A measuring device for in-process measurement of test pieces during a machining operation on a machine tool, in particular a grinding machine, has a base body, and a measuring head movable between a neutral position and a measuring position and which is connected to the base body via a rod assembly which is configured and set up in such a way that the measuring head in the measuring position follows orbital rotations of a test piece about a rotational axis. The measuring head has a measuring sensor which is deflectable along a linear axis for recording measured values during a measuring operation. A control apparatus is provided for controlling the measuring operation. The control apparatus is configured and set up in such a way that the measuring device may be calibrated in a calibration mode.