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This paper formulates the difference in base frequency and maximum torque between distributed and concentrated windings taking into account the air-gap modulation of concentrated-winding permanent magnet (PM) motors. The design superiority is typically confirmed for each winding type during a development period by using time-consuming finite element analysis (FEA). We propose a quantification that enables motor designers to easily judge, at the initial design stage, a superior winding type and to shorten a design period. Throughout our formulation, we found that the distributed-winding PM motors, in principle, have larger q-axis inductance and smaller d-axis inductance than the concentrated-winding motors, which leads to a decrease in the base frequency. On the other hand, the distributed winding inherently has higher winding factor and needs shorter stack length of core than the concentrated winding for identical torque output, which results in an increase in the base frequency. And also, we theoretically quantified the difference in reluctance-torque contribution between the two winding types and found that it was too small to have much impact on practical design. We applied the proposed formulae to a 0.2-kW concentrated-winding Nd-Fe-B magnet motor and were able to quantify the base frequency, the maximum torque, and the minimum stack length of core for a distributed-winding motor with high accuracy without having to rely on FEA. The FEA and measurement results demonstrated the validity of the proposed approach for the fabricated distributed-winding PM motor. [ABSTRACT FROM AUTHOR]