Eddy current losses in rotor permanent magnets (PM) of synchronous machines are calculated for sinusoidal stator currents and for PWM inverter supply. Three calculation methods are compared in the FE environment: a) time-stepping method, b) quasi-static method, c) semi-analytical post-processing. These 2D methods are with end effect coefficients, and they consider the time variation of currents and of the rotor position. Whereas method a) includes the variation of flux-density over the magnet cross section and the reaction field of the eddy currents, method b) is neglecting the reaction field. Method c) in several variants features either neglecting of the eddy current reaction field or an averaging of the flux density along the magnet width or height. Neglecting the reaction field is possible for materials with low conductivity and low permeability like rare-earth magnets for low to medium frequencies up to several kHz. The quasi-static methods need less computation time, but depend on the machine geometry like stator MMF wave length, slot pitch, segmented vs. massive magnets and small or big magnet height. The comparison of methods a), b), c) is given for two different stator geometries of permanent magnet synchronous machines with open vs. semi-closed slots and surface-mounted vs. buried magnets.