An analytical formulation that calculates the thermodynamic properties of zirconium carbide and zirconium nitride has been produced using the n-dimensional Debye function. The results of the heat capacity and entropy calculated here for ZrM (M=N and C) were compared with the literature data, and are found to be in agreement. This agreement shows that the used method would be useful to calculate the thermophysical properties (heat capacity, entropy, etc.) of materials such as ZrC and ZrN.