We conducted a comparative study of various reconstructions for the (001) surfaces of SrTiO3, BaTiO3, SrZrO3 and BaZrO3 perovskites through calculations within the density functional theory. The atomic structure, the thermodynamic stability and the charge distribution of ideal AO or BO2 terminations, as well as the so-called AO or BO2 double layer reconstructions were analysed, and it was found that of all the BO2 double layer reconstructions the most stable are the (2 x 2) and the (root 2 x root 2) ones. This is mainly due to stress release through the formation of long B-chains. On Ti-based perovskites, these double layer reconstructions were found to be thermodynamically stable, which was not the case for Zr-based perovskites, for which AO terminations dominated most of the stability domain. We also found that the BO2 double layer reconstructions are accompanied by a substantial charge redistribution, with an almost neutral surface plane. This charge redistribution has important consequences for the reactivity and the behaviour of the electric field close to the surface.