In the paper, the issue of determining the horizontal curvature of the railway track axis was discussed to define unknown geometric characteristics of the measured route (location of straight and arched sections, circular arc radii, transition curve lengths, etc.). This problem has not been solved yet, and so far geometrical characteristics have been identified by approximate methods (e.g. horizontal arrow chart). Operating the angles of tangent to the geometrical layout (resulting from the very definition of curvature) seems very difficult in a real railway track reproduced on the basis of measurements. Therefore, a new concept has emerged to determine the curvature of the track not with the use of tangent but corresponding chords. In this way, the idea of curvature determination using the method of changing the slope angles of the moving chord was developed. Verification of the proposed method, carried out on a clearly defined basic geometric system of tracks, showed a sufficient compliance of the obtained curvature charts with the charts of the corresponding geometric solution. In order to use this method, one must know the coordinates of the points of a given section of the route in the Cartesian system.