A synchronous-machine starting device comprising: an electric power conversion unit converting supplied electric power into AC power and supplying the AC power to an armature of a synchronous machine; an AC voltage detection unit detecting an AC voltage supplied to the armature of said synchronous machine; an AC current detection unit detecting an AC current supplied to the armature of said synchronous machine; a rotor position detection unit detecting a position of a rotor of said synchronous machine based on said detected AC voltage and said detected AC current; and an electric power conversion control unit controlling said electric power conversion unit based on the detected position of said rotor, said rotor position detection unit including: an induction voltage operating unit calculating a first-phase induction voltage and a second-phase induction voltage induced to the armature of said synchronous machine based on a position signal representing the position of said rotor, an estimated rotational speed of said rotor, said detected AC voltage, and said detected AC current; and a feedback operating unit calculating an error of said position signal based on said calculated first-phase induction voltage and second-phase induction voltage, calculating position of said rotor and said estimated rotational speed based on said calculated error, and outputting a position signal representing said calculated position of said rotor to said electric power conversion control unit, characterised in that said feedback operating unit calculating said error based on a result of division performed using said first-phase induction voltage as a dividend and said second-phase induction voltage as a divisor, wherein said feedback operating unit makes a switch between calculation of said error based on a result of division performed using said first-phase induction voltage as a dividend and said second-phase induction voltage as a divisor, and calculation of said error based on a result of division performed using said first-phase induction voltage as a dividend and fixing the divisor at a predetermined value. an electric power conversion unit converting supplied electric power into AC power and supplying the AC power to an armature of a synchronous machine; an AC voltage detection unit detecting an AC voltage supplied to the armature of said synchronous machine; an AC current detection unit detecting an AC current supplied to the armature of said synchronous machine; a rotor position detection unit detecting a position of a rotor of said synchronous machine based on said detected AC voltage and said detected AC current; and an electric power conversion control unit controlling said electric power conversion unit based on the detected position of said rotor, said rotor position detection unit including: an induction voltage operating unit calculating a first-phase induction voltage and a second-phase induction voltage induced to the armature of said synchronous machine based on a position signal representing the position of said rotor, an estimated rotational speed of said rotor, said detected AC voltage, and said detected AC current; and a feedback operating unit calculating an error of said position signal based on said calculated first-phase induction voltage and second-phase induction voltage, calculating position of said rotor and said estimated rotational speed based on said calculated error, and outputting a position signal representing said calculated position of said rotor to said electric power conversion control unit, an induction voltage operating unit calculating a first-phase induction voltage and a second-phase induction voltage induced to the armature of said synchronous machine based on a position signal representing the position of said rotor, an estimated rotational speed of said rotor, said detected AC voltage, and said detected AC current; and a feedback operating unit calculating an error of said position signal based on said calculated first-phase induction voltage and second-phase induction voltage, calculating position of said rotor and said estimated rotational speed based on said calculated error, and outputting a position signal representing said calculated position of said rotor to said electric power conversion control unit, characterised in that said feedback operating unit calculating said error based on a result of division performed using said first-phase induction voltage as a dividend and said second-phase induction voltage as a divisor, wherein said feedback operating unit makes a switch between calculation of said error based on a result of division performed using said first-phase induction voltage as a dividend and said second-phase induction voltage as a divisor, and calculation of said error based on a result of division performed using said first-phase induction voltage as a dividend and fixing the divisor at a predetermined value.