An ellipsoid is a mathematical model of the shape of the earth. Mathematically, it is a 3-dimensional shape formed by rotating an ellipse around the shorter of the two axes. The earth's shape is approximately ellipsoidal because the centrifugal force at the equator distorts it slightly. The figure below is enormously exaggerated; the earth would appear to be spherical at the scale of the image.

An ellipsoid is described by two numbers. In the figure below, a is the semi-major axis or equatorial radius, and b is the semi-minor axis or polar radius. When used in calculations, other numbers derivable from a and b are more convenient, and so sometimes an ellipsoid is specified in terms of those other quantities.

• f is the flattening, and is defined to be (a - b) / a.

• e is the eccentricity, and is defined as e2 = 2f - f2.

An ellipsoid is independent of a ["datum"], but a datum will always specify which ellipsoid is to be used. Various ellipsoids have used to approximate the shape of the earth. A few are listed below.

 Ellipsoid Date a b flattening Description WGS 84 1984 6,378,137.0 6,356,752.3 1/298.257223563 Used by the NAVSTAR GPS system. The ellipsoid is very nearly the same as the GRS80. The minor difference in the flattening has no effect on practical calculations. GRS 80 1980 6,378,137.0 6,356,752.3 1/298.257222101 Used by the NAD83 datum. Clarke 1866 6,378,206.4 6,356,583.8 1/294.978 Used by the NAD27 datum, and for older maps within the U.S. Airy 1830 6,377,563.4 6,356,256.9 1/299.325 Used by older maps within Great Britain Bessel 1841 6,377,397.2 6,356,079.0 1/299.153 Used by older maps within Central Europe