Gear Ratio Calculator
Enter the teeth on the driving and driven gears of each stage. Add the input speed and torque to see the output.
Worked examples
Single stage
20 teeth driving 60 teeth, 1,500 rpm, 10 N m
3 to 1, 500 rpm, 30 N m
Torque multiplies, speed divides.
Two stages
20:60 then 15:45
9 to 1
3 x 3.
About Gear Ratio Calculator
The gear ratio is the number of teeth on the driven gear divided by the number of teeth on the driving gear. A ratio greater than one slows the output and multiplies the torque, which is how a low gear lets a bicycle climb a hill. A ratio less than one speeds the output up and reduces the torque, as in an overdrive. Power stays the same, apart from losses, so speed and torque trade against each other.
When gears are chained in stages, the ratio of the whole train is the product of the ratios of each stage. This calculator accepts up to three stages. Give the input speed to find the output speed, and the input torque to find the output torque, reduced by the efficiency you set. Each pair of external gears reverses the direction of rotation, so the page also tells you whether the output turns the same way as the input.
How to use Gear Ratio Calculator
- Enter the teeth on the driving and driven gear for the first stage.
- Add the second and third stages if there are any.
- Optionally enter the input speed in rpm, the input torque and the efficiency.
- Read the overall ratio, the output speed and torque and the direction.
Common uses
- Designing a gearbox or a geared motor
- Working out a bicycle or motorbike gear ratio
- Finding the output speed of a clock or toy mechanism
- Checking a compound gear train for a model or robot
Frequently asked questions
How do I calculate a gear ratio?
Divide the teeth on the driven gear by the teeth on the driving gear. A 20 tooth gear driving a 60 tooth gear gives 3 to 1.
What does a ratio of 3 to 1 do?
The output turns three times slower than the input and has three times the torque, before losses.
How do multiple stages combine?
Multiply the ratios. Two stages of 3 to 1 give 9 to 1 overall.
Does an idler gear change the ratio?
No. An idler only reverses the direction. The ratio depends on the first driving gear and the last driven gear.