Induction Motor Formulas
Induction motor formulas for synchronous speed, slip, shaft torque and full-load current, with a 55 kW worked example and a table of speeds by pole count.
The formulas
| To find | Formula |
|---|---|
| Synchronous speed | Ns = 120 × f / p |
| Slip | slip % = (Ns − N) / Ns × 100 |
| Shaft torque | T = 9548.8 × P / N, or 60 × P / (2π × N) with P in watts |
| Full-load current (three-phase) | I = P × 1000 / (η × √3 × V × pf) |
| Input power | Pin = P / η |
f is the supply frequency in hertz, p the number of poles, N the rotor speed in rpm, P the shaft power in kW, V the line voltage in volts, η the efficiency and pf the power factor as fractions. Nameplate values take precedence over these planning figures.
Worked example: 55 kW, 4-pole, 1,480 rpm, 415 V
The efficiency is 0.93 and the power factor 0.88.
- Ns = 120 × 50 / 4 = 1,500 rpm
- Slip = (1,500 − 1480) / 1,500 × 100 = 1.333%
- T = 9548.8 × 55 / 1480 = 354.9 N·m
- I = 55 × 1000 / (0.93 × √3 × 415 × 0.88) = 93.49 A
Synchronous speed by number of poles
| Poles | 50 Hz | 60 Hz |
|---|---|---|
| 2 poles | 3,000 rpm | 3,600 rpm |
| 4 poles | 1,500 rpm | 1,800 rpm |
| 6 poles | 1,000 rpm | 1,200 rpm |
| 8 poles | 750 rpm | 900 rpm |
Frequently asked questions
Which speed do I use for torque?
The loaded shaft speed from the nameplate, such as 1,480 rpm. Using the synchronous speed of 1,500 rpm understates the torque.
What is a normal slip?
Typically 1% to 5% at full load for a standard cage motor. Larger motors have lower slip.
How high is the starting current?
Direct-on-line starting commonly draws five to eight times the full-load current. Star-delta starting reduces both the current and the torque to one third.
Why is the shaft power not the same as the input power?
The motor loses some power as heat in the windings, core and bearings. The input power is the shaft power divided by the efficiency.
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