Belt-drive fan speed

Estimate driven fan speed from pulley pitch diameters, motor speed and a specified slip allowance.

How this calculation works

This tool applies the inverse relationship between rotational speed and pulley pitch diameter. Enter motor speed, the driving pulley's effective pitch diameter, the driven pulley's effective pitch diameter and an assumed net speed-slip percentage. Multiply motor speed by the driver-to-driven diameter ratio to obtain ideal fan speed. Applying the slip reduction gives the estimated driven speed. The additional pitch-line-speed result uses the driver's circumference and motor revolutions per second; it is a driver surface speed rather than a measurement of the slipping belt. Use effective pitch diameters consistently rather than arbitrary outside dimensions. The arithmetic does not establish acceptable pulley sizes, belt loading, tension or fan speed. Manufacturer limits, guarding and the suitability of the whole drive remain separate checks.

Inputs and units

Motor speed (r/min)
Driver pitch diameter (mm)
Driven pitch diameter (mm)
Net speed slip (%): User-specified overall reduction from the ideal speed ratio.

Method and formula

Nfan,ideal = Nmotor × Ddriver/Ddriven; Nfan = Nfan,ideal(1−slip/100); driver pitch-line speed = π Ddriver Nmotor/60 with Ddriver in m.

Worked example

Example inputs

Motor speed: 1500 r/min
Driver pitch diameter: 100 mm
Driven pitch diameter: 200 mm
Net speed slip: 2 %

Calculation steps

Ideal fan speed = 1500 × 100 / 200 = 750 r/min.
Slip-adjusted fan speed = 750 × (1 − 2 / 100) = 735 r/min.
Driver pitch-line speed = π × (100 / 1000) × 1500 / 60 ≈ 7.853982 m/s.

Example results

Driven fan speed: 735 r/min
Ideal no-slip fan speed: 750 r/min
Driver pitch-line speed: 7.853981634 m/s

Example notes

Check fan maximum speed, pulley minimum size, belt ratings and guarding with the manufacturers.

Assumptions

Diameters are effective pitch diameters; the provided slip is a net speed reduction.

Limitations

No belt tension, horsepower rating, center-distance or critical-speed design.
Pitch-line speed is the driver surface speed, not a measured belt speed with slip.
Preliminary educational check; verify inputs and equipment data before design or operation.

Sources

Pennsylvania Department of Education: Belt and pulley ratios: Page 1: angular-speed ratio is the inverse pulley-diameter ratio