Abstract: In a method for machining a chamfer at a pipe end, clamped in a radial clamping device, to exact positional and dimensional tolerances as a function of a measured course of an inner and an outer diameter of the pipe, an actual position of the pipe end clamped in the radial clamping device is determined with a first sensing device. Based on the determined actual position, in a controlled manner a machining tool is quickly advanced to the pipe end. With a second sensing device at least one of the actual inner diameter of the pipe and the actual outer diameter of the pipe is determined, and optionally the course of one of the actual inner diameter and the actual outer diameter about the circumference of the pipe is also determined. The machining tool is adjusted based on one of the actual inner diameter, the actual outer diameter, the nominal inner diameter and the nominal outer diameter.