Pulley Speed Calculator — Fan RPM, Drive Ratio and Belt Length
On a belt-driven fan — centrifugal, roof exhaust or large axial — the cheapest way to change airflow is to change a pulley (sheave). Enter the motor rpm and both pitch diameters to get fan rpm, belt speed, wrap angle and belt length; enter a target fan rpm and the calculator sizes the new pulley and warns whether the motor has enough power.
No signup · Works on mobile · Formulas shown below · Updated 2026-11-02
Engineering estimate for preliminary sizing. Verify against the fan curve, local codes and your system measurements before purchase. Ask a Longwell engineer to check your duty point free of charge.
Pulley speed and belt length formulas
Drive ratio i = d₂ / d₁ ≈ n₁ / n₂ Fan speed n₂ = n₁ × d₁ / d₂ × (1 − ε) // ε = slip, about 1–3 % for V-belts Belt speed V = π × d₁ × n₁ / 12 // fpm, d in inches Wrap, small pulley α ≈ 180° − 57.3° × (d₂ − d₁) / C Open-belt length L ≈ 2C + π(d₁ + d₂)/2 + (d₂ − d₁)² / (4C) // Use pitch diameters, not the outside diameter of the sheave
When a new pulley changes the fan speed, airflow, pressure and power follow the fan laws: airflow ∝ rpm, pressure ∝ rpm², power ∝ rpm³. Raising fan speed by 10 % therefore needs about 33 % more motor power.
Fan rpm for common motor speeds and pulley ratios (2 % slip)
Motor (60 Hz)
i = 1
i = 1.25
i = 1.6
i = 2
i = 2.5
i = 3.15
2-pole 3,450 rpm
3,381
2,705
2,113
1,691
1,352
1,073
4-pole 1,750 rpm
1,715
1,372
1,072
858
686
544
6-pole 1,140 rpm
1,117
894
698
559
447
355
8-pole 870 rpm
853
682
533
426
341
271
Fan speeds in rpm. On a 50 Hz supply, motor and fan speeds are about 5/6 of these values (e.g. a 4-pole motor runs about 1,450 rpm).
Worked example: 10 % short on airflow — which pulley do I change?
Given: a 4-pole motor at 1,750 rpm, 5 in. motor pulley, 8 in. fan pulley, 20 in. centers. The fan runs about 1,072 rpm and the measured airflow is about 10 % below design.
Target speed = 1,072 × 1.10 ≈ 1,180 rpm
Option A — fan pulley = 5 × 1,750 × 0.98 / 1,180 ≈ 7.27 in.; choose the nearest standard sheave
Option B — motor pulley = 1,180 × 8 / (1,750 × 0.98) ≈ 5.50 in.
Power × 1.10³ ≈ 1.33: a fan drawing 3.0 BHP now needs about 4.0 BHP — confirm the motor nameplate HP covers it
The belt length changes with the pulley size; recalculate and pick a standard belt.
Load the preset “Short on airflow” to see both options and the fan-law changes.
Frequently Asked Questions
How do you calculate pulley speed?
Driven pulley rpm = driver rpm × driver diameter ÷ driven diameter, minus about 1–3 % belt slip. For a 1,750 rpm motor with a 5 in. motor pulley and an 8 in. fan pulley: 1,750 × 5 ÷ 8 × 0.98 ≈ 1,072 rpm.
Should I use the outside diameter or the pitch diameter?
Use the pitch (datum) diameter — the diameter at the belt's pitch line. A V-belt sheave's outside diameter is slightly larger, so using it introduces errors in both speed and belt length.
What should I check before speeding up a fan?
Power rises with the cube of speed — about 33 % more for a 10 % speed increase — and you must stay below the fan's maximum rated rpm and bearing limits. If the motor lacks margin, change the motor too, or switch to a direct-drive EC fan.
How do you calculate belt length?
For an open drive, L ≈ 2C + π(d₁ + d₂)/2 + (d₂ − d₁)²/(4C), where C is the center distance. Choose the nearest standard belt, then recalculate or adjust the center distance on site, leaving take-up for tensioning.
Belt drive or direct-drive EC fan?
A belt drive lets you change speed by swapping pulleys, but brings belt losses, slip, belt replacement and re-tensioning. A direct-drive EC fan has no belt losses, adjusts speed continuously and needs little maintenance, so EC fans often replace belt-driven fans in new projects and energy retrofits — estimate the payback with the EC vs AC savings calculator.
Link to or Cite This Tool
This calculator is free to reference in articles, forums, specifications and course material. Please credit it with a link:
<a href="https://www.longwellfans.com/resources/belt-drive-pulley-calculator/">Pulley Speed & Belt Length Calculator (Belt-Drive Fans)</a> by LONGWELL Fans
