What is the formula for synchronous speed?

• A. Ns = f / P
• B. Ns = 60 f / P
• C. Ns = 120 f / P
• D. Ns = 120 P / f

Answer: (C)

Synchronous speed is the mechanical speed at which the rotor would turn if it locked to the rotating stator field. The electrical frequency f (in Hz) represents how many magnetic cycles occur each second. With P poles, there are P/2 pole pairs, so the rotating field cycles P/2 times for every revolution of the rotor. This gives the relationship f = (P/2) × (Ns/60). Solving for Ns (in rpm) yields Ns = 120 f / P.

For example, at 60 Hz, a machine with six poles spins at Ns = 120 × 60 / 6 = 1200 rpm; with four poles, Ns = 120 × 60 / 4 = 1800 rpm.

Other forms don’t give rpm correctly: they either miss the 120 factor, place the factors incorrectly, or invert the relationship, so they don’t produce the actual synchronous speed in rpm.