The term fundamental plane is used for a three-way relation observed in the characteristics of elliptical galaxies, that forms a plane in the space involving (logarithms of) the effective radius of the galaxy (Re), the mean intensity (<I>e, for the mean intensity out to Re, a specification for a surface brightness measurement), and the stellar velocity dispersion at the center, σo. In other words, in the space, (log Re, log <I>e, log σo). As it is empirical, various efforts have produced slightly different equations, but here is one example:
log Re = 1.24 log σo - 0.82 log <I>e
Re = σo1.24 <I>e-0.82
Since the velocity dispersion and surface brightness are observable, the relation yields information about the galaxy's radius and through other relations, additional characteristics.
While observations have shown the relation, some classes of elliptical galaxies do not fit, and the relation is more reliable if they are excluded.