Sheave ratio & driven speed
Driven speed and drive ratio from the two sheave diameters and the driver RPM — plus belt rim speed, so you can check a speed change or size a new sheave.
Sheave / pulley ratio & driven speed · V-belt drive
N₂ = N₁ × D₁ / D₂
What this gives you
Enter the two sheave (pulley) diameters and the driver's speed and this returns the driven speed, the drive ratio, and the belt rim speed. A belt drive turns the two sheaves at the same rim (belt) speed, so the smaller sheave spins faster in exact proportion to the diameters: N₂ = N₁ × D₁ / D₂, where D₁/N₁ are the driver (motor) sheave and D₂/N₂ are the driven. The drive ratio is simply D₂ / D₁ — greater than 1 is a speed reduction, less than 1 is a step-up. Switch the Mode selector to Solve driven dia and it runs the formula backward from a target driven speed — D₂ = D₁ × N₁ / N₂ — so you can size the sheave you need to hit a set RPM. The Units selector switches the diameters between inches and millimetres and reports rim speed in ft/min or m/s to match.
When you use it
This is the calculation behind every fan, pump, blower, or conveyor sheave change. Need a fan to run 15 percent slower to knock down airflow? Ratio the sheaves. Swapped a motor and the driven machine is now overspeeding? Check it here before you cut a belt. The rim speed — π·D₁·N₁ ÷ 12, in feet per minute — is the other number that matters: standard cast-iron sheaves are typically rated to about 6,500 fpm, and running past that is how sheaves come apart. If your rim speed is climbing toward that limit, you need a ductile-iron or spun sheave, not a bigger one.
Field note — use pitch diameter, not the OD you measure
The diameter in this formula is the pitch diameter — where the belt's tension line rides in the groove — not the outside diameter you put a tape across. On a V-belt sheave the pitch line sits a little below the rim, so the OD runs a fraction of an inch larger than the pitch diameter. For a quick ratio the OD is close enough because the small error cancels in the D₁/D₂ ratio, but if you want the driven RPM to land dead-on, pull the pitch diameters from the sheave data sheet.
Worked example
A 1750 RPM motor carries a 6 in driver sheave belted to a 12 in driven sheave. Driven speed is 1750 × 6 ÷ 12 = 875 RPM, a 2.00 : 1 reduction. Belt rim speed is π × 6 × 1750 ÷ 12 = about 2,749 fpm — well inside the limit for a standard sheave. Want 1,000 RPM at the driven shaft instead? Solve the ratio backward: D₂ = D₁ × N₁ ÷ N₂ = 6 × 1750 ÷ 1000 = 10.5 in.