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A gear ratio tells you how a gear pair trades speed for torque. It's the number of teeth on the driven (output) gear divided by the driving (input) gear — and it decides whether the output turns slower and stronger, or faster and weaker.
Enter the tooth counts, optionally an input speed, and get the ratio, the output RPM and the torque multiplier.
How is it calculated?
Ratio, speed and torque
| Quantity | Formula |
|---|---|
| Gear ratio | driven teeth ÷ driving teeth |
| Output speed | input speed ÷ ratio |
| Torque multiplier | ratio |
A ratio written "4 : 1" means the driving gear turns four times for every one turn of the driven gear.
Reduction vs overdrive
A ratio above 1 is a *reduction*: the output turns slower than the input but with more torque — the trade-off in low gears, winches and the first gear of a car. A ratio below 1 is an *overdrive*: faster output, less torque, like a bicycle's high gear on the flat. At exactly 1 the two gears turn at the same speed.
Speed and torque trade off
Gears can't create energy, so what you gain in one you lose in the other. Reduce the speed by a factor of 4 and (ignoring friction) you multiply the torque by 4. This is why you shift to a low gear to climb a hill — more turning force at the cost of speed.
Where it helps
Bicycle and car gearing, machine and robotics drivetrains, 3D-printer and CNC design, and understanding a transmission. For a chain of gears, multiply the individual ratios together to get the overall ratio.
Worked example
A driving gear with 10 teeth turns a driven gear with 40 teeth. The gear ratio is 40 ÷ 10 = 4, written 4 : 1 — a reduction. If the input spins at 2,000 rpm, the output turns at 2,000 ÷ 4 = 500 rpm, four times slower, but with four times the torque. Swap the gears (40 driving, 10 driven) and you get a 0.25 : 1 overdrive: 8,000 rpm out, a quarter of the torque.
FAQ
How do I calculate a gear ratio?+
Divide the number of teeth on the driven (output) gear by the number on the driving (input) gear. 40 driven over 10 driving is a 4 : 1 ratio.
What does a 4:1 gear ratio mean?+
The driving gear makes four turns for every single turn of the driven gear. The output runs four times slower but delivers roughly four times the torque.
What is the difference between reduction and overdrive?+
A ratio above 1 is a reduction — slower, stronger output. A ratio below 1 is an overdrive — faster, weaker output. Exactly 1 means equal speed.
How does gear ratio affect torque?+
Torque is multiplied by the gear ratio. A 4 : 1 reduction quadruples the torque while quartering the speed, ignoring friction losses, because gears trade speed for force.
How do I find the ratio of a gear train?+
Multiply the ratios of each meshing pair in the train. Two 3 : 1 stages in series give an overall 9 : 1 ratio.