Motors and transformers
Synchronous speed
- where
- synchronous speed (rpm)
- supply frequency (Hz)
- total number of poles
Explain this equation
Gives the speed of the rotating magnetic field in an AC motor from the supply frequency and the number of poles. It is the actual speed of a synchronous motor and the ceiling for an induction motor.
f is the supply frequency in hertz, 50 Hz in the UK. p is the total number of poles, not pole pairs. nₛ is the field speed in revolutions per minute.
The field moves on by one pole pair for each supply cycle, so it turns f ÷ (p/2) revolutions per second. Multiplying by 60 for minutes gives 120 × f / p; the 120 is just 60 × 2.
At 50 Hz, 2 poles gives 3000 rpm, 4 poles 1500, 6 poles 1000 and 8 poles 750. Double the frequency with a drive and the speed doubles.
Watch out: a 4-pole motor has 2 pole pairs, and entering pairs as poles doubles the answer. An induction motor's shaft runs a little below this because of slip.
The rotating magnetic field speed depends on frequency and total pole count. More poles at the same frequency give lower field speed.
An induction motor normally runs below this speed in motoring operation. The difference is accounted for by slip, introduced later.
Enter your values to see the result.
Common mistake
Entering two pole pairs as two poles.
Limits
Use total poles, not pole pairs; this is field speed, not automatically rotor speed.
Sources
The tools calculate the displayed equation. They do not automatically choose cable sizes, approve installations, supply current regulatory tables, certify equipment or replace inspection and testing.