Gear Ratio Calculator
Gear ratio, output rpm, and output torque from tooth counts.
What it does
A gear pair trades speed for torque at a fixed rate. The big gear turns slower than the pinion driving it, by exactly the ratio of their teeth. Put 1800 rpm into a 12 tooth pinion driving a 36 tooth gear and the output turns at 600 rpm with three times the torque.
The tool above runs that trade both ways. Enter both tooth counts plus input speed and torque, and it prints the ratio, output speed, and ideal output torque. A unit switch keeps torque in N-m or ft-lb to match the manual on the bench.
Engineering courses state the same relations. UC San Diego machine design notes output speed over input speed as the inverse tooth ratio with power preserved, Carnegie Mellon works a 15 driving 30 example to a ratio of 2, and Swarthmore shows torque rising as angular velocity falls across the mesh.
The ideal needs one correction in service. Each gear mesh keeps a few percent as heat and noise, so real output torque lands below the printed number. Ratio and speed hold exactly; torque is where efficiency bites.
How to use
- Count the teeth on the drive (input) gear.
- Count the teeth on the driven (output) gear.
- Enter the input speed in rpm.
- Enter the input torque and pick its unit.
- Read the ratio first, then output speed and torque.
- Knock a few percent off torque per mesh for real boxes.
Formula
- drive
- Teeth on the input gear, 5 to 500.
- driven
- Teeth on the output gear, 5 to 500.
- rpm
- Input shaft speed in revolutions per minute.
- torque
- Input shaft torque in the selected unit.
Teeth and pitch diameters give the same ratio. Torque units follow the input unit selector (N-m or ft-lb); speed always reads in rpm.
Worked example
Example: 12 driving 36 at 1800 rpm
Defaults: 12 drive teeth, 36 driven teeth, 1800 rpm, 10 N-m input torque.
- Inputs: 12 tooth drive, 36 tooth driven, 1800 rpm in, 10 N-m in.
- Ratio: 36 / 12 = 3:1.
- Output speed: 1800 / 3 = 600 rpm.
- Output torque: 10 x 3 = 30 N-m.
- Tool shows 3:1, 600 rpm, 30 N-m.
Reference table
| Drive x Driven | Ratio | Effect |
|---|---|---|
| 12 x 12 | 1:1 | Same speed and torque |
| 12 x 24 | 2:1 | Half speed, double torque |
| 12 x 36 | 3:1 | Third speed, triple torque |
| 15 x 30 | 2:1 | Half speed, double torque |
| 20 x 60 | 3:1 | Third speed, triple torque |
Limits
- Ideal math only. Friction losses sit outside the numbers.
- Single pair only. Trains multiply stage by stage.
- Ignores backlash, wear, and tooth strength limits.
- Steady speed only. Shifting and slip differ.
Common mistakes
- Dividing drive by driven instead of driven by drive.
- Reading ratio as speed gain instead of reduction.
- Forgetting torque units when comparing with a spec.
- Ignoring mesh losses on high reduction stacks.
- Counting teeth on the wrong gear of the pair.
Try it yourself
Quick checks. Answers sit tucked under each question.
20 driving 40 at 1000 rpm and 5 N-m?
Ratio 40 / 20 = 2:1. Speed 1000 / 2 = 500 rpm. Torque 5 x 2 = 10 N-m.
15 driving 30 at 1200 rpm and 8 ft-lb?
Ratio 30 / 15 = 2:1. Speed 1200 / 2 = 600 rpm. Torque 8 x 2 = 16 ft-lb.
Questions
How is gear ratio defined?
Driven teeth divided by drive teeth. A 36 tooth gear driven by a 12 tooth pinion gives 3:1.
How does output speed follow?
Divide input speed by the ratio. At 3:1, 1800 rpm in gives 600 rpm out.
How does output torque follow?
Multiply by the ratio in the ideal case. At 3:1, 10 N-m in gives 30 N-m out, minus friction losses.
Can I use diameters instead of teeth?
Yes. Pitch diameters give the same ratio as teeth: driven diameter over drive diameter. A 6 in gear driven by a 2 in pinion is 3:1.
Reduction or overdrive: what changes?
Lower speed with higher torque, or the reverse. Gears trade one for the other while power stays constant.
How do I allow for losses?
Real boxes lose a few percent per mesh. Multiply ideal torque by efficiency, often 0.95 to 0.98 per gear pair.