Normal calculation of the carrier harmonic iron losses (CHILs) brought by the pulse width modulated (PWM) voltage source inverter in interior permanent magnet synchronous motors by the time-stepping finite-element analysis (TSFEA) with short time steps is very time-consuming. In this study, a novel method for fast calculation is proposed, where a combination of the frozen differential reluctivity tensor method and the time-harmonic finite-element analysis is proposed to investigate the relationship between PWM voltage harmonics and the corresponding CHILs, with which the CHILs in stator and rotor are fastcalculated with the voltage harmonics in stator and rotor reference frames, respectively. Besides, the eddy current reaction effect in electrical steel sheets on the CHILs at high frequency is considered by an analytical method and validated with the TSFEA. The results reveal that eight parameters are recommended to calculate the CHILs at different operating conditions, which vary with the fundamental current. Consequently, the CHIL map over the entire operating conditions can be fastcalculated using the analytical spectra of the PWM voltages. Experiment on a specimen is conducted to validate the accuracy of the proposed method, which shows it depends on whether the equivalent differential permeability of the silicon steel can be accurately modelled.