The Faber–Jackson relation is an early empirical power-law relation between the luminosity and the central stellar velocity dispersion of elliptical galaxies, first noted by the astronomers Sandra M. Faber and Robert Earl Jackson in 1976. The original relation can be expressed mathematically as:
where the index is observed to be approximately equal to 4, but depends on the range of galaxy luminosities that is fitted. The Faber–Jackson relation is now understood as a projection of the fundamental planes of elliptical galaxies. One of its main uses is as a tool for determining distances to external galaxies.