Energetics of rare earth, yttrium, and scandium stabilized zirconia and hafnia have been systematically investigated by oxide melt solution calorimetry. The enthalpies of formation with respect to the oxide end members were simultaneously fit to a quadratic function to extract interaction parameters and enthalpies of transition of the oxide end members to the fluorite structure. ZrO2-SmO1.5 and HfO2-SmO1.5 show the most exothermic enthalpies of formation and interaction parameters, whereas ZrO2-ScO1.5 has the least exothermic enthalpy of formation and interaction parameter. This suggests that the ZrO2-ScO1.5 system shows the least short range order among all investigated systems, consistent with its high ionic conductivity. The extrapolated enthalpy of transition of the rare earth oxide end members to the cubic fluorite structure increase to more endothermic values with decreasing cation size. The gamma-cubic fluorite phase transition in ZrO2-ScO1.5 was investigated by differential scanning calorimetry (DSC). The phase transition is reversible, occurs at 1000 degrees-1200 degrees C and shows hysteresis (similar to 100 degrees C). The enthalpy of transition is endothermic on heating and increases from 1.7 +/- 0.1 kJ/mol (22 mol% ScO1.5) to 2.9 +/- 0.2 kJ/mol (30 mol% ScO1.5).