The present embodiment is a high rotor pole switched reluctance machine (HRSRM) which provides a plurality of combinations of the number of rotor poles Rn and number of stator poles Sn utilizing a numerical relationship defined by a mathematical formula, Rn=2Sn−Fp, when Sn=m×Fp, wherein Fp is the maximum number of independent flux paths in the stator when stator and rotor poles are fully aligned, and m is the number of phases. The mathematical formulation provides an improved noise performance and design flexibility to the machine. The mathematical formulation further provides a specific number of stator and rotor poles for a chosen m and Fp. The HRSRM can be designed with varying number of phases. The HRSRM provides a smoother torque profile due to a high number of strokes per revolution.