We propose a method to determine the effective parameters for toroidal cores. We have found the method effective in generating the initial flux-magnetomotive-force curve, as well as minor and major flux-MMF loops for a wide range of commercial toroids, using three commercial power manganese-zinc (MnZn) ferrites. In the method, a material-dependent function is used to approximate the initial magnetization curve. Material-independent, geometry-dependent expressions are then derived for the effective parameters. We compare initial-magnetization-based le and Ae with those published by core producers.