Synchronous Speed & Slip Calculator
Enter frequency, poles and rotor speed to get synchronous speed, slip, rotor frequency and torque.
Step-by-step
- Enter valid values to begin.
Torque from T = 5252 × HP / rpm. The breakdown point uses the Kloss approximation with the ratio entered (about 2.5 for a NEMA design B motor). Constant-slip scaling for a VFD is an approximation that ignores V/Hz boost and thermal limits.
Synchronous Speed and Slip: Why an Induction Motor Never Quite Keeps Up
Core Engineering Principles
Feed three-phase current to a stator wound with P poles and you get a magnetic field that rotates at a fixed speed set only by the frequency and the number of poles: Ns = 120 × f / P. A 4-pole motor on 60 Hz has a field turning at 1,800 rpm. The rotor has to chase that field, but it can never catch it. If the rotor turned at exactly synchronous speed, the field would stand still relative to the rotor bars, no voltage would be induced, no current would flow, and there would be no torque. So the rotor lags, and the difference is slip.
Slip is the useful number on the plant floor. At no load it’s a fraction of a percent. At full load a typical NEMA B motor runs 2 to 3% below synchronous, say 1,750 rpm on a 4-pole 60 Hz machine. Rotor frequency equals slip times line frequency, so at full load a 60 Hz motor’s rotor sees only about 1.7 Hz. Torque is roughly proportional to slip near the operating point, which is why a motor at 1,780 rpm is lightly loaded and one at 1,720 rpm is working hard. Slip is also how you estimate load without a clamp meter, and it’s the reason a VFD speed reference gives you a speed that sags a little under load.
Torque (lb·ft) = 5252 × HP / N • T (N·m) = 9550 × kW / N • Kloss: T / Tmax = 2 / (s/sb + sb/s)
NEC & Standard References
NEMA MG-1 sets the standard frame sizes and the speed-torque design letters. Design B, the general-purpose motor, has full-load slip typically 1.5 to 3%, design C has more starting torque and similar slip, and design D has high slip of 5 to 13% for punch presses and hoists. NEMA MG-1 1.17 defines synchronous speed and slip. IEC 60034-1 specifies rated speed and tolerances, and lets the manufacturer vary rated speed by ±20% of the slip. NEC 430.7(A) requires the nameplate to show full-load rpm, so you always have the number to compare. For variable speed, NEMA MG-1 Part 30/31 covers inverter-fed operation.1. Synchronous speed = 120 × 60 / 4 = 1,800 rpm.
2. Slip = (1,800 − 1,750) / 1,800 = 2.78% (50 rpm).
3. Rotor frequency = 0.0278 × 60 = 1.67 Hz.
4. Full-load torque = 5,252 × 50 / 1,750 = 150 lb·ft.
5. Breakdown torque on a design B motor is about 2.5 times full-load torque, near 375 lb·ft, at around 13% slip, which is about 1,560 rpm.
- Don’t reduce poles by swapping motors blindly. A 1,750 rpm motor and a 3,550 rpm motor have very different torque for the same horsepower, and a pump or fan load changes with the cube of speed.
- Slip rising means load or voltage trouble. If a motor you tuned at 1,775 rpm now runs at 1,740, check for voltage unbalance, a bad bearing, a loose coupling and a fouled load before you replace anything.
- A fan on a 50 Hz motor run at 60 Hz speeds up 20% and the power rises by 73%. Check the motor and the driven load rating first.