BenchGear, Pulley & Belt Calculator
Ratio, output speed, and torque for a gear, sprocket, or pulley drive — plus exact belt length and angle of wrap when you give a centre distance.
Belt geometry
Formula
Wall charts approximate belt length as
2C + 1.57(D + d) + (D − d)² ÷ 4C. That drops the higher-order terms and
runs slightly short — by 0.5 mm on a typical drive, but by 10 mm when the pulleys
are very unequal. This page reports the exact closed form and shows the
approximation beside it, so you can match a catalog that used the shorthand.
Assumptions
- Ratio is driven ÷ driver throughout, so a value above 1 is a reduction: output turns slower, torque rises by the same factor.
- Torque multiplication is ideal. Real drives lose a few percent per stage to friction, and a belt loses more as it slips.
- Belt length is the pitch length of an open drive. Crossed belts, idlers, and serpentine routing are not modeled.
- Pulley sizes are pitch diameters, not outside diameters. On a V-belt those differ by the groove geometry.
- A wrap angle much below 120° on the driven pulley is where slip becomes the limit, whatever the length says.
Worked example
A 14-tooth driver into a 42-tooth driven sprocket is 3.00 : 1. At 1800 rpm in, the output turns 600 rpm and torque triples. Two pulleys of 200 mm and 100 mm on a 500 mm centre distance need a belt 1476.2 mm long, wrapping 191.5° on the large and 168.5° on the small.
Related
- Bearing sizes — what the shafts run in
- All calculators