Synchronous speed
n_s = 120 x f / p = 60 x f / pole pairs: 4 poles at 50 Hz is 120 x 50 / 4 = 1500 1/min, at 60 Hz 1800 1/min. The supply frequency in Hz, p the number of poles, n_s in 1/min.
Reference tool — arithmetic, not a motor selection
Motor speed calculator.
Synchronous speed · poles · slip · generator
Speed, poles, slip.
Type a line (1480 1/min 50 Hz; 4 poles 60 Hz; 6 pole 50 Hz to 60 Hz; generator 4 poles 1800 1/min) or fill in the fields: the line and the fields stay in step.
Examples:
All 130 engineering tools
Enter the rated speed from the nameplate and the supply frequency, and the calculator finds the poles, the synchronous speed and the slip: n_s = 120 x f / p, s = (n_s - n) / n_s. From the poles and the frequency it works out the synchronous speed, from the poles and a speed the frequency of a generator, and for another supply frequency the synchronous speed at it. The working is shown with your numbers, and the result is a line you can copy or add to a request.
Arithmetic only: the calculator gives no typical slips or rated speeds for a pole count, and for another supply frequency it states the synchronous speed and nothing more. The power, torque, current and voltage at the other frequency, and whether the motor suits it, are for the motor maker data and a rewind or rating check.
How it is worked out
Frequency and poles.
Poles and slip from a plate
The poles from the synchronous speed nearest above the rated speed: 1480 1/min at 50 Hz is 4 poles, 1500 1/min. The slip s = (1500 - 1480) / 1500 = 1.33 %, or 20 1/min. Above the synchronous speed the slip is negative, as for an induction generator.
Generator and another supply
A generator frequency f = n x p / 120: 4 poles at 1800 1/min is 60 Hz. The synchronous speed scales with the supply frequency: 6 poles is 1000 1/min at 50 Hz and 1200 1/min at 60 Hz, x 1.2.
| Poles | Pole pairs | n_s at 50 Hz, 1/min | n_s at 60 Hz, 1/min |
|---|---|---|---|
| 2 | 1 | 3000 | 3600 |
| 4 | 2 | 1500 | 1800 |
| 6 | 3 | 1000 | 1200 |
| 8 | 4 | 750 | 900 |
| 10 | 5 | 600 | 720 |
| 12 | 6 | 500 | 600 |
This is the arithmetic of n_s = 120 x f / p, not rated speeds: an induction motor runs below the synchronous speed by its slip, which comes from the nameplate. 1/min, r/min and min-1 are the same unit.
Sources
The synchronous speed n_s = 120 x f / p, with p the number of poles, agrees in the Wikipedia article Induction motor and in the Engineering ToolBox reference (synchronous speed from the frequency and the poles); the form with pole pairs, n = 60 x f / p with p the pole pairs, is in the Wikipedia article Synchronous motor and the Russian Wikipedia article on the induction machine. The slip s = (n_s - n) / n_s, as a ratio, a percentage or in 1/min, agrees in the Wikipedia article Induction motor, the Engineering ToolBox page on induction motor slip and the Russian article. The negative slip of generator operation is in the Wikipedia article Induction generator and the Russian article. The generator frequency f = n x p / 120 follows the Wikipedia article Alternator (N = 120 f / P) and the article Synchronous motor (the speed is locked to the supply frequency); the table of synchronous speeds of 2 to 12 poles at 50 and 60 Hz agrees in the article Alternator and the Engineering ToolBox table. The motor or generator maker data always come first.
Before you work it out
Questions about motor speed
How is the synchronous speed of a motor worked out?
The synchronous speed is the speed of the rotating field: n_s = 120 x f / p, with the supply frequency f in Hz, the number of poles p and n_s in 1/min (also written r/min or min-1). A 4-pole machine at 50 Hz: 120 x 50 / 4 = 1500 1/min; at 60 Hz, 1800 1/min. Counted in pole pairs it is the same: n_s = 60 x f / pole pairs = 60 x 50 / 2 = 1500 1/min. A synchronous machine turns at this speed; an induction motor turns below it by its slip.
How do I find the poles and the slip from a nameplate speed?
Take the synchronous speed nearest above the rated speed at the plate frequency. 1480 1/min at 50 Hz: 60 x 50 / 1480 = 2.03 pole pairs, so 2 pole pairs, 4 poles and a synchronous speed of 1500 1/min. The slip is s = (n_s - n) / n_s = (1500 - 1480) / 1500 = 0.0133 = 1.33 %, or 20 1/min. The slip comes from the figures on the plate: the calculator gives no typical slips. For a generator, add the word generator or the poles: a synchronous generator turns at its synchronous speed, an induction generator above it.
What is the difference between the poles and the pole pairs?
The poles come in pairs, a north and a south pole, so a machine has an even number of poles and half as many pole pairs: 4 poles are 2 pole pairs. English texts mostly write n_s = 120 x f / p with p the poles; Russian and German texts often write n = 60 x f / p with p the pole pairs, and the Russian 2p = 4 means 4 poles. Both give the same speed. The calculator reads 4 poles, 2 pole pairs and 2p = 4; it asks which is meant when a bare p = 2 is typed, and refuses an odd number of poles.
What happens to the synchronous speed when a 50 Hz motor runs on 60 Hz?
The synchronous speed scales with the frequency: x 60 / 50 = x 1.2. A 6-pole machine: 1000 1/min at 50 Hz, 1200 1/min at 60 Hz; the other way, x 50 / 60. That arithmetic is all this calculator states. What happens to the power, torque, current, voltage and rated speed at the other frequency, and whether the motor suits it, is a matter for the motor maker data and a rewind or rating check.
How is the frequency of a generator worked out?
Turn the formula round: f = n x p / 120. A 4-pole generator at 1800 1/min gives 1800 x 4 / 120 = 60 Hz; at 1500 1/min, 50 Hz. A synchronous generator turns at exactly this speed for its frequency. An induction generator runs above its synchronous speed, and the calculator works out its negative slip when the speed, the poles or the word generator and the frequency are entered.
Can the slip be negative?
Yes, when the shaft turns above the synchronous speed: s = (n_s - n) / n_s is then below zero. 4 poles at 50 Hz turning at 1520 1/min: (1500 - 1520) / 1500 = -1.33 %. This is how an induction machine runs as a generator, driven through its shaft. For a motor a negative slip means the poles, the frequency or the speed entered do not fit together, and the calculator says so.
A motor, a generator or their parts?
Send the line and the nameplate photo.
The calculator works out the synchronous speed, the poles, the slip and the frequency only. When a motor, a generator or their parts are needed, such as bearings, a fan or a terminal box, send the line from the calculator with a photograph of the nameplate, and Vessel Core checks the details before an offer goes back.
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