarily because the geoid is not a simple mathematical surface.1

The geoid is an equipotential surface that reflects the irregular distribution of mass within the Earth, leading to gravity anomalies that make it complex to model. In contrast, a reference ellipsoid—a surface generated by rotating an ellipse about its minor axis—provides a straightforward geometric form. Because this ellipsoid is defined by simple parameters like the semimajor axis and flattening, it allows for much simpler mathematical calculations compared to the irregular geoid.123

While the geoid remains essential for determining precise elevations and understanding Earth's gravity field, the reference ellipsoid serves as a more practical, manageable geometric representation for general geodetic positioning and mapping.12