Pulley, Belt & Gear Ratio
Speed and torque through belt, gear, or chain drives with up to four stages, plus open-belt length and wrap angle from the centre distance.
Bigger driven,
slower and stronger.
Ratios, stages, and the belt geometry that people get wrong.
Ratio, speed, torque
For each stage the ratio is driven ÷ driver — pitch diameters for belts, tooth counts for gears and chains. Output speed = input speed ÷ ratio; output torque = input torque × ratio × efficiency; power out = power in × efficiency. Stages multiply. A ratio above 1 is a reduction; below 1 an overdrive. If you know power rather than torque, torque is derived from P = 2π·n·T ÷ 60.
Belt length and wrap
Open belt on two pulleys: L ≈ 2C + π(D1 + D2)/2 + (D2 − D1)² ÷ 4C, and the wrap on the small pulley ≈ 180° − 2·asin((D2 − D1) ÷ 2C). Under about 120° of wrap a V-belt slips under load; the utility warns. Belt speed = π × D1 × n1 is shown because classical V-belts are limited to roughly 30 m/s. Order the belt by its standard pitch length nearest to L and adjust C.
What is left out
Belt slip and creep (typically 1–3 %), chain polygonal effect, gear module and centre distance checks, service factors, and the drive's power rating are not modelled; enter an efficiency and pick the belt or chain from the maker's tables. Inputs stay in your browser; the same four anonymous usage counts as the rest of the site apply.