This paper presents a unique method for simulating permanent magnet motors without time-consuming numerical methods used in the conventional magnetic circuit method. The conventional method gives us average values like torque and power over specified periods of time, but it is usually very difficult and time-consuming to obtain instantaneous characteristics like cogging torques and torque ripples. The convolution operations method we present, however, considers relative angle variations of stator magnetic circuits and rotor magnetic circuits. As a result, it makes uses of instantaneous values possible. The authors compare the new method with the coventional method and verify that calculating cogging torque values and back-emf values is possible with the proposed new convolution method.