Four calculations in one place: the synchronous speed of an AC motor from its poles and supply frequency (with slip for the running speed), the rpm needed for a surface speed on a given diameter, the surface speed at a known rpm, and the driven speed of a belt or pulley drive.
Worked example
These are example values. Change any entry above and press Calculate to run your own numbers.
Synchronous speed
1,800 rpmN = 120 × f ÷ poles
Speed at 3% slip
1,746 rpmN × (1 − slip)
An induction motor runs slightly below synchronous speed, by the slip, which grows with load. The nameplate full-load rpm is the figure to use for a real motor.
How it works
Rotational speed links a motor, the machine it drives and the speed of the product or tool. An induction motor's speed is set by its pole count and the supply frequency. A wheel, roll or drill has a rim speed that follows from its diameter and rpm. A pulley pair changes speed in the ratio of their diameters.
The formulas
Synchronous speed (rpm) = 120 × frequency (Hz) ÷ number of poles
Full-load speed on the nameplate is a few percent lower, by the slip.
Frequently asked questions
How do you calculate motor rpm from poles and frequency?
Synchronous rpm is 120 times the frequency divided by the number of poles. A 4-pole motor on 60 Hz is 120 × 60 ÷ 4 = 1,800 rpm, and on 50 Hz it is 1,500 rpm. A 2-pole motor on 60 Hz is 3,600 rpm.
Why is the nameplate rpm lower than synchronous speed?
An induction motor has to run slightly slower than the rotating field to produce torque. The difference is the slip, usually a few percent and larger at full load. A 4-pole 60 Hz motor with 3% slip runs at about 1,746 rpm. The nameplate figure is the one to use for a real motor.
How do I find the rpm for a given surface speed?
Divide the surface speed by the circumference. A 300 mm diameter wheel has a circumference of 0.942 m, so a rim speed of 1,649 m/min needs about 1,750 rpm. The calculator accepts m/min, ft/min (SFM) and m/s, and diameters in mm or inches.
How do pulley sizes change speed?
The driven speed is the driver speed times the ratio of driver diameter to driven diameter. A 100 mm driver at 1,750 rpm turning a 250 mm driven pulley gives 700 rpm. Use the pitch diameter of a V-belt or timing pulley where you have it.
Does belt slip change the result?
A little. A V-belt can lose a percent or two of speed under load. A timing (toothed) belt or a chain does not slip, so the ratio holds exactly. The pulley result here is the no-slip figure.
Can a drive run a motor faster than its synchronous speed?
A variable frequency drive changes the supply frequency and so the synchronous speed. Running above the base frequency reduces the torque available, and the motor and the driven machine have their own speed limits, so check the nameplate and the manufacturer before doing it.
