Gear Ratio Calculator
Calculate the gear ratio, output speed and output torque for one or two gear stages from the tooth counts. Example: a 20 tooth driver turning a 60 tooth gear at 1,800 RPM gives a 3:1 ratio, 600 RPM output and about 3 times the torque.
Type the problems from this lesson and check each step.
Show steps
How to use the Gear Ratio Calculator
- Enter the number of teeth on the driver gear and the driven gear.
- For a compound train, enter the teeth of the second stage too.
- Add the input speed, input torque and efficiency to see output speed and torque, then press Calculate.
Formula and method
Gear ratio = driven gear teeth / driver gear teeth. For several stages multiply the stage ratios. Output speed = input speed / ratio. Output torque = input torque x ratio x efficiency. The same ratio comes from the diameters or radii of the gears.
Worked example: 20 tooth driver, 60 tooth driven, 1,800 RPM, 10 N m
| Step | Result |
|---|---|
| Ratio (60 / 20) | 3:1 |
| Output speed (1,800 / 3) | 600 RPM |
| Ideal output torque (10 x 3) | 30 N m |
| At 98% efficiency | 29.4 N m |
Common ratios
| Driver teeth | Driven teeth | Ratio | Output at 1,800 RPM |
|---|---|---|---|
| 20 | 20 | 1.00:1 | 1800 RPM |
| 20 | 40 | 2.00:1 | 900 RPM |
| 20 | 60 | 3.00:1 | 600 RPM |
| 30 | 15 | 0.50:1 | 3600 RPM |
| 12 | 48 | 4.00:1 | 450 RPM |
Gear reduction and overdrive
A ratio above 1 slows the output and multiplies torque. It is used in gearboxes and winches. A ratio below 1 speeds the output and reduces torque. It is used in overdrive gears and some bicycle gears.
Compound gear trains
A compound train places two gear pairs in series on a shared shaft. Its ratio is the product of the pair ratios, which lets you reach large ratios in a small space. Idler gears only change the direction of rotation.
Frequently asked questions
How do I calculate gear ratio?
Divide the number of teeth on the driven gear by the number of teeth on the driver gear.
What does a 3:1 gear ratio mean?
The driver turns three times for each turn of the driven gear.
What happens to torque when speed drops?
Torque rises by about the same factor, minus friction losses.
What is a compound gear train?
Two or more gear pairs in series; multiply their ratios.
Do idler gears change the ratio?
No, they only reverse direction.
How do I find gear ratio from diameter?
Divide the driven diameter by the driver diameter.
Sources
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