Induction Motor Calculations

Motor Efficiency and Power Factor

First, it is important to identify which KW you are referring to. There is mechanical output power and electrical input power.

Electric circuits are rated in electrical input power and mechanical systems in mechanical shaft power.

For the purposes of the description, let us identify these as KW_e and KW_m Where KW_e is the electrical input power and KW_m is the mechanical output power.

The power rating of an induction motor is usually the rated shaft power of that motor. (KW_m)

The efficiency of the induction motor is the ratio between the mechanical output power and the electrical input power.
eff = KW_m/KW_e

The power factor of an electrical circuit is the ratio between the electrical KW input to the KVA input, so pf = KW_e/KVA

The mechanical shaft power is therefore KW_m = KVA x pf x eff
The electrical input power is KW_e = KVA x pf

So KVA = KW_m / pf / eff = KW_m / (pf x eff) = KW_e / pf

Be careful to ensure that you know whether you are referring to mechanical output power (usual with motors) or electrical input power.

Motor Synchronous Speed

The synchronous speed is a function of the frequency of the supply and the number of poles in the stator winding.
RPM = F x 120/ P

F = Supply Frequency (Hz)
P = Number of poles

Motor Torque

The torque produced by an induction motor is a function of the shaft power and the shaft speed where the torque reduces with speed for constant power.

T = 9.5493 x P / RPM

T = Torque (Nm)
P = Power (KW)

T = 5252 x P / RPM

T= Torque (lb-ft)
P= Power (HP)