Field modeling becomes simpler if strong field nonuniformities are solved theoretically. The early obtained formulas for 2-D ldquocornerrdquo and ldquoconstrictionrdquo permeances pertain to right angle configurations. In this paper, using a conformal mapping, the field in the vicinity of arbitrary angle vertex is studied and the fringing permeance determined. The results are applied to permeance evaluation of lunate cross section grooves from the rotors of certain types of reluctance motors. Closed-form expressions are obtained, in good agreement with finite element analysis. Combined with the finite element method, obtained results offer the possibility to make simpler and more accurate analytical calculations of motors and other magnetic devices and to better evaluate magnetic forces that act on them.