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How does the geoid differ from a reference ellipsoid?

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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 reference ellipsoid serve different purposes in defining the Earth's shape. While the reference ellipsoid is a simple, smooth geometric model used for mathematical convenience in geodetic calculations, the geoid is a complex, irregular physical model.12

The primary differences include:

Mathematical vs. Physical: The reference ellipsoid is a perfect ellipsoid of revolution defined by specific parameters like the semimajor and semiminor axes. In contrast, the geoid is an equipotential surface that coincides with mean sea level and is everywhere perpendicular to the pull of gravity.123
Regularity: Because of Earth's internal mass variations and density heterogeneities, the geoid is irregular and contains undulations. The reference ellipsoid ignores these local mass concentrations to provide a consistent, simplified surface.132
Utility: The ellipsoid is used as a reference for horizontal positioning, whereas the geoid is essential for measuring precise elevations, as it represents the surface to which water would naturally conform.13