Gear ratio calculation: speed, torque and tooth count
Gear ratio is the one number that links motor speed to output speed and input torque to output torque. Once you can count teeth and read it both ways, sizing a drive — gearbox, chain, or belt — stops being guesswork.
What gear ratio actually means
A gear ratio is simply the ratio of the driven (output) gear's tooth count to the driver (input) gear's tooth count. A ratio of 3:1 means the output shaft turns once for every three turns of the input — it runs a third of the speed and, ignoring losses, delivers three times the torque. That trade is the whole point of a gearbox: you buy torque with speed, or speed with torque.
The gear ratio formula
Because meshing gears share the same module, tooth count is proportional to pitch diameter — so you can equally write the ratio as the ratio of the two pitch diameters. For a multi-stage gearbox, the total ratio is the product of the individual stage ratios: a 4:1 stage feeding a 5:1 stage gives 20:1 overall.
Speed down, torque up
The two consequences of a reduction ratio follow directly:
This is why a small, fast, cheap motor plus a reduction gearbox often beats a large, slow, direct-drive motor: you generate power where it is efficient and convert it to torque where you need it.
Module, pitch and centre distance
Two gears only mesh if they share the same module (m), the millimetres of pitch diameter per tooth. Pitch diameter d = m · N. From there the centre distance between two meshing gears is:
Mismatch the module and the teeth simply will not engage — a surprisingly common error when mixing gears from two suppliers.
Worked example
A 1450 rpm motor delivering 10 N·m must drive a conveyor head shaft at about 290 rpm.
- Required ratio: i = 1450 / 290 = 5:1
- Tooth counts: a 20-tooth pinion needs a 20 × 5 = 100-tooth gear
- Output torque: Tout = 10 × 5 × 0.97 = 48.5 N·m
- Centre distance (module 2): a = 2 × (20 + 100) / 2 = 120 mm
So a single 5:1 spur stage turns a 10 N·m, 1450 rpm motor into a 48.5 N·m, 290 rpm output — exactly the conveyor duty, with the gearbox footprint set by the 120 mm centre distance.
Quick reference: common ratios
| Pinion teeth | Gear teeth | Ratio | Output speed (1450 rpm in) |
|---|---|---|---|
| 20 | 40 | 2:1 | 725 rpm |
| 20 | 60 | 3:1 | 483 rpm |
| 20 | 100 | 5:1 | 290 rpm |
| 15 | 150 | 10:1 | 145 rpm |
| 12 | 240 | 20:1 | 72.5 rpm |
Run any combination — tooth count, module, centre distance and torque — through the gear ratio calculator to skip the arithmetic.
Common mistakes
- Inverting the ratio. Driven over driver gives reduction; flipping it gives an overdrive you did not intend.
- Mixing modules. Two gears of different module will not mesh, whatever their tooth counts.
- Ignoring worm efficiency. A 70% worm drive delivers far less output torque than the ratio alone suggests.
- Forgetting multi-stage multiplication. Total ratio is the product of stages, not the sum.
- Too few pinion teeth. Below about 17 teeth, standard 20° involute gears undercut and weaken unless profile-shifted.
If you are procuring cut gears against a drawing, balloon the tooth, bore and runout callouts before sending the print to a vendor so the FAI is unambiguous. CadNexa's auto-ballooning tool numbers every GD&T callout on a PDF gear drawing in the browser, and you can log the measured results on a ready inspection template.
Frequently asked questions
How do you calculate gear ratio?
Divide the number of teeth on the driven gear by the number of teeth on the driver gear. A 60-tooth gear driven by a 20-tooth pinion has a ratio of 60 / 20 = 3, written 3:1. The same value equals the ratio of input speed to output speed.
Does a higher gear ratio mean more torque?
Yes. A higher reduction ratio multiplies torque by that ratio (minus efficiency losses) while dividing output speed by the same ratio. A 5:1 reduction gives roughly five times the input torque at one-fifth the speed.
How do I find the centre distance between two gears?
Centre distance equals the module multiplied by the sum of the two tooth counts, divided by two: a = m · (N1 + N2) / 2. For module 2 with 20 and 60 teeth, that is 80 mm.
Why must meshing gears share the same module?
Module sets the tooth size — the pitch diameter per tooth. Two gears with different modules have differently sized teeth that cannot engage correctly, regardless of their tooth counts.