Find the gear ratio of one or more gear, chain or belt stages, with the output speed, the torque after losses and which way the output shaft turns.
A 12-tooth gear turning a 36-tooth gear makes the second one turn three times slower and three times harder. That trade of speed for torque is what every gearbox, bicycle and winch is built on. Enter the teeth on each pair of gears, or the sprockets on a chain or the pulleys on a belt, and this calculator works out the overall ratio. It also gives the output speed and torque, and which way the last shaft turns.
Add as many stages as the train has. In a compound gearbox each driven wheel shares its shaft with the next driving wheel, so the ratios multiply. A table shows the speed and torque after every stage, and a drawing shows each wheel at a size proportional to its tooth count.
The calculator opens with one stage of 12 driving teeth and 36 driven teeth, an input of 1500 rpm and 10 N·m, and 98% efficiency. It reports:
Load Sample moves on to a two-stage 12:36 and 15:45 reducer (9 : 1, 161.11 rpm from 1,450), a 40:20 overdrive that doubles the speed, and a bicycle with a 50-tooth chainring and a 25-tooth sprocket. Pedalling at 90 rpm turns that wheel at 180 rpm, the same way round, since a chain does not reverse rotation.
Each stage’s ratio is the driven count divided by the driving count, and the total is the product of all of them. Output speed is the input divided by that total. Output torque is the input times the total, reduced by the efficiency once for every stage: 98% is typical for a spur gear mesh and 95–97% for a chain. Direction flips at every pair of meshing gears and stays the same through a chain or belt. That is why two gear stages turn the output the same way as the input. For a belt, enter the two pulley diameters instead of tooth counts. A gear with a fractional tooth count is refused: “Stage 1: gears have whole numbers of teeth. For belt pulleys, switch the stage to chain/belt and enter the diameters.”
An idler gear between two others changes the direction but not the ratio. To model one, add it as its own stage with equal driving and driven counts. Planetary and worm gears follow different formulas and are not covered here. Belts slip by 1–3% under load, so a belt drive turns a little slower than the ratio says. The efficiency figure is a single value applied to every stage, so enter the lowest you expect if your stages differ.
Stages, from the input shaft to the output
In a compound train the driven wheel of one stage sits on the same shaft as the driving wheel of the next. For belts, enter pulley diameters in any one unit.
Gear ratio
3 : 1
Reduction: slower and stronger at the output
Output speed
500 rpm
Output torque
29.4 N·m
Output turns
opposite to input
Wheels drawn to the size of their tooth count; the shaded wheel is the input, the orange ring is the output.
| Stage | Ratio | Speed after | Torque after | Turns |
|---|---|---|---|---|
| 1: 12 → 36 | 3 : 1 | 500 rpm | 29.4 N·m | reversed |
Ratio = driven ÷ driving, multiplied across stages. Output speed = input ÷ ratio; output torque = input × ratio × efficiency per stage. Each pair of meshing gears reverses the direction; a chain or belt does not.