Motor Synchronous Speed, Slip, and Rotor Frequency
The synchronous speed Ns = 120 x frequency / poles, the slip relative to the nameplate full-load speed.
Example
You enter
- Line frequency (Hz) 60
- Poles (even integer) 4
- Nameplate full-load speed (rpm) 1750
You get
- Synchronous speed 1800 rpm
- Slip 2.7778
- Rotor (slip) frequency 1.67 Hz
Checked against published worked examples from: WEG Electric Corp.; U.S. Department of Energy, Motor Challenge Program.
Details, formula, and sources
ScopeThe synchronous speed Ns = 120 x frequency / poles, the slip relative to the nameplate full-load speed, and the rotor (slip) frequency, for commissioning a motor, reading a VFD parameter set, or diagnosing a wrong-speed complaint. The nameplate full-load speed governs.
Formula or tableNs = 120 x f / P (the 120 carries the 60 s/min x 2 poles-per-pole-pair bridge); slip = (Ns - rated_rpm) / Ns; slip_pct = slip x 100; rotor (slip) frequency = slip x f.
Source and editionFirst-principles AC-machine speed relation; classical induction-machine theory.
Free accessFirst-principles physics; no licensed source required.
What governsEstimate. AHJ and licensed professional govern.
API field namesline_freq_hz, poles, rated_rpm, sync_rpm, slip_pct, rotor_freq_hz
- Rated speed the nameplate full-load speed governs the slip; a speed near synchronous indicates a lightly loaded machine, rising slip indicates loading or a rotor faultmotor nameplate / manufacturer
- Pole count the stator pole count is an even integer (2, 4, 6, 8, ...)AC-machine construction