The invention relates to a sensor device (1) for detecting a rotation, having - a position transmitter (2) with a shaft element (20) which has a first and a second shaft end (22), wherein the rotation to be detected is introduced via the first shaft end, and the shaft element contains a magnet element (51) at the second shaft end (22), - a sensor element (5) for detecting the rotation of the magnet element, and - a housing part (70) with at least two sections (80, 90) which are separated from each other. The shaft element (20) of the position transmitter (2) is mounted on the first section (80), and the sensor element (5) is arranged in the second section (90). The invention is characterized in that the housing part (70) and the shaft element (20) each have a first bearing portion (29) which is shaped so as to taper towards the shaft end in the region of the second shaft end (22), the shaft element (20) being supported on the housing part (70) on the first bearing portion in order to support the position transmitter on the housing part (70).