How do I calculate a gear ratio?

Divide the teeth on the driven (output) gear by the teeth on the driver (input) gear. A 42-tooth gear driven by a 14-tooth pinion is 42 ÷ 14 = 3:1. A ratio above 1 means the output turns slower than the input and with more torque; below 1 means faster and with less.

How does gearing change speed and torque?

They trade off. A 3:1 reduction turns the output at a third of the input speed but multiplies the torque roughly threefold, minus losses. Overdrive works the other way — an output faster than the input gives back speed at the cost of torque. The tool shows both from your input figures.

What is a compound or two-stage ratio?

When two gear pairs sit in series, the overall ratio is the two multiplied together. A 3:1 followed by a 2:1 is 6:1 overall. Fill in the second pair here and the tool multiplies them; leave it blank and it just uses the first stage.

Which gear is the driver?

The one the power comes in on — the motor or engine side. The driven gear is the one it turns, on the output side. Getting them the right way round matters, because swapping them inverts the ratio and turns a reduction into an overdrive.

Gear ratio calculator

This is the arithmetic of tooth counts and an ideal, loss-free drive. Real gearboxes lose a few percent to friction, and torque a shaft can actually carry is a mechanical limit this tool says nothing about. Use it to plan the ratio, not to rate the hardware.

Enter the tooth counts for the driver and driven gears and the tool gives the ratio. Add a second pair for a compound drive, and an input speed or torque, to see how the output turns and pulls once the gearing has had its say.

Worked example

A 14-tooth pinion driving a 42-tooth gear is 42 ÷ 14 = 3:1. Feed it 1,800 RPM and the output turns 1,800 ÷ 3 = 600 RPM, while 10 N·m in becomes about 30 N·m out. Add a 2:1 second stage and the overall ratio is 6:1 — 300 RPM and roughly 60 N·m.

The formula

ratio = driven ÷ driver · output RPM = input ÷ ratio · output torque = input × ratio

Speed and torque are inverse across a gear pair: whatever the ratio takes off the speed it adds to the torque, in an ideal drive. Stages in series multiply, so a compound ratio is simply the product of each pair's driven-over-driver.

Questions

How do I calculate a gear ratio?: Divide the teeth on the driven (output) gear by the teeth on the driver (input) gear. A 42-tooth gear driven by a 14-tooth pinion is 42 ÷ 14 = 3:1. A ratio above 1 means the output turns slower than the input and with more torque; below 1 means faster and with less.
How does gearing change speed and torque?: They trade off. A 3:1 reduction turns the output at a third of the input speed but multiplies the torque roughly threefold, minus losses. Overdrive works the other way — an output faster than the input gives back speed at the cost of torque. The tool shows both from your input figures.
What is a compound or two-stage ratio?: When two gear pairs sit in series, the overall ratio is the two multiplied together. A 3:1 followed by a 2:1 is 6:1 overall. Fill in the second pair here and the tool multiplies them; leave it blank and it just uses the first stage.
Which gear is the driver?: The one the power comes in on — the motor or engine side. The driven gear is the one it turns, on the output side. Getting them the right way round matters, because swapping them inverts the ratio and turns a reduction into an overdrive.

Related tools

New tools, now and then

We add calculators most weeks. Drop your email and get a short note when a new one lands — nothing else, no selling your address, one-click out.