The secondary electron distribution N(E) obtained with a spherical grid retarding field analyser is digitized and stored in a multichannel analyser. The experimental intensities of Auger lines are accurately determined by numerically substracting the background in the N(E) distribution and taking the area under the resulting peaks. Broadening of the lines due to several experimental factors, the multiple structure of the lines and the characteristic energy losses are taken into account. The absolute atomic densities on the surface are deducted from the Auger line intensities by a simple theoretical model. A comparison is made with atomic densities on the surface which are known either from the crystal structure (cleaved muscovite) or from Rutherford backscattering experiments (thin layers of Cu, Ag, Ti) or simply from the specific weight in the case of bulk materials (C, Cu, Ag, Ti). The maximum deviation is smaller than a factor 2. Generally, the values differ by less than 30%, which shows that AES, performed in this way, can give reliable quantitative results for densities ranging from a fraction of a monolayer to the bulk material.