Authalic Sphere

An authalic sphere is a sphere with the same surface area as a given reference ellipsoid, used where an equal-area calculation must work on a sphere rather than an ellipsoid. Authalic means equal area. For the WGS 84 ellipsoid the authalic radius is about 6,371.0072 km, one of the IUGG mean-radius values alongside the arithmetic mean radius and the volumetric radius, all close to 6,371 km. Equal-area map projections and area computations on the globe map ellipsoidal latitude to authalic latitude on this sphere so that areas are preserved. It is a computational surface, not a physical model of Earth.