RPM Calculator
RPM, or revolutions per minute, is the standard measure of rotational speed for wheels, motors, pulleys, spindles, and any other rotating part. Knowing the RPM of a component lets you match drive ratios, select belt or chain sizes, check that a motor stays within its rated speed, and convert rotational motion into linear velocity. This calculator covers two common situations. The first is working out the wheel RPM of a vehicle from its road speed and tyre diameter. You enter the speed in km/h and the overall wheel diameter in metres and the tool returns the RPM the wheel must spin at to maintain that speed, along with the angular velocity in radians per second and the surface speed at the rim. The second mode calculates the synchronous speed of an AC induction or synchronous motor from the supply frequency and the number of poles. The formula is 120 times the frequency divided by the pole count. On a standard 50 Hz New Zealand supply, a 4-pole motor runs at 1500 RPM synchronously, while a 2-pole motor runs at 3000 RPM. The actual shaft speed of an induction motor is slightly lower than the synchronous speed due to rotor slip, typically 2 to 5 percent less at full load. You can switch between the two modes using the selector below. All results are rounded to one or two decimal places. Use these figures for planning and design estimates; always verify against manufacturer data sheets for safety-critical applications.
How it works
For wheel RPM, convert vehicle speed in km/h to metres per minute by multiplying by 1000 and dividing by 60. Wheel circumference equals pi times diameter in metres. RPM equals speed in m/min divided by circumference. Angular velocity in rad/s equals RPM times 2 pi divided by 60. Surface speed in m/s equals vehicle speed in km/h divided by 3.6. For motor RPM, the synchronous speed formula is RPM = 120 times frequency divided by number of poles. This is the no-load theoretical speed; induction motors run slightly slower under load due to slip.
Worked example
A vehicle travels at 60 km/h on wheels with a 0.65 m diameter. Speed in metres per minute = 60 times 1000 divided by 60 = 1000 m/min. Wheel circumference = pi times 0.65 = 2.0420 m. Wheel RPM = 1000 divided by 2.0420 = 489.7 RPM. Angular velocity = 489.7 times 2 pi divided by 60 = 51.28 rad/s. Surface speed = 60 divided by 3.6 = 16.67 m/s. For the motor mode: 50 Hz supply with 4 poles gives 120 times 50 divided by 4 = 1500 RPM.
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