Synchronous Speed⚠ unverified
Electrical / Motors · Compute the synchronous speed of an AC machine
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| f | f | Hz | 1.0 | Supply line frequency |
| poles | poles | — | 1.0 | Number of magnetic poles of the machine |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | ns | rpm | Synchronous speed, in revolutions per minute (rpm) |
The science & history
Understanding the Parameters
- Frequency $f$ — one AC cycle advances the field by one pole‑pair; higher $f$ means a faster field.
-
Poles $p$ — more poles divide the field's rotation into smaller steps, so the field turns slower (a 4‑pole 60 Hz machine runs at 1800 rpm; an 8‑pole at 900 rpm).
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$n_s$ — the field (and synchronous‑rotor) speed; induction rotors run slightly below it (see Slip).
Derivation (Approaching a Proof)
A set of stator windings spaced for $p$ poles ($p/2$ pole‑pairs), fed by an AC line of frequency $f$, produces a field that advances one pole‑pair per electrical cycle. In one second the field completes $f$ cycles, i.e. $f/(p/2) = 2f/p$ mechanical revolutions per second. Converting to per minute:
$$n_s = \frac{2f}{p}\times 60 = \frac{120\,f}{p}\ \text{rpm}.$$
(Equivalently the angular synchronous speed is $\omega_s = 2\pi f/(p/2) = 4\pi f/p$ rad/s.) The number is exact and depends only on line frequency and pole count — not on load or voltage.
History
Synchronous speed is a property of the rotating magnetic field, discovered independently by Galileo Ferraris and Nikola Tesla in the 1880s. Fixing machine speed to the grid frequency is why AC motors run at standardised speeds (e.g. 3600/1800/1200 rpm at 60 Hz) and is the basis of synchronous clocks and generators.
Related Concepts: Slip, Three-Phase Power, Maximum Torque, Starting Torque
Notes: Registry calculator synchronous-speed (unverified). Exact field speed; actual induction
rotor speed is $n = n_s(1-s)$ (see Slip).