Gear Ratio Calculator

Find the gear ratio and output speed from tooth counts.

Unit system

Inputs

teeth
teeth
rpm
%

Results

Gear ratio

3:1
Output speed
500 rpm
Torque multiplier
3 ×

Results describe the speed and torque magnitudes for a single gear pair. They do not assess tooth strength, backlash or gear loading. Two meshing external gears rotate in opposite directions.

Formula · How it works

Formula

i = Z₂ / Z₁; n₂ = n₁ / i; M = i × η

Ratio i = driven teeth / driver teeth. Output speed = input speed / i. Torque multiplier = i × η, where η is efficiency as a fraction. A 100% efficiency setting gives the ideal torque multiplier.

Worked example

A 20-tooth driver turns a 60-tooth driven gear at an input speed of 1,450 rpm. The ratio is 3:1 and output speed is 483.33 rpm. At 95% efficiency, output torque is 2.85 times input torque.

How it works

A ratio above 1 reduces output speed and increases torque. A ratio below 1 increases output speed. Efficiency reduces transmitted torque and power, while the speed ratio follows the gear tooth counts.

Common questions

What does a 3:1 ratio mean?

The driver makes three turns for each turn of the driven gear. Output speed is one third of input speed; ideal output torque is three times input torque.

How should I choose efficiency?

Use a measured or supplier-provided value for the operating conditions. Use 100% only for the ideal, loss-free comparison.