The experimental phase diagrams at T=0 of the refractory compounds ZrC, NbC and MoC have been reproduced with great accuracy from first principles theory. The energy of formation for these compounds has been calculated for several phases and stoichiometries in order to understand, for example, the differences and changes in homogeneity ranges found in these systems. This determination of relative phase stabilities for a wide range of concentrations is necessary for first principles determination of phase diagrams for these compounds with complex bonding and structural properties as well as technological importance.