An approach to predict the air-gap flux density and voltage harmonics in large synchronous machines is presented. Combining a small number of solutions of magnetostatic finite-element analysis (FEA) with harmonic analysis, the approach allows designers to rapidly investigate the source of flux density harmonic predictions. The method provides the ability to trace flux density predictions to individual mmf-permeance combinations and applies to machines with both integral and fractional slot windings, with arbitrary skew. Predicted results are compared with that of measured values of open- and short-circuit air-gap flux density in one machine. Open-circuit voltage predictions for five machines are compared with measurements and predictions using commercial FEA.