Pulley Speed Ratio / Driven RPM Calculator

Pulley speed-ratio formula

Rearranging for driven speed gives:

The speed multiplier shown by the calculator is the reciprocal of the ratio:

Worked speed-reduction example

For d₁ = 100 mm, d₂ = 250 mm, and n₁ = 1,500 rpm:

1. Speed ratio: i = 250 / 100 = 2.5:1.
2. Speed multiplier: 1 / 2.5 = 0.4×.
3. Driven speed: n₂ = 1,500 × 100 / 250 = 600 rpm.
4. Ideal belt speed from the driver is 7.853982 m/s.

Because the ratio is above 1, this is a speed reduction. In the ideal model, the driven pulley turns at 40% of driver speed.

Speed increase and direct drive

When the driver pulley is larger than the driven pulley, i is below 1 and the driven pulley rotates faster. For example, a 250 mm driver, 100 mm driven pulley, and 1,500 rpm driver produce 3,750 rpm driven speed.

Equal reference diameters produce a 1:1 ratio and equal ideal RPM. The calculator reports these relationships explicitly so that ratio convention is not inferred from the number alone.

Use one consistent pulley reference system

Both pulley diameters must refer to the belt pitch line on one consistent system. ISO belt terminology distinguishes pitch, datum, effective, and outside diameters, including correction terms when datum or effective lines differ from the pitch line.

Do not combine an outside diameter for one pulley with a datum or pitch diameter for the other. Use the pulley and belt manufacturer’s documented reference values. A ratio can be numerically precise and still be physically wrong when incompatible diameter definitions are mixed.

Ideal ratio versus actual operating speed

ISO 1081 defines speed ratio from pitch diameters without allowance for slip and creep. This makes the formula appropriate for preliminary kinematics, but an actual friction-belt drive can run at a different driven RPM.

Actual differences can come from slip under load, belt creep, elastic stretch, wear, pulley groove condition, tension, contamination, temperature, and measurement uncertainty. Synchronous belt drives largely prevent gross slip when correctly engaged, but still require the correct pitch diameters and manufacturer design process.

Belt speed and next calculations

The calculated belt speed reuses the same canonical engine as the Belt Speed / Pulley RPM Calculator. Results above 30 m/s trigger a conservative engineering review warning because permissible speed varies by belt profile, construction, pulley balance, and manufacturer.

Use the V-Belt Length / Center Distance Calculator separately when the drive also requires datum length, center distance, and wrap-angle checks.

Engineering scope and limitations

This calculator assumes one open two-pulley drive with parallel shafts and no idler. Both pulleys rotate in the same direction. It excludes:

• crossed, quarter-turn, compound, variable-speed, cone-pulley, and multi-pulley arrangements;
• slip, creep, belt stretch, wear, loaded diameter changes, and transient overspeed;
• pulley groove or tooth geometry, belt profile, belt selection, and catalog availability;
• center distance, belt length, wrap angle, installation allowance, and take-up;
• power, torque, efficiency, service factor, belt count, tension, shaft or bearing load;
• pulley material, balance acceptance, vibration, guarding, temperature, contamination, maintenance, and service life.

Use the result as a transparent ideal speed relationship, then verify the complete drive with current manufacturer data and operating measurements.