Case 1
- Driver gear teeth
- 12
- Driven gear teeth
- 36
3.000
Open with these valuesGear Ratio Calculator
3.000:1
Result: 3.000 :1Count the teeth on both gears and divide the driven (output) count by the driver (input) count. A 12-tooth driver turning a 36-tooth gear gives 3, written 3:1 — the driver turns three times for one turn of the output. Above 1 is a reduction, below 1 an overdrive.
The numbers at a glance
Held fixed: Driver gear teeth 12.
| Driven gear teeth | Result |
|---|---|
| 10 | 0.833 |
| 20 | 1.667 |
| 30 | 2.500 |
| 36Your value | 3.000 |
| 40 | 3.333 |
| 50 | 4.167 |
| 60 | 5.000 |
| 70 | 5.833 |
Worked examples
Case 2
- Driver gear teeth
- 36
- Driven gear teeth
- 12
0.333
Open with these valuesCase 3
- Driver gear teeth
- 13
- Driven gear teeth
- 31
2.385
Open with these valuesHow it's calculated
ratio = driven teeth ÷ driver teeth
- StepCount the teeth on the driver gear — the one the motor turns.
- StepCount the teeth on the driven gear that carries the output shaft.
- ResultRead the ratio: above 1 is a reduction, below 1 an overdrive.
Reference table
| Driver, driven teeth | Character | Ratio |
|---|---|---|
| 36, 12 | Overdrive, output spins faster | 0.333 |
| 1, 1 | Direct drive | 1 |
| 20, 40 | Halved output speed | 2 |
| 13, 31 | Typical chain sprocket pair | 2.385 |
| 10, 25 | Two-and-a-half to one | 2.5 |
| 12, 36 | Three-to-one reduction | 3 |
Questions
How do I calculate a gear ratio?
Divide the number of teeth on the driven (output) gear by the number on the driver (input) gear. A 12-tooth driver turning a 36-tooth driven gear gives 36 ÷ 12 = 3:1, so the driver spins three times for every turn of the output.
Which gear is the driver and which is the driven?
The driver is connected to the power source — motor, engine or pedal — and supplies the rotation. The driven gear receives it through the mesh and turns the output shaft. Swap them and you get the reciprocal, so count carefully.
What is the difference between a reduction and an overdrive?
A ratio greater than 1 is a reduction: the output turns slower than the input but with more torque, which suits heavy loads and climbing. A ratio below 1 is an overdrive: faster output, less torque, good for speed at low engine revs.
How does the ratio affect output speed?
Output speed is the input speed divided by the ratio. With a 3:1 reduction at 1000 rpm the output shaft turns at about 333 rpm; with a 0.333:1 overdrive it turns at 3000 rpm.
Can I use pulley or sprocket diameters instead of teeth?
For a chain or belt drive of the same pitch, yes — the ratio of diameters equals the ratio of tooth counts. Teeth are still the safer input, because you can count them exactly while a diameter has to be measured.
Sources and last check
Information, not professional advice.