What this calculator does
A gear pair trades speed for torque. Driving a large gear with a small one slows the output and multiplies the torque by the same factor, which is exactly the same bargain a lever makes.
The ratio depends only on tooth counts, not on gear size directly, since teeth must be the same size to mesh. That is why the ratio can be read straight off a gearbox specification without measuring anything.
The formula
Divide the output gear teeth by the input gear teeth. Output speed is the input speed divided by that ratio, and output torque is the input torque multiplied by it, ignoring losses.
| Term | Meaning |
|---|---|
| Gear ratio | Output teeth divided by input teeth. Above 1 means reduction: slower and stronger. |
| Reduction | A ratio above 1, which lowers speed and raises torque. |
| Overdrive | A ratio below 1, which raises speed and lowers torque. |
The inputs explained
| Field | What to enter |
|---|---|
| Input (driver) gear teeth | The number of teeth on the driving gear. |
| Output (driven) gear teeth | The number of teeth on the driven gear. |
| Input speed (rpm) | The input speed in rpm, typically the motor speed. |
| Input torque (N·m) | The input torque in newton metres. |
When to use it
Choosing a gearbox reduction
A motor rarely turns at the speed a load needs, and the ratio bridges the gap while multiplying torque.
Working out bicycle gearing
Chainring and sprocket tooth counts form exactly this ratio, which determines how far one pedal turn moves the bike.
Checking a drive train
Knowing the ratio lets output speed and torque be predicted from the motor specification.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does the driving gear size change the output?
A 36 tooth output gear driven by pinions of increasing size.
| Driver teeth | Gear ratio (GR) | Output torque |
|---|---|---|
| 12 teeth | 3.000 : 1 | 15.000 N·m |
| 18 teeth | 2.000 : 1 | 10.000 N·m |
| 24 teeth | 1.500 : 1 | 7.500 N·m |
| 36 teeth | 1.000 : 1 | 5.000 N·m |
Questions
Does a gear pair create power?
No. Ignoring friction, power out equals power in. Torque rises exactly as much as speed falls, so the product stays constant. Gears redistribute rather than generate.
Why do tooth counts matter rather than diameters?
Because meshing gears must have the same tooth size, so diameter is proportional to tooth count anyway. Counting teeth is simply more precise and easier to do.
What does a ratio below 1 mean?
Overdrive: the output turns faster than the input but with less torque. Top gear in a car often works this way, letting the engine run slower than the wheels.
Do gears reverse direction?
A pair of external gears turns in opposite directions. Adding an idler gear between them restores the original direction without changing the overall ratio.
For the torque being multiplied, see the torque calculator. For the same speed-for-force trade in a lever, see the lever mechanical advantage calculator.