Universal mathematical relations between the mean relative size of metallic crystallites (d(rel(VS))) and their dispersion (FE) in supported metal catalysts have been developed. The relations are : d(rel)(VS) = 5.01/FE for FE < 0.2, and d(rel(VS)) = 3.32/FE1.23 for 0.2 equal to or less than FE equal to or less than 0.92, where d(rel(VS)) = d(VS)/d(at), (d(VS)) is the volume-surface mean diameter of an assembly of particles of different sizes, and d(at) is the atomic diameter of a given metal. It is shown that for FE > 0.2 the commonly used definition of d(VS) should be modified. The developed relations apply well to various thermodynamically probable crystallite shapes including fee cubooctahedra of varying geometry, icosahedra, surface-reconstructed cubooctahedra, bcc rhombic dodecahedra, and hcp truncated bipyramids. The new relations are more precise than the commonly used equation d(VS) = a/FE, where a is a constant specific to a given metal.