What this calculator does
The Gear Ratio Calculator describes what happens when one gear drives another. Enter the number of teeth on the driver (input) gear and the driven (output) gear, the input speed, and — if you know it — the input torque. The calculator returns the gear ratio, the output speed, the output torque adjusted for the efficiency you specify, and the power transmitted through the pair.
The same arithmetic applies to sprockets on a chain, pulleys on a timing belt, and to a first approximation even to belt-and-pulley drives without slip. It works in N·m or lb·ft and runs entirely in your browser, in English, Arabic, and Spanish.
How to use the Gear Ratio Calculator
- Count the teeth on the driving gear (N1) and on the driven gear (N2). Both must be whole numbers.
- Enter the input speed of the driver gear in RPM.
- Optionally enter the input torque and choose its unit (N·m or lb·ft).
- Set the efficiency — a single spur-gear mesh is typically 96–98%, so the default of 97% is a good starting point. For each additional stage, apply the efficiency again (two stages ≈ 0.97 × 0.97).
- Click "Calculate" to see the ratio, output speed, output torque, and transmitted power.
Formulas
A ratio above 1 is a speed reduction: the output turns slower and, thanks to the conservation of power, delivers proportionally more torque (minus the efficiency loss). A ratio below 1 is an overdrive: faster output with less torque.
Examples
- A 20-tooth pinion drives a 60-tooth gear at 1,500 RPM with 10 N·m input, η = 97%: ratio i = 3 : 1, output speed = 500 RPM, output torque = 10 × 3 × 0.97 ≈ 29.1 N·m, and transmitted power ≈ 1.57 kW (2.1 hp).
- A 12-tooth sprocket drives a 36-tooth sprocket: i = 3 : 1 — the same ratio as 20 : 60. Tooth count only matters through the ratio.
- A 60-tooth gear driving a 20-tooth pinion at 600 RPM: i = 0.333, so the output spins at 1,800 RPM — a 3× speed increase with about a third of the torque.
Frequently asked questions
Does the size of the teeth change the result?
No. The ratio depends only on the tooth counts (or, for belts and friction drives, on the diameters). Tooth size, module, and diametral pitch affect strength and meshing, not the ratio.
How do I calculate a multi-stage gearbox?
Work stage by stage: the output of the first pair is the input of the next. Total ratio is the product of the stage ratios (a 1:3 stage followed by a 1:4 stage gives 1:12), and overall efficiency is the product of the stage efficiencies.
What efficiency should I enter?
Use 96–98% for one spur or helical gear mesh, 94–96% for bevel gears, 90–95% for a single worm stage depending on the lead angle, and 95–98% for chain drives. The calculator applies your value once — for multiple stages, multiply the efficiencies yourself and enter the product.
Why is output torque always slightly less than ratio × input torque?
Friction in the mesh converts part of the input power into heat. That loss appears as reduced output torque; the speed relation n2 = n1 ÷ i, however, is exact because both gears share the same tooth-spacing speed.
Can I use it for pulleys?
Yes — enter the pulley diameters instead of tooth counts (the ratio logic is identical), and remember that flat belts and V-belts can slip a little under load, so the real output speed may be 1–2% lower.
Is my data saved or sent anywhere?
No. Every calculation runs in your browser, and nothing you type is stored or sent to a server.
Related calculators
Other free calculators commonly used with this tool: Bolt Torque Calculator, Belt & Pulley Calculator, and Cutting Speed & Feed Calculator.
Want a deeper walkthrough? Read our gear ratio guide.