A sensor device for determining a position ϕ1 of a rotor of an electrical machine, for example an electric motor or electric generator. The sensor device comprises a number r of sensors, which detect the magnetic field generated by the rotor and/or a permanent magnet rotating with the rotor, and an electronic circuit which is configured to detect and digitalize the sensor signals a1 to ar and to form a signal vector {right arrow over (a)}=(a1, . . . , ar), to form a measurement vector {right arrow over (q)} according to a predetermined linear function g to {right arrow over (q)}=g({right arrow over (a)}), to calculate a vector {right arrow over (p)}=Mrot1·{right arrow over (q)}, wherein {right arrow over (p)} is a 2-component vector with the components p1 and p2 and Mrot1 is a 2×n matrix, and to determine the position ϕ1 of the rotor to ϕ1=a tan 2(p2, p1). The invention further concerns a control device for an electric motor with such a sensor device.