This article presents an analytical expression of the first, the third, and the fifth harmonic component for axial field of magnetic deflectors made of straight or tapered saddle coils or straight toroidal coils in air. In particular, the expressions for the tapered saddle coils and also for the fifth components for straight saddle and toroidal coils have not been derived so far. The existence of the analytical expressions for the simple but important problems of magnetic deflectors in free space is quite advantageous for the check of the correct mesh layout for the more general problems. The axial field functions are compared with those computed with the first order finite element method for the same geometry, with very good agreement of the results. ©1997 American Institute of Physics.