We derive an analytical expression for the scattering of an s-polarized plane wave from a perfectly conducting self-affine one-dimensional surface in the framework of the Kirchhoff approximation. We show that most of the results can he recovered by means of a scaling analysis. We identify the typical slope taken over one wavelength as the relevant parameter controlling the scattering process. We compare our predictions with direct numerical simulations performed on surfaces of varying roughness parameters and confirm the broad range of applicability of our description up to very large roughness. Finally are verify that a nonzero electrical resistivity, provided that it is small, does not invalidate our results.