The rotating stator field and the rotor of an induction machine do not generally turn at the same speed. Their relative speed is described by slip.

If the synchronous speed is $n_s$ and the rotor speed is $n_r$,

$$s=\frac{n_s-n_r}{n_s}.$$

Starting and synchronous speed

At standstill,

$$n_r=0,$$

so

$$s=1.$$

At synchronous speed,

$$n_r=n_s,$$

so

$$s=0.$$

An induction motor under load normally operates with a small positive slip:

$$0<s<1.$$

Rotor electrical frequency

The rotor sees the magnetic field changing at the relative speed. Its induced electrical frequency is therefore

$$f_r=sf_s,$$

where $f_s$ is the stator supply frequency.

At starting, rotor frequency equals stator frequency; as the rotor approaches synchronous speed, rotor frequency falls.

Beyond synchronous speed

If an externally driven rotor turns faster than the rotating field, then $n_r>n_s$ and slip becomes negative. The induction machine can then operate regeneratively, transferring mechanical energy back toward the electrical system.

Slip is therefore the variable linking rotor speed to the induced rotor voltages, currents and torque.