A 15-phase induction machine supplied by voltages with third-order harmonic injection has nonsinusoidal magneto-motive forces distribution. This paper introduces a distributed magnetic circuit approach to perform magnetic circuit calculations in order to determine the magnetizing inductance for both the fundamental and third-harmonic component. The proposed approach divides the half-pole or one-pole machine model into a large number of fan-shaped sectors. The air-gap flux densities for all sectors are then solved iteratively. The fundamental and third-harmonic inductances are extracted via Fourier analysis of air-gap flux density distribution. Calculated fundamental and third-order harmonic inductances are compared with those obtained from no-load tests of a 15-phase prototype induction machine. The good agreement between calculated and experimental results verifies the accuracy of the presented method.