In this paper, the authors present a method for determining the contact radii required to calculate contact stresses, even for distorted rail-wheel contact geometries. This deformation is most often caused by wear between the wheel and rail. In the method used, the authors employ numerical differentiation to derive the required radius values from the data of discrete points defined in the Cartesian x-y coordinate system. The authors validate the applicability of their method on a rail head of 60E1 geometry without wear. A further objective of research is to validate the method for worn geometries. The presented method will help experts obtain a more accurate view of the magnitude of contact stresses, as the formulas used in everyday practice are often significantly incorrect, to the detriment of safety. Thus, by going beyond methods that use a single radius value, they also demonstrate that the calculation of accurate values requires knowledge of four radius values, two of which can be determined effectively using the presented methodology.