For a spheroid with equatorial semi-major axis  and polar semi-minor axis , the angular velocity  about  is given by Maclaurin's formula
where  is the eccentricity of meridional cross-sections of the spheroid,  is the density and  is the gravitational constant. The formula predicts two possible equilibrium figures, one which approaches a sphere () when  and the other which approaches a very flattened spheroid () when . The maximum angular velocity occurs at eccentricity  and its value is , so that above this speed, no equilibrium figures exist. The angular momentum  is
where  is the mass of the spheroid and  is the mean radius, the radius of a sphere of the same volume as the spheroid.