Pulley Ratio Converter

Pulley systems transfer rotational motion between shafts using a belt. The relationship between pulley diameters and their speeds (RPM) follows a simple inverse ratio.

The fundamental pulley formula:

• Driver RPM x Driver Diameter = Driven RPM x Driven Diameter
• Or equivalently: RPM1 x D1 = RPM2 x D2

Solving for each variable:

• Driven RPM = (Driver RPM x Driver Diameter) / Driven Diameter
• Driver RPM = (Driven RPM x Driven Diameter) / Driver Diameter
• Driven Diameter = (Driver RPM x Driver Diameter) / Driven RPM
• Driver Diameter = (Driven RPM x Driven Diameter) / Driver RPM

The speed ratio (also called transmission ratio):

• Speed Ratio = Driver Diameter / Driven Diameter = Driven RPM / Driver RPM
• A ratio greater than 1 means speed increase (overdrive).
• A ratio less than 1 means speed reduction (underdrive).
• A ratio of exactly 1 means both pulleys spin at the same speed.

Written with a colon, the smaller side is normalised to 1, so a 3-inch driver on a 9-inch driven pulley is a 1:3 reduction and the same pair swapped is a 3:1 increase. Say which way round it goes rather than trusting the colon alone; plenty of shop conversations go wrong at exactly this point.

Practical example: A motor runs at 1,750 RPM with a 3-inch pulley driving a 9-inch pulley on a machine.

• Driven RPM = (1,750 x 3) / 9 = 583 RPM
• Speed ratio = 3/9 = 1:3 (the machine runs at one-third the motor speed)
• Belt speed = pi x (3/12) ft x 1,750 = 1,374 FPM, comfortably inside the V-belt limit
• Torque at the machine = 3x the motor torque, since the speed fell to a third

Measure the pitch diameter, not the rim. Every number above assumes the diameter of the circle the belt actually rides on. A V-belt sits down inside its groove, so the outside edge of the sheave measures larger than the pitch diameter, typically by a few tenths of an inch on small pulleys. Use the manufacturer’s pitch diameter where you have it. A flat belt or a poly-V riding on the surface is close enough to the measured diameter that it does not matter.

Common applications:

Important design considerations:

• The belt speed (feet per minute) should not exceed the manufacturer’s recommendation, typically 5,000-6,500 FPM for standard V-belts.
• Belt speed = pi x Pulley Diameter (ft) x RPM.
• Very high speed ratios (above 6:1) should use multiple stages rather than a single belt drive.
• Torque is inversely proportional to speed: when you reduce speed by half, you double the available torque.
• When selecting pulleys, consider the minimum recommended pulley diameter for the belt width being used.