A sensorless control apparatus may include: a speed command unit configured to output a speed command to an electric motor; a current detector unit configured to detect electric current flowing through the electric motor if a voltage being output according to the speed command is supplied to the electric motor; a rotor angle calculation unit configured to calculate a magnetic flux of a rotor of the electric motor based on the detected electric current and the voltage being output according to the speed command, and to calculate an angle of the rotor from the calculated magnetic flux; and/or an out-of-step sensing unit configured to sense an out-of-step of the rotor according to a comparison of the calculated angle of the rotor with an angle of the rotor estimated based on a sensorless control algorithm.