Molecular-dynamics calculations are reported on fluids of hard ellipsoids over a range of densities and for several ellipsoidal aspect ratios. The pair correlation functions obtained from the simulations are expressed as functions of the minimum surface-to-surface separation, s, measured along the surface normal, ŝ, and angles measured relative to the surface normal. Both isotropic and orientational correlations exhibit simpler behavior in the surface-to-surface than in the more customary center-to-center coordinate representation. For the hard-ellipsoid fluid, the isotropic part of the pair correlation function, giso(s), behaves much like that of a hard-sphere fluid. The surface-to-surface coordinates are well suited for studying pressure and collision rates because these properties depend upon surface contact distributions. They are also useful for studying the orientational order parameter, g2, because they enable one to readily identify a long-range part and geometrical excluded volume contribution.