Measuring system with a machine bed, in which a workpiece can be received along a receiving axis, and a sensor device, which can be moved in a number of directions in relation to the machine bed and has a touch sensor for sensing points in a machine coordinate system of the measuring system and has at least one optical sensor (190, 195) for measuring the contour of the workpiece, wherein the measuring system has the following features: a reference module, which is fastened at a fixed point of the machine bed of the measuring system and has at least a first measuring point and a second measuring point, the touch sensor, which can be moved along at least one sensor measuring axis and is designed to sense the first measuring point and the second measuring point in order to detect an alignment of the sensor measuring axis with respect to the machine coordinate system in order to detect a change in an angle of the sensor measuring axis with respect to the machine coordinate system, wherein the measuring system is designed to calibrate a first calibrating position of the first measuring point and provide a first reference position and to calibrating a second calibrating position of the second measuring point and provide a second reference position by using the touch sensor in a calibration process, wherein the touch sensor is designed to measure a first current position of the first measuring point and to measure a second current position of the second measuring point, the measuring system having an evaluation device, which is designed to compare the current first position with the first reference position and the second current position with the second reference position and to detect an incorrect setting of the sensor measuring axis with respect to the machine coordinate system if the first current position deviates from the first reference position and/or the second current position deviates from the second reference position and/or to detect a correct setting of the sensor measuring axis with respect to the machine coordinate system if the first current position corresponds to the first reference position and/or the second current position corresponds to the second reference position, and a correction device, which is designed to correct the sensor measuring axis or a measuring formula for measuring the workpiece by using the current first position and the current second position if the incorrect setting is detected. a reference module, which is fastened at a fixed point of the machine bed of the measuring system and has at least a first measuring point and a second measuring point, the touch sensor, which can be moved along at least one sensor measuring axis and is designed to sense the first measuring point and the second measuring point in order to detect an alignment of the sensor measuring axis with respect to the machine coordinate system in order to detect a change in an angle of the sensor measuring axis with respect to the machine coordinate system, wherein the measuring system is designed to calibrate a first calibrating position of the first measuring point and provide a first reference position and to calibrating a second calibrating position of the second measuring point and provide a second reference position by using the touch sensor in a calibration process, wherein the touch sensor is designed to measure a first current position of the first measuring point and to measure a second current position of the second measuring point, the measuring system having an evaluation device, which is designed to compare the current first position with the first reference position and the second current position with the second reference position and to detect an incorrect setting of the sensor measuring axis with respect to the machine coordinate system if the first current position deviates from the first reference position and/or the second current position deviates from the second reference position and/or to detect a correct setting of the sensor measuring axis with respect to the machine coordinate system if the first current position corresponds to the first reference position and/or the second current position corresponds to the second reference position, and a correction device, which is designed to correct the sensor measuring axis or a measuring formula for measuring the workpiece by using the current first position and the current second position if the incorrect setting is detected.