Pulley and Belt Calculator
Calculate driven pulley RPM, speed ratio, open or crossed belt length, wrap angle on the small pulley and belt speed from diameters and center distance.
Interactive calculator · Method PULLEY-BELT-1.0 · Last reviewed: 2026-11-04
Calculate your scenario
Driven RPM = driver RPM × driver diameter ÷ driven diameter (no slip).
Your inputs
Default worked example. Edit the inputs to calculate your scenario.
Default worked example
Driven RPM = 1,750 × 60 ÷ 75 = 1,400; open belt length = 712.28 mm at 250 mm centers.
How to use the calculator
Pick the length unit, enter both pitch diameters, the shaft center distance, the driver speed and whether the belt runs open or crossed.
What the result means
A 60 mm driver at 1,750 RPM turning a 75 mm pulley on 250 mm centers drives it at 1,400 RPM and needs an open belt about 712.28 mm long, with 176.56° of wrap on the small pulley.
Formula and units
Driven RPM = driver RPM × driver diameter ÷ driven diameter (no slip). Open belt: β = asin((D − d) ÷ 2C), length = 2√(C² − ((D − d)/2)²) + π(D + d)/2 + (D − d)β, wrap on the small pulley = 180° − 2β. Crossed belt: β = asin((D + d) ÷ 2C), length = 2√(C² − ((D + d)/2)²) + (D + d)(π/2 + β), wrap = 180° + 2β. The common approximation 2C + π(D + d)/2 + (D ∓ d)² ÷ 4C is shown for comparison. Belt speed = π × driver diameter × RPM.
Worked examples
60 mm to 75 mm pulleys on 250 mm centers: Driver pulley pitch diameter: 60 mm or in; Driven pulley pitch diameter: 75 mm or in; Center distance between shafts: 250 mm or in; Driver speed: 1750 RPM; Length unit: mm; Belt arrangement: open.
Example result: Driven pulley speed: 1,400 RPM; Speed ratio (driven ÷ driver diameter): 1.25 : 1; Belt pitch length: 712.28 mm; Belt length by common approximation: 712.28 mm; Wrap angle on smaller pulley: 176.56°; Belt speed: 5.498 m/s.
3 in to 9 in pulleys on 20 in centers: Driver pulley pitch diameter: 3 mm or in; Driven pulley pitch diameter: 9 mm or in; Center distance between shafts: 20 mm or in; Driver speed: 1725 RPM; Length unit: in; Belt arrangement: open.
Example result: Driven pulley speed: 575 RPM; Speed ratio (driven ÷ driver diameter): 3 : 1; Belt pitch length: 59.3 in; Belt length by common approximation: 59.3 in; Wrap angle on smaller pulley: 162.75°; Belt speed: 1,354.8 ft/min.
Limitations and common mistakes
Ideal pitch-diameter geometry with no belt slip, stretch or thickness. Use pitch diameters, not outside diameters, when matching a belt size. This does not rate power capacity, belt tension, bearing loads or guarding; use the belt and pulley maker’s data for those.
Measuring the outside diameter of a V-belt pulley instead of its pitch diameter, which makes the computed belt too long and the speed ratio slightly wrong.
Sources and assumptions
Method PULLEY-BELT-1.0; last formula review 2026-11-04. Sources and their supported claims. Calculation methodology.