A general approach for fitting Landau-Devonshire thermodynamic potentials directly from first principles is developed for simple displacive ferroelectric perovskite materials. As the first step, a PbTiO3 potential is parameterized completely from density functional theory calculations as a test case, under the only assumption that the transition between the non-polar and polar phases is of first order. The utility of this approach is assessed by comparing quantities characterizing the phase transition, dielectric and piezoelectric properties and equibiaxial strain-temperature phase diagrams with the predictions of several thermodynamic potentials parameterized from experimental data. In the second step, a similar parameterization is generated for a fictitious polar perovskite SnTiO3, enabling us to predictively evaluate an approximate equibiaxial strain-temperature-spontaneous polarization' phase diagram for its thin films.