Synchronous motor speed, power, and torque
Rotating mechanical power equals torque multiplied by angular speed. Motor torque can therefore be estimated from mechanical shaft output and RPM.
For a synchronous machine, speed is fixed by supply frequency and pole count. If electrical input power is used, efficiency must first convert it to mechanical shaft output.
How to use the motor torque calculator
- Choose power basis: Select mechanical shaft output or electrical input.
- Enter power: Use kW or horsepower; provide efficiency for electrical input.
- Enter speed: Supply known RPM or calculate synchronous RPM from frequency and poles.
- Calculate: Review torque, converted shaft power, speed, and angular speed.
Formula and variables
Use shaft power in watts and angular speed in radians per second. Synchronous speed Ns is in RPM.
τ = Pshaft/ω; ω = 2πN/60; Ns = 120f/p- τ — Shaft torque
- Mechanical turning moment (N·m)
- Pshaft — Shaft power
- Mechanical output power (W)
- N — Shaft speed
- Rotational speed (rpm)
- f — Supply frequency
- Electrical frequency (Hz)
- p — Poles
- Positive even pole count
Four-pole 50 Hz motor
A four-pole synchronous motor delivers 10 kW at 50 Hz.
- Power
- 10 kW shaft output
- Frequency
- 50 Hz
- Poles
- 4
- Ns = 120 × 50/4 = 1500 rpm
- τ = 10,000/[2π(1500)/60]
Result: Shaft torque is approximately 63.662 N·m.
The torque corresponds to the stated mechanical output at synchronous speed.
Understanding your results
Torque falls as speed rises at fixed power
The same shaft power produces less torque at a higher rotational speed.
- More poles reduce synchronous speed at the same frequency.
- Higher efficiency increases shaft output for a fixed electrical input.
- Nameplate power commonly refers to rated mechanical output, but verify documentation.
- Starting, pull-out, and transient torque require motor-specific data.
Assumptions
- The entered power and speed describe the same operating point.
- Efficiency is entered as a fraction of real electrical input converted to shaft output.
- Frequency and pole count define synchronous speed for the selected machine model.
Limitations
- Does not calculate electromagnetic torque angle, power factor, losses by component, starting torque, pull-out torque, or thermal limits.
- Does not replace manufacturer torque-speed curves or nameplate data.
- Efficiency may vary with load, voltage, and operating conditions.
Common mistakes
- Using electrical input directly as shaft power.
- Using RPM where radians per second are required.
- Entering an odd pole count.
- Confusing synchronous speed with induction-motor loaded speed.
Practical use cases
Motor sizing checks
Convert rated mechanical power and speed into nominal shaft torque.
Electrical machines coursework
Connect frequency, poles, synchronous speed, and torque.
Frequently asked questions
Why include efficiency?
Torque uses mechanical shaft power. Efficiency converts electrical input into an estimated mechanical output.
Is synchronous speed the same as induction motor speed?
No. An induction motor normally runs below synchronous speed because it requires slip.
Sources and review
- Improving Motor and Drive System Performance — U.S. Department of Energy. Accessed 2026-07-14.
- Electrical Science, Volume 4 — U.S. Department of Energy. Accessed 2026-07-14.
Reviewed 2026-07-14.