Gear Ratio Calculator
Compute a gear ratio from tooth counts, and the resulting output speed.
Formula
ratio = driven teeth / drive teeth
Inputs
- Driven gear teeth
- Drive (input) gear teeth
- Input speed (RPM)
What it does
The gear ratio is the driven gear’s teeth divided by the driving gear’s teeth. It sets the output speed and how much torque is multiplied.
Where it's used
Gearboxes, bicycle gearing, robot drivetrains and 3D-printer extruders.
How to use it
- Enter the teeth on the driven (output) gear.
- Enter the teeth on the drive (input) gear.
- Enter the input speed to see the output speed.
The formula explained
- Ratio
- driven teeth / drive teeth
- Output speed
- input rpm / ratio
- Output torque
- ≈ input torque × ratio (minus friction losses)
Worked example
A 15-tooth pinion driving a 60-tooth gear at 1500 rpm.
Inputs:
- Driven gear teeth: 60
- Drive (input) gear teeth: 15
- Input speed: 1500 RPM
The calculator gives:
- Result: 4 : 1
- Output speed: 375 RPM
Tips and common mistakes
- A ratio above 1 slows the output down and multiplies torque.
- In a gear train, multiply the ratios of each stage.
- An idler gear changes the direction, not the ratio.
Questions people ask
How much torque comes out of the gearbox?
Input torque × ratio × efficiency. A 4 : 1 reduction turns 10 N·m into about 40 N·m, a little less in practice — a good spur-gear stage loses only a few per cent.
How do I work out a gear train with several stages?
Multiply the ratio of each stage. A 4 : 1 stage followed by a 3 : 1 stage gives 12 : 1, so 1500 rpm in becomes 125 rpm out.
Does this work for belts, chains and bicycles?
Yes — use pulley diameters or sprocket teeth instead of gear teeth. A bicycle with a 48-tooth chainring and a 16-tooth rear sprocket turns the wheel 3 times for every turn of the pedals.
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Enter your values to get the result with the formula, substituted values and an explanation of each step.