Gear Ratio Calculator
Gear ratio from tooth counts — and what it does to speed and torque. Single pair or a two-stage compound train, with output RPM and torque so you can see the trade you are making.
Gear Ratio Is a Trade, Not Just a Number
A gear ratio is the driven tooth count divided by the driver tooth count — but what matters is what it does. Every ratio trades speed for torque or torque for speed. Gear down and the output turns slower but stronger; gear up and it spins faster but weaker. This tool shows the ratio and both sides of that trade at once.
Reduction vs Overdrive
A ratio above 1 is a reduction: speed drops by the ratio, torque rises by it — what you want between a motor and a wheel or a winch drum. A ratio below 1 is an overdrive: speed rises, torque falls, as in a bicycle in top gear. The speed and torque always move in opposite directions, and the product (power) stays the same apart from friction losses.
Compound Gear Trains
When one pair cannot give enough reduction, stages are chained. The overall ratio is the product of the stage ratios, so two 3:1 stages give 9:1 in a fraction of the space. The compound mode multiplies the stages for you and reports the overall result.
Frequently Asked Questions
Teeth or diameters?
Either — the ratio is the same whether you use tooth counts or pitch diameters, since teeth are evenly spaced around the pitch circle.
Does the ratio change power?
No. In an ideal gear set power in equals power out; the ratio just redistributes it between speed and torque. Real meshes lose a few percent each, which is why efficiency is included.
Which gear is the driver?
The driver is the input gear (connected to the motor or crank); the driven is the output. Swapping them inverts the ratio, turning a reduction into an overdrive.
Related calculators
- Torque Calculator — the torque the ratio multiplies.
- Mechanical Force Calculator — force from that output torque.
- Three-Phase Power Calculator — size the driving motor.
- Engineering Unit Converter — torque and speed units.