Density of states calculations for the tight-binding model with diagonal disorder are presented. An instanton approach is used to calculate the tails of the spectrum, including all prefactors. It is shown that a Hartree resummation improves the predictions. Furthermore, an effective-medium approximation is used to calculate the density of states in the band. Combining both approaches, a prediction is obtained for all energies. Large numerical simulations have been performed to check the validity of the approach for the Anderson model with Gaussian and with binary disorder on square and simple cubic lattices. The theory agrees well with the simulations.