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Pulley RPM Calculator

Find the driven pulley RPM in any belt drive

Result

656
2.67:1

How it is calculated

A belt moves at one speed over both pulleys, so rim speed is the same on each: diameter times rpm is constant. That gives driven rpm = driver rpm × driver diameter ÷ driven diameter, rounded to a whole number. The tool also shows the ratio driven diameter ÷ driver diameter written as N:1, which is how many turns of the driver make one turn of the driven pulley.

The two diameters just have to use the same unit (mm, inches); the unit cancels out. All three inputs must be greater than zero. The formula assumes no belt slip and measures the effective diameter at the belt contact. For a V-belt that is the pitch diameter, which is a little smaller than the outside diameter. A ratio above 1 means the driven pulley turns slower than the driver, and below 1 means it turns faster.

Worked example

A 1750 rpm motor with a 3 inch pulley drives a machine pulley of 8 inches.

Driven speed: 1750 × 3 ÷ 8 = 656.25, shown as 656 rpm. Ratio: 8 ÷ 3 = 2.67, shown as 2.67:1, so the motor turns 2.67 times for each turn of the machine pulley. Swapping to a 5 inch driven pulley would raise the speed to 1050 rpm.

Try this example →

Common mistakes

  • Swapping the driver and driven pulleys. The motor pulley goes in the driver fields; swapping them gives 4667 rpm instead of 656 in the example.
  • Mixing units, such as one diameter in inches and the other in millimetres. They have to match, or the result is off by a factor of 25.4.
  • Using outside diameter for V-belts where the pitch diameter applies. The result is slightly off, which matters when you need an exact speed.
  • Expecting the speed to match exactly in practice. Belt slip and load reduce the real driven speed a little.
  • Reading the ratio as a speed multiplier. 2.67:1 here is a reduction: the driven shaft is slower, not faster.

About this calculator

This calculator finds a driven pulley's speed in a belt drive using N₂ = N₁ × D₁/D₂, where N₁ and D₁ are the driver pulley's RPM and diameter, and D₂ is the driven pulley's diameter. This follows from the belt moving at the same linear speed over both pulleys (v = πDN for each), so a smaller driven pulley must spin faster to match that shared belt speed, and a larger one must spin slower — the same principle behind gear ratios, just applied to a belt-and-pulley system instead of meshing teeth.

Mechanics and machinists use this to select pulley sizes for engines, air compressors, and conveyor drives when a target output speed is needed from a fixed-speed motor, and industrial maintenance techs use it to diagnose whether a swapped pulley has changed a machine's operating speed from spec.

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