How do you calculate gear ratio?

Gear ratio is the number of teeth on the driven gear divided by the number on the driving gear. A ratio above 1 reduces speed and increases torque; below 1 does the opposite.

What is a reduction gear?

A reduction gear has a ratio greater than 1, so the output turns slower than the input but with more torque, which is why low gears help a vehicle climb or pull away.

Gear Ratio Calculator

This gear ratio calculator works out the ratio of a pair of meshing gears from their tooth counts, and shows what that does to the output speed and torque. A gear ratio compares the driven gear, the one receiving the power, with the driving gear, the one supplying it, and it is found by dividing the number of teeth on the driven gear by the number on the driving gear. The ratio is the heart of how machines trade speed for turning force: a ratio greater than 1 is a reduction, where the output turns more slowly than the input but with proportionally more torque, while a ratio less than 1 is an overdrive, spinning the output faster with less torque. You enter the teeth on the driving and driven gears, and optionally an input speed and torque, and the calculator returns the ratio, the resulting output speed as the input divided by the ratio, and the output torque as the input multiplied by the ratio. This is exactly the trade-off behind the low and high gears in a vehicle, the cassette on a bike, and the reduction gearboxes in machinery and power tools, where the right ratio matches an engine or motor to the job. Enter the tooth counts to see the ratio and its effect straight away.

Driving gear teeth

Driven gear teeth

Input speed (RPM, optional)

Input torque (Nm, optional)

3.00 : 1

gear ratio (reduction)

Output speed1,000 RPM

Output torque150 Nm

How it works

The calculator divides the driven gear teeth by the driving gear teeth to get the ratio. The output speed is the input speed divided by the ratio, and the output torque is the input torque multiplied by the ratio, since gears conserve power by trading speed against force.

Worked example

A 12 tooth driving gear turning a 36 tooth driven gear gives a ratio of 36 over 12, which is 3 to 1. An input of 3000 RPM becomes 1000 RPM at the output, while 50 Nm of torque becomes 150 Nm.

Related calculators

Force Calculator: F equals m a.
Power Converter: watts and horsepower.
Velocity Calculator: speed and distance.
Ratio Calculator: simplify ratios.

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