What a gear ratio is
When two gears mesh, the gear ratio compares their sizes: number of teeth on the driven gear divided by the number on the driving gear. The same applies to belt and chain drives, using pulley diameters or sprocket teeth.
Ratio = driven teeth ÷ driving teeth
A ratio above 1 is a reduction: the output turns slower but with more torque. Below 1 it is an overdrive: faster, with less torque. Power is conserved, minus friction losses.
The formulas
- Output speed = input speed ÷ ratio
- Output torque = input torque × ratio × efficiency
- Power (W) = torque (N·m) × speed (RPM) × 2π ÷ 60
- For several stages, multiply the ratios: a 3:1 stage followed by a 4:1 stage gives 12:1.
Worked example: a 12-tooth pinion driving a 36-tooth gear
- Ratio: 36 ÷ 12 = 3:1, a reduction.
- Motor at 1,750 RPM, typical of a 4-pole motor on 60 Hz: the output turns at 1,750 ÷ 3 = 583 RPM.
- Input torque of 7.5 lb·ft with 97% efficiency: 7.5 × 3 × 0.97 = 21.8 lb·ft at the output.
- The motor delivers about 1,808 W (2.4 hp) after losses.
Other driven gear sizes (12-tooth pinion, 1,750 RPM)
| Driven teeth | Ratio | Output speed |
|---|---|---|
| 12 | 1:1 | 1,750 RPM |
| 18 | 1.5:1 | 1,167 RPM |
| 24 | 2:1 | 875 RPM |
| 36 | 3:1 | 583 RPM |
| 48 | 4:1 | 438 RPM |
| 72 | 6:1 | 292 RPM |
Typical efficiencies
| Drive | Efficiency per stage |
|---|---|
| Spur or helical gears | 95–98% |
| Planetary gearbox | 95–97% |
| Chain drive | 95–98% |
| V-belt | 93–96% |
| Worm gear | 50–90%, depending on the ratio |
Bicycles and cars
- Bikes: with a 50-tooth chainring and a 25-tooth cog, the ratio is 0.5: the rear wheel turns twice per pedal stroke. Cyclists often express it as gear inches: (chainring ÷ cog) × wheel diameter in inches, here 2 × 27 = 54 inches.
- Cars: a transmission in 1st gear might be 3.5:1 and the differential 3.7:1, for an overall ratio of about 13:1. In top gear, an overdrive below 1:1 lowers engine RPM on the highway.
Practical tips
- Gears that mesh must have the same tooth size (module or diametral pitch).
- Avoid ratios where one tooth count divides the other exactly when wear matters: a “hunting tooth” combination such as 12 and 37 spreads wear evenly.
- The direction reverses with each pair of external gears; an idler gear restores it without changing the ratio.