Constant-energy surfaces are calculated for a number of different energies using three different potential functions for copper. Each surface is specified by values for 26 066 radii in k space, the radii being calculated with the Korringa-Kohn-Rostoker band-theory method. The Fermi surfaces obtained are used to discuss the available experimental results. Values for the electronic contribution to the low-temperature specific heat that are not clouded by statistical errors or interpolation difficulties are calculated. The density-of-states curve for a range of energies above the d bands is calculated using the Chodorow potential. Questions concerning the convergence of the calculation are treated in detail.