Synchronous Speed Calculator
The speed of the rotating magnetic field in AC machines, with poles, frequency, slip and rotor speed.
Inputs
Results
Formula breakdown
Speed versus frequency
Speed versus number of poles
Machine and calculation diagram
Synchronous speed table (rpm)
| Poles | Pole pairs | 50 Hz | 60 Hz | 400 Hz |
|---|
Typical full-load slip (approximate)
| Machine | Slip |
|---|
Speed conversion
| Quantity | Value |
|---|
| rpm | rev/s | rad/s | deg/s |
|---|
Key formulas and references
- Chapman, Electric Machinery Fundamentals, McGraw-Hill.
- Fitzgerald, Kingsley & Umans, Electric Machinery, McGraw-Hill.
- Sen, Principles of Electric Machines and Power Electronics, Wiley.
- Boldea & Nasar, The Induction Machine Handbook, CRC Press.
- IEC 60034-1, Rotating electrical machines: rating and performance.
- NEMA MG 1, Motors and Generators.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| N_s | Synchronous speed | RPM |
| f | Supply frequency | Hz |
| P | Number of poles | dimensionless |
What it means
The synchronous speed N_s of an AC induction motor is the speed of the rotating magnetic field in the stator. It is given by N_s = 120·f / P, where f is the supply frequency in Hz and P is the number of poles. The synchronous speed is the speed at which the rotor would rotate if there were no slip (which is never achieved in an induction motor). Motors with different pole numbers have different synchronous speeds: a 2‑pole motor at 50Hz has N_s = 3000 RPM; a 4‑pole has 1500 RPM. The synchronous speed is used to calculate slip and to determine the motor’s speed range. Example: For a 4‑pole motor supplied with 50Hz, N_s = 120*50/4 = 1500 RPM. The rotor runs slightly slower (e.g., 1450 RPM) to produce torque.
Worked example
Synchronous Speed – Practical Example
Real‑World| Parameter | Value |
|---|---|
| f | 50 Hz |
| P | 4 |
| Formula | Ns = 120·f / P |
Common mistakes
Watch unit consistency and the assumptions behind the formula; misapplying it outside its valid conditions is the most frequent error.Applications
Synchronous speed N_s = 120·f/P (RPM) is the rotational speed of the stator magnetic field in an AC motor. It depends on the supply frequency and the number of poles. Engineers use it to design motor windings, to select motors for variable speed drives, and to understand the operation of synchronous machines. By adjusting the frequency, they can control the motor speed. This formula is fundamental to AC motor theory and is used in motor design and application.
- AC motor design and pole configuration
- Variable frequency drive (VFD) speed control
- Synchronous generator and alternator design
- Motor selection for constant or variable speed applications
- Educational understanding of motor speed
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