Gear Ratio Calculator
Calculate gear ratio, output speed and output torque from driver and driven tooth counts. Handles compound multi-stage gear trains with a per-stage breakdown, applies a per-mesh efficiency to the torque, and reports the ratio as a decimal, as N:1 and as a speed change.
Input
A compound train multiplies the ratio of every stage together.
The input gear — the one connected to the motor.
The output gear — the one being turned.
Speed of the driver gear. Leave blank to get the ratio only.
Torque at the driver gear. Leave blank to skip the torque rows.
Applied once per stage. Spur gears run about 97–98% per mesh, worm drives far lower. Leave at 100% for the ideal case.
Output
| Quantity | Value |
|---|---|
| No data yet | |
| Stage | Driver → Driven | Stage ratio | Speed out (rpm) | Torque out (N·m) |
|---|---|---|---|---|
| No data yet | ||||
Guides
A gear ratio is just one division — driven teeth ÷ driver teeth — but the numbers that follow from it are what you actually need: how fast the output turns, how much torque it makes, and what happens once you chain several stages together. This calculator does all of it, for a single pair or a full compound train.
How to use it
- Leave Gear Train on Single gear pair and enter the driver tooth count (the gear the motor turns) and the driven tooth count (the gear being turned).
- Add the input speed in rpm and, if you care about torque, the input torque in N·m. Either can be left blank — the ratio still comes out.
- Drop the efficiency per mesh below 100% to see the torque a real gearset delivers after friction.
For a gearbox with more than one reduction, switch to Compound train and list the stages one per line, driver first:
20, 60
15, 45
Commas, colons (20:60) and slashes (20/60) all parse the same way, and # lines are ignored, so you can paste straight from a spec sheet. The stage table then shows the ratio, speed and torque leaving each stage, and the summary multiplies them into a total.
The formulas
stage ratio = driven teeth ÷ driver teethtotal ratio = ratio₁ × ratio₂ × …— a compound train multiplies, it does not addoutput speed = input speed ÷ total ratiooutput torque = input torque × total ratio × η^n, where η is the per-mesh efficiency and n the number of stages
What does a 3:1 ratio actually mean?
The output turns once for every three turns of the input, at three times the torque (minus losses). A ratio above 1 is a reduction — slower and stronger, which is what most gearboxes are for. A ratio below 1 is an overdrive: faster, weaker, and quoted as 1:2 rather than 0.5:1.
Do idler gears change the ratio?
No. An idler sitting between the driver and the driven gear reverses the direction of rotation but cancels out of the ratio entirely, so leave it out of the calculation. Only the first and last gear in each stage matter.
What efficiency should I use?
About 97–98% per mesh for spur or helical gears, 90–95% for bevel gears, and anywhere from 40% to 85% for a worm drive depending on the lead angle. The losses compound: three spur meshes at 97% leave 91% of the input torque, not 97%.
Privacy
Everything is calculated in your browser. No values are sent to a server.
Related tools
Once you know the output speed and torque, the Shaft Power & Torque Calculator converts between power, torque and rpm to size the motor. If the drive is a belt rather than a gear pair, the Belt Length Calculator works out belt length and wrap angles from pulley diameters. For bicycle drivetrains — chainrings, cogs and gear inches — use the Bicycle Gear Ratio Calculator instead.