This paper proposes a sensorless control scheme for a surface-mounted permanent-magnet synchronous machine (PMSM) based on the back-electromotive force voltage. It is a direct estimation method, meaning the rotor position is directly calculated based on stator-current measurements and the stator voltage commands as well as on the knowledge of stator resistance and stator inductance, but without the use of an asymptotic observer or integration of speed, respectively, flux. The estimated angle is filtered and used directly for sensorless field-oriented current and torque control. Analogously, the rotor speed is also directly calculated and used for sensorless speed control. A polar stator-current coordinate representation is chosen for the stator currents such that the scheme is easily extendable with filters to cope with measurement noise. A comparison to a reduced-order observer highlights the robustness advantage. Experimental results confirm good dynamical performance, even at low speeds.