The classical plan of the railway is seen as a flat curve characterized by the projection of the car’s center of gravity onto the horizontal plane. The railway plan is described as a single flat curve. The authors argue that the railway plan on the curve will be a spatial curve. Therefore, it is recommended to consider the spatial aspects in curved sections, with each railway curve evaluated individually. In this context, the inner rail’s graph on the curve will be a flat circle; the outer graph will form a spatial curve. The distance between the corresponding points of the curves should be equal to the path’s width. This research focuses on the mathematical definition of equations for curves, which describe the lines of railway rails. The inner rail is treated as a flat curve, while the outer rail is represented by a spatial curve. The equations of these curves are formulated based on the parameters of the specific route. The primary parameter is the distance between the ends of the straight sections connected by the curved section under study. The spatial curve, representing the outer rail, is chosen so that its projection onto the horizontal plane forms a graph of the clothoid curve.