An apparatus for ascertaining data required for reprofiling a worn railroad wheel, comprising means (15) for fixing at least one wheel (13) of a wheel set relative to a defined reference point, at least one sensing device (12) including sensing means for gaging the surface of the wheel to be reprofiled or trued, carrier means for supporting said sensing device, drive means (17, 18) connected to said carrier means for moving said sensing device at least in a radial direction and in an axial direction relative to the wheel to be trued by respectively moving said carrier means, displacement measuring means (19, 20) arranged for ascertaining the size of the displacement in the mentioned radial and axial directions relative to said reference point, computer means (21) operatively connected to said displacement measuring means (19, 20) for processing data provided by the displacement measuring means, drive control means operatively connected to said drive means (17, 18) and to said computer (21) for controlling the movement of said drive means, said sensing means of said sensing device (12) comprising at least one sensor (6, 11, 14) and further displacement sensing means (10) connected to said at least one sensor (6, 11, 14) for ascertaining the size of the sensing movement in a sensing direction, and means (29) connecting said further displacement sensing means (10) to said computer (21) for providing further data to said computer (21) for providing truing information to be used in a subsequent truing operation, and wherein said at least one sensor (6, 11, 14) comprises a bell-crank type contact lever having a first lever arm (6) which is displaceable and rotatable in parallel to a radial plane of the wheel to be trued and a second arm (11) arranged perpendicularly to said first lever arm (6), said second arm (11) carrying a sensor member (14) at its free end, and means for converting at least a limited rotational movement of said first lever arm (6) into a longitudinal movement which is at least approximately proportional to said limited rotational movement, said further displacement sensing means (10) being arranged for ascertaining the size of said longitudinal movement relative to said reference point which is in a fixed position relative to said sensing device (12).