How to use the Synchronous Speed & Slip Calculator
- 1. Enter frequency and polesFor example 50 Hz and 4 poles.
- 2. Give rotor speed or slipWhichever the question gives you.
- 3. See the resultsAdd air-gap power to also get rotor copper loss and torque.
Induction motor speed formulas
The stator field rotates at the synchronous speed Ns = 120 f / P rpm. The rotor runs slightly slower, and the slip is s = (Ns − Nr) / Ns. Rotor currents have frequency fr = s f. The air-gap power Pg splits as Pg : rotor copper loss : mechanical power = 1 : s : (1 − s), and gross torque is T = Pg / ωs, with ωs = 2πNs/60.
Worked example: 4-pole, 50 Hz motor at 1,440 rpm. Ns = 120 × 50 / 4 = 1,500 rpm, s = 60/1,500 = 0.04 (4%) and fr = 0.04 × 50 = 2 Hz. With Pg = 10 kW, rotor copper loss = 0.4 kW, mechanical power = 9.6 kW and T = 10,000 / 157.08 = 63.7 N·m.
Exam questions
- A 6-pole, 50 Hz motor has 3% slip. Find the rotor speed (970 rpm).
- Find the number of poles of a 50 Hz motor running near 960 rpm (6 poles, Ns = 1,000).
- Find the rotor copper loss if the rotor input is 20 kW at 4% slip (0.8 kW).
- Why can an induction motor never run at synchronous speed?
Synchronous speeds at 50 Hz are 3,000, 1,500, 1,000, 750 and 600 rpm for 2, 4, 6, 8 and 10 poles. Full-load slip of small motors is usually a few percent.
Frequently asked questions
Why can't the rotor reach synchronous speed?
At Ns there is no relative motion between the field and the rotor, so no voltage is induced, no rotor current flows and there is no torque.
What does negative slip mean?
The rotor is driven faster than Ns, so the machine works as an induction generator and feeds power back.
How do I find the number of poles from the speed?
Find the synchronous speed just above the rated speed (for example 1,500 rpm for 1,440 rpm) and use P = 120 f / Ns.
Is this tool free?
Yes. You enter your name and WhatsApp number once to see your result, and all other Uncodemy tools then open without the form.