In a belt drive the belt runs at one speed, so each pulley's diameter × RPM stays equal: D₁·N₁ = D₂·N₂. That makes pulley speed inversely proportional to diameter — a bigger driven pulley turns slower, a smaller one faster. Choosing the pulley ratio is how you gear a motor up or down: enlarge the driven pulley to reduce speed (and gain torque), shrink it to increase speed. The unit doesn't matter since the diameters cancel; only their ratio counts.
Reviewed: June 20, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: the belt-drive speed relation D₁N₁ = D₂N₂.
The pulley speed equations
The shared belt speed makes the product of diameter and rotational speed the same on both pulleys, so to find the driven speed, multiply the driver's diameter and speed and divide by the driven diameter. The speed ratio is the inverse of the diameter ratio, and because power is conserved, the torque ratio is the inverse of the speed ratio — a speed reduction is a torque increase. Any consistent diameter unit works.
Worked example — a speed-reduction drive
Scenario: A motor pulley of 100 mm runs at 1000 RPM and drives a 200 mm pulley. What is the driven speed?
The driven pulley turns at 500 RPM — half the motor speed, because it's twice the diameter. Double it again to 400 mm and the speed drops to 250 RPM (a 4:1 reduction); use a 50 mm driven pulley instead and it spins up to 2000 RPM. Each reduction in speed brings a matching increase in torque, which is exactly how belt drives trade a motor's high speed for the torque a load needs.
Frequently Asked Questions
N₂ = D₁·N₁/D₂. 100 mm at 1000 RPM driving 200 mm → 500 RPM.
N₁/N₂ = D₂/D₁ — the inverse of the diameter ratio. 2× diameter = half speed.
Yes — slower, but with proportionally more torque. Inverse to diameter.
Opposite to speed. Half the speed ≈ double the torque (power is conserved).
Any — they cancel. Use the same unit for both (mm or in); for V-belts use pitch diameter.