Gear Ratio Calculator
A 20-tooth gear driving a 60-tooth gear gives a 3:1 ratio, so the output turns at a third of the speed with three times the torque. This gear ratio calculator works from tooth counts, reporting the ratio, output RPM for any input speed, and the torque multiplication. The trade is always the same: speed for torque, or torque for speed.
Quick answer
Gear ratio = driven gear teeth / driving gear teeth.
Gear ratio
3:1
Output RPM
1000
Torque multiplier
3x
Type
Reduction (slower, stronger)
What this tells you
- •Gear ratio = driven gear teeth / driving gear teeth.
- •A ratio above 1 is a reduction, slower output with more torque. Below 1 is an overdrive, faster output with less.
- •Output RPM = input RPM / ratio, and output torque multiplies by the ratio (minus small friction losses).
- •The same math covers bike sprockets, car differentials, and shop machinery.
How to Use
- 1Count (or read) the teeth on the driving gear, the one connected to the power source.
- 2Count the teeth on the driven gear, the one delivering the output.
- 3Enter the input RPM if you want the output speed.
- 4Read the ratio, output RPM, and torque multiplier.
How It Works
Formula
ratio = driven teeth / driving teeth, output RPM = input RPM / ratioMeshed gears move tooth for tooth, so a 60-tooth gear needs three turns of a 20-tooth partner to complete one revolution. That is a 3:1 ratio: at 3,000 input RPM the output spins 1,000 RPM, and the output shaft delivers roughly three times the input torque, since power (speed times torque) is conserved apart from friction.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
20-tooth driving a 60-tooth
A classic reduction, trading two thirds of the speed for triple torque.
Bike: 48-tooth chainring to 12-tooth cog
An overdrive. Each pedal turn spins the wheel four times, the high gear for speed.
Car final drive, 13 to 41 teeth
A typical differential ratio, listed on spec sheets as 3.15.
Ratio Effects at 3,000 Input RPM
How different ratios trade speed for torque.
| Ratio | Output RPM | Torque multiplier |
|---|---|---|
| 0.5:1 (overdrive) | 6,000 | 0.5x |
| 1:1 (direct) | 3,000 | 1x |
| 2:1 | 1,500 | 2x |
| 3:1 | 1,000 | 3x |
| 4:1 | 750 | 4x |
| 10:1 | 300 | 10x |
Common mistakes
- Dividing the teeth the wrong way. The ratio is driven over driving, so a small gear driving a big one gives a ratio above 1, a reduction.
- Expecting torque multiplication without the speed cost. Gears conserve power, so tripling torque always means a third of the speed.
- Ignoring intermediate (idler) gears in the count. Idlers reverse direction but leave the overall ratio untouched, only the first and last gears matter.
- Reading a bike's big-to-small setup as a reduction. Chainring to smaller cog is an overdrive, that is why high gears are hard to pedal.