The geoid is the equipotential surface that would coincide with the mean ocean surface of the Earth if the oceans and atmosphere were in equilibrium, at rest relative to the rotating Earth.

The geoid, also known as an orthodrome, of a sphere is the intersection of the sphere and a plane that passes through the center point of the sphere.

The geoid, also know as ellipsoid of revolution, is a quadric surface obtained by rotating an ellipse about one of its principal axes.