A detection method of a rotary speed of a rotating shaft of an induction motor, wherein the detection method is that when a power input P is supplied to the induction motor, the rotary speed of the rotating shaft of the induction motor is detected, the detection method comprising: a step I, comprising: when the power input P is supplied, setting a loss power to be P L, dividing the loss power P L into a non-depending loss power A that does not depend on the rotary speed of the rotating shaft of the induction motor and a depending loss power B that depends on the rotary speed; considering a difference between the power input P and the non-depending loss power A as a first order approximation value PM 1 of mechanical output of the induction motor; and from an equation PM 1 = αS 1 (α is a motor constant) of an output PM 1 given in the induction motor and a slip S 1, obtaining a first order approximation value of the rotary speed of the rotating shaft N 1 = N S (1 - S 1) (Ns is a synchronous speed); a step II, based on the first order approximation value N 1, obtaining the depending loss power B 1; and a step III, comprising: considering a second order approximation value PM 2 of the output of the induction motor as P - (A + B 1); and from an equation PM 2 = αS 2 (α is the motor constant) of the output PM 2 given in the induction motor and the slip S 2, obtaining a second order approximation value of the rotary speed of the rotating shaft, N 2 = N S (1 - S 2) (N S is the synchronous speed). a step I, comprising: when the power input P is supplied, setting a loss power to be P L, dividing the loss power P L into a non-depending loss power A that does not depend on the rotary speed of the rotating shaft of the induction motor and a depending loss power B that depends on the rotary speed; considering a difference between the power input P and the non-depending loss power A as a first order approximation value PM 1 of mechanical output of the induction motor; and from an equation PM 1 = αS 1 (α is a motor constant) of an output PM 1 given in the induction motor and a slip S 1, obtaining a first order approximation value of the rotary speed of the rotating shaft N 1 = N S (1 - S 1) (Ns is a synchronous speed); when the power input P is supplied, setting a loss power to be P L, dividing the loss power P L into a non-depending loss power A that does not depend on the rotary speed of the rotating shaft of the induction motor and a depending loss power B that depends on the rotary speed; considering a difference between the power input P and the non-depending loss power A as a first order approximation value PM 1 of mechanical output of the induction motor; and from an equation PM 1 = αS 1 (α is a motor constant) of an output PM 1 given in the induction motor and a slip S 1, obtaining a first order approximation value of the rotary speed of the rotating shaft N 1 = N S (1 - S 1) (Ns is a synchronous speed); a step II, based on the first order approximation value N 1, obtaining the depending loss power B 1; and a step III, comprising: considering a second order approximation value PM 2 of the output of the induction motor as P - (A + B 1); and from an equation PM 2 = αS 2 (α is the motor constant) of the output PM 2 given in the induction motor and the slip S 2, obtaining a second order approximation value of the rotary speed of the rotating shaft, N 2 = N S (1 - S 2) (N S is the synchronous speed). considering a second order approximation value PM 2 of the output of the induction motor as P - (A + B 1); and from an equation PM 2 = αS 2 (α is the motor constant) of the output PM 2 given in the induction motor and the slip S 2, obtaining a second order approximation value of the rotary speed of the rotating shaft, N 2 = N S (1 - S 2) (N S is the synchronous speed).