An apparatus is disclosed for measuring the position of a vehicle or a surface thereof on a roadway. The apparatus comprises at least one radar transmitter, which is arranged in a transmitting position above the plane of the roadway and transmits radar beams downwardly, a plurality of radar receivers, which are distributed above the plane of the roadway in different receiving positions at distances from one another, receive reflections of the radar beams from beneath, and convert the reflections into a received signal, and an evaluation device, which is connected to the radar transmitter and the radar receivers and is configured to measure the said position from the transmitting position, the receiving positions and the received signals.