The paper presents a numerical algorithm for the theoretical calculation of the thermodynamic cycle of a pulsed detonation based engine, based on the Zeldovich - von Neumann - Doring detonation model, together with the algorithm employed to perform them, and a numerical application. The results are compared to numerical data obtained for the Chapman - Jouguet detonation thermodynamic parameters using the NASA - Glenn Chemical Equilibrium Program CEA2. As a reference, the thermodynamic cycle of a Brayton engine operating under the same conditions of compressor pressure ratio and fuel mass flow rate is computed and included in the paper. It is found that the CEA2 detonation model predicts a very low engine thermodynamic efficiency, while the ZND model yields a higher efficiency of the detonation based engine with respect to the Brayton cycle engine. The specific work of the detonation engine is higher than the Brayton engine, but the power remains lower. Copyright