In this letter the core-core-valence Auger transitions of an atomic impurity, both in bulk or adsorbed on a jellium-like surface, are computed within a DFT framework. The Auger rates calculated by the Fermi golden rule are compared with those determined by an approximate and simpler expression. This is based on the local density of states (LDOS) with a core hole present, in a region around the impurity nucleus. Different atoms, Na and Mg, solids, Al and Ag, and several impurity locations are considered. We obtain an excellent agreement between KL1V and KL23V rates worked out with the two approaches. The radius of the sphere in which we calculate the LDOS is the relevant parameter of the simpler approach. Its value only depends on the atomic species regardless of the location of the impurity and the type of substrate. (C) 2003 Elsevier B.V. All rights reserved.