An improved three-dimensional analytical model for axial-flux permanent-magnet eddy-current couplings is presented in this paper. As the problem is solved in a 3-D cylindrical coordinate system, the proposed model directly takes into account the radial edge effects and the curvature effects on the torque prediction without the need of any correction factor. It is shown that the new analytical model is very accurate, even for the geometries where the curvature effects are very pronounced. Another advantage of the proposed model is the great reduction of computation time compared to 3-D finite elements simulations and an easier adaptation for parametric studies and optimization.