Gear Ratio Calculator
Gear ratio, output speed and torque — single or compound, with road speed.
Results update as you type.
About this calculator
A gear ratio compares the teeth on the driven (output) gear to the driving (input) gear: ratio = driven / driving. It is the fundamental trade-off of gearing — a ratio above 1 is a reduction that turns the output slower but multiplies torque, while a ratio below 1 is an overdrive that spins faster but with less torque. Concretely, output RPM = input RPM ÷ ratio and output torque = input torque × ratio, so speed and torque always move in opposite directions (ignoring friction losses), keeping the power roughly constant.
As a worked example, a 10-tooth driving gear meshing with a 35-tooth driven gear gives a ratio of 35 / 10 = 3.5:1. Feed it 1,000 rpm and 20 N·m and the output turns at 1,000 / 3.5 ≈ 286 rpm but delivers 20 × 3.5 = 70 N·m. For a compound gear train, add a second pair under advanced options and the overall ratio is the product of the two stages — a 3:1 stage feeding a 2:1 stage gives 6:1 total. Enter a tyre diameter and final drive ratio and the tool also works out road speed from the wheel rpm.
Gear ratios are how machines match a power source to a load: low gears give a car or bicycle the torque to climb and accelerate, high gears give efficient cruising, and reduction gearboxes let small fast motors drive heavy slow loads. The same principle sizes winches, conveyors, clock mechanisms and drill speeds.
Frequently asked questions
How is gear ratio calculated?
Divide the number of teeth on the driven gear by the number on the driving gear. A 35-tooth driven gear on a 10-tooth driver is 35 / 10 = 3.5:1.
How does gear ratio affect speed and torque?
A reduction ratio of 3.5:1 turns the output 3.5 times slower than the input but multiplies torque by 3.5, ignoring friction losses.
What is a compound gear ratio?
When two gear pairs are in series, the overall ratio is the product of the two: a 3:1 stage feeding a 2:1 stage gives 6:1 total reduction.
What is the difference between a reduction and an overdrive?
A reduction ratio is greater than 1: it slows the output and multiplies torque, good for climbing and starting loads. An overdrive is less than 1: it speeds the output up but reduces torque, good for efficient high-speed cruising.
Does gearing create free power?
No. Gears trade speed for torque, not the other way around — the output power can never exceed the input, and real gears lose a few percent to friction. If torque goes up by 3.5×, speed drops by the same factor so power stays about the same.
How does the calculator work out road speed?
From the wheel rpm (input rpm ÷ total ratio ÷ final drive) and the tyre circumference (π × diameter). Enter a tyre diameter in inches and a final drive ratio and it returns the speed in both mph and km/h.
Which gear is the "driving" gear?
The driving (or input) gear is the one connected to the power source — the motor or pedal side. The driven (output) gear is on the load side. Swapping which is which inverts the ratio, turning a reduction into an overdrive.
API — use this calculator from code
Call this calculator as a free JSON endpoint — no key required. Send the field values below as query parameters or JSON. Read the full API docs →
Endpoint
GET https://calculator.free/api/v1/gear-ratio/curl
curl "https://calculator.free/api/v1/gear-ratio/?driving=10&driven=35&rpm=1000"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/gear-ratio/?" + new URLSearchParams({
"driving": "10",
"driven": "35",
"rpm": "1000"
}));
const data = await r.json();
console.log(data.results);Results are estimates for general guidance only, not financial, medical or tax advice.