Gear Ratio Calculator
A gear ratio is the number of teeth on the driven gear divided by the number on the driving gear. It sets both the change in speed and the change in torque, in opposite directions.
Gear ratio
3
- Output speed in rpm
- 1,000
- Torque multiplication factor
- 3
- Output torque in newton metres
- 120
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
ratio = driven teeth / driving teeth
- N_driven
- Tooth count on the driven, or output, gear
- N_driving
- Tooth count on the driving, or input, gear
- ratio
- Gear ratio; above one is a reduction, below one is an overdrive
- rpm_out
- Output speed, equal to input speed divided by the ratio
How to check the result by hand
- 1
Count the teeth on both gears
Count every tooth on the driving gear and on the driven gear. Meshing gears share a tooth pitch, so the counts are directly comparable and no diameter measurement is needed.
- 2
Divide the driven count by the driving count
36 divided by 12 gives a ratio of 3. A result above one is a reduction; a result below one is an overdrive; exactly one leaves the speed unchanged.
- 3
Divide the input speed by the ratio
3000 revolutions per minute through a ratio of 3 becomes 1000 at the output. In a reduction the output always turns more slowly than the input.
- 4
Multiply the input torque by the same ratio
40 newton metres multiplied by 3 gives 120. Speed falls and torque rises by the same factor, which is what keeps the transmitted power constant.
- 5
Multiply the ratios together for a multi-stage box
A 3 to 1 stage followed by a 2 to 1 stage gives 6 overall. Apply the combined ratio once to the speed and once to the torque rather than working through each stage separately.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate Gear Ratio page.