A permanent magnet synchronous machine, in particular a three-phase machine of a vacuum pump (13, 15), comprising: a rotor (14, 16); a device for determining an angle and an angular velocity of the rotor (14, 16) at low rotational speeds of the rotor (14, 16) below an operating speed of the permanent magnet synchronous machine by means of a back electromagnetic force, which can be detected based on at least two voltages induced by the rotor (14, 16), in an encoderless operation of the permanent magnet synchronous machine, wherein the device comprises: an analog-to-digital converter which digitizes the at least two induced voltages; an averaging device which calculates at least two averaged voltages via a variable number N of measurement values of the at least two digitized voltages; a determination module which determines the variable number N in dependence on the rotational speed of the rotor (14, 16); and an estimation module which estimates the angle and the angular velocity of the rotor (14, 16) based on the at least two averaged voltages, characterized in that the determination module initializes the number N with a predetermined value and iteratively adjusts the number N in dependence on the determined angular velocity, wherein the determination module increases the number N when the angular velocity falls below a lower threshold value and reduces the number N when the angular velocity exceeds an upper threshold value. a rotor (14, 16); a device for determining an angle and an angular velocity of the rotor (14, 16) at low rotational speeds of the rotor (14, 16) below an operating speed of the permanent magnet synchronous machine by means of a back electromagnetic force, which can be detected based on at least two voltages induced by the rotor (14, 16), in an encoderless operation of the permanent magnet synchronous machine, wherein the device comprises: an analog-to-digital converter which digitizes the at least two induced voltages; an averaging device which calculates at least two averaged voltages via a variable number N of measurement values of the at least two digitized voltages; a determination module which determines the variable number N in dependence on the rotational speed of the rotor (14, 16); and an estimation module which estimates the angle and the angular velocity of the rotor (14, 16) based on the at least two averaged voltages, an analog-to-digital converter which digitizes the at least two induced voltages; an averaging device which calculates at least two averaged voltages via a variable number N of measurement values of the at least two digitized voltages; a determination module which determines the variable number N in dependence on the rotational speed of the rotor (14, 16); and an estimation module which estimates the angle and the angular velocity of the rotor (14, 16) based on the at least two averaged voltages, the determination module initializes the number N with a predetermined value and iteratively adjusts the number N in dependence on the determined angular velocity, wherein the determination module increases the number N when the angular velocity falls below a lower threshold value and reduces the number N when the angular velocity exceeds an upper threshold value.