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Gear Ratio Calculator

Find the gear ratio from the number of teeth on the driven and driver gears.

gear-ratio-calculator
Result
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In summary: Gear ratio is driven teeth divided by driver teeth. A 40-tooth driven gear with a 10-tooth driver gear gives a ratio of 4.00 : 1.

How gear ratio works

The gear ratio is the number of teeth on the driven gear divided by the teeth on the driver gear. A 40-tooth driven gear paired with a 10-tooth driver gives 4.00 : 1, meaning the driver turns four times for each turn of the driven gear. A ratio above 1 trades speed for torque.

Teeth are used rather than diameters because the teeth must mesh — every tooth that leaves the driver arrives at the driven gear, so the tooth counts fix the relationship exactly. Diameters give the same answer for standard gears, but tooth counts are easier to check and are not affected by wear. A gear ratio is a ratio in the ordinary arithmetic sense, and the ratio calculator will reduce it to its simplest form.

How to use this calculator

Count the teeth on the driven gear (the output) and the driver gear (the input, connected to the power source), then enter both. The result is expressed as a ratio to 1. The driver must have at least one tooth, so a zero entry returns a dash.

Swapping the two entries is the classic mistake and gives the reciprocal — 0.25 : 1 instead of 4.00 : 1. If the answer looks inverted, check which gear is actually driven by the motor or pedals. Gearing trades speed for turning effort but never creates energy, so the power calculator shows what actually reaches the wheels.

Speed and torque trade-off

A ratio greater than 1 (gear reduction) increases torque and reduces output speed; a ratio under 1 does the opposite. This is why low gears help a vehicle climb hills. Torque at the output relates to the applied force and lever arm — see the torque calculator.

Gears never create energy — power is torque times rotational speed, so whatever a reduction gains in torque it gives back in speed.

Frequently asked questions

How do I calculate gear ratio?
Divide the driven gear's teeth by the driver gear's teeth. 40 ÷ 10 gives a 4.00 : 1 ratio.
What does a 4:1 gear ratio mean?
The driver gear turns four times for every single turn of the driven gear, increasing torque.
Which gear is the driver?
The driver is the input gear connected to the power source; the driven gear is the output.
Does a higher ratio mean more speed?
No — a higher ratio means more torque but lower output speed. A ratio below 1 increases speed.
What about an idler gear between the two?
An idler does not change the ratio at all — it only reverses the direction of rotation. The overall ratio still depends solely on the first driver and the final driven gear, so an idler can be ignored in the arithmetic.
How this tool works

The formula behind this tool is written out in full in the sections above, so you can check the maths yourself. Every calculator on Calculorium is verified against worked examples with automated tests before it is published, and pages are reviewed as formulas or standards change. Nothing you type is sent anywhere — the calculation runs entirely in your browser. Read how we build and check these tools.

Last updated: July 27, 2026 · Calculations run in your browser. Estimates for information only.