We construct with a differential scanning calorimeter (DSC) a phase diagram for the ethylene carbonate (EC)-dimethyl carbonate (DMC) binary system for its liquid-solid phase equilibria. We determine the eutectic composition of the binary system using an enthalpic method that we devised based on the composition dependence of the enthalpy of solidus melting, with highly consistent results. We also discuss the merits and limitations of this enthalpic method.