Gear Ratio Calculator
A 20-tooth gear driving a 60-tooth gear produces a 3:1 ratio, 1,000 output RPM from 3,000 input RPM, and an ideal 3x torque multiplier. This gear ratio calculator uses the tooth counts of a driving gear and a driven gear to find the ratio, output shaft speed, and theoretical torque change. It works for a basic pair of meshed external gears as well as a pair of sprockets connected by a chain. The result helps you check how a proposed gear pair will affect a machine, bicycle, motor drive, or small mechanical project. A larger driven gear creates a reduction that lowers output speed and raises ideal torque. A smaller driven gear creates an overdrive that raises output speed and lowers ideal torque. Enter whole tooth counts and a nonnegative input speed to compare setups before choosing parts.
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.
- •A 1:1 ratio keeps the same speed and ideal torque magnitude, although the output rotation direction reverses for two external gears.
- •An idler gear can change rotation direction or spacing without changing the numerical ratio between the first and last gears.
- •The torque multiplier is theoretical and does not subtract bearing, chain, tooth-contact, or lubrication losses.
How to Use
- 1Identify the driving gear, which receives power from the motor, crank, engine, or input shaft, then enter its whole number of teeth.
- 2Identify the driven gear, which turns the output shaft or wheel, then enter its whole number of teeth.
- 3Enter the input speed in revolutions per minute. Use 0 RPM if you only need the ratio and theoretical torque multiplier.
- 4Calculate the result and read the formatted ratio. A value above 1:1 is a reduction, while a value below 1:1 is an overdrive.
- 5Compare the output RPM with the input RPM to see the speed change, then use the torque multiplier as an ideal planning figure.
- 6For a multi-stage drive, calculate each pair separately and multiply the unrounded stage ratios to find the overall ratio.
How It Works
Formula
ratio = driven teeth / driving teeth, output RPM = input RPM / ratioDivide the driven gear's tooth count by the driving gear's tooth count. Meshed gears advance the same number of teeth at their contact point, so a 60-tooth driven gear needs three full turns of a 20-tooth driver to complete one revolution. The ratio is 60 / 20 = 3, which the calculator displays as 3:1. Output speed is the input speed divided by that ratio, so 3,000 / 3 = 1,000 RPM. The ideal torque multiplier equals the same ratio, so an input torque of 10 N m would correspond to 30 N m at the output before losses. If the driven gear is smaller, such as 12 teeth driven by 48 teeth, the ratio is 12 / 48 = 0.25. Dividing input RPM by 0.25 multiplies speed by four, while ideal output torque falls to one quarter of input torque. Two external gears also rotate in opposite directions, but direction is not part of the numerical ratio reported here.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
20-tooth driving a 60-tooth
The ratio is 60 / 20 = 3. Output speed is 3,000 / 3 = 1,000 RPM, and the ideal torque multiplier is 3. This reduction gives up two thirds of the input speed in exchange for three times the theoretical output torque.
Bike: 48-tooth chainring to 12-tooth cog
The ratio is 12 / 48 = 0.25. Dividing the 90 RPM crank speed by 0.25 gives 360 RPM at the rear sprocket and wheel hub. This is an overdrive, so the ideal output torque is 0.25 times the input torque before drivetrain losses.
Car final drive, 13 to 41 teeth
The unrounded ratio is 41 / 13 = 3.153846. The calculator displays 3.154:1 and divides 2,600 by the unrounded ratio to return 824.4 RPM. A specification sheet may shorten this final-drive ratio to 3.15.
18-tooth pinion driving a 54-tooth gear
The tooth-count calculation is 54 / 18 = 3. The output speed is 1,800 / 3 = 600 RPM, and the ideal torque multiplier is 3. This could suit a motor-driven mechanism that needs more turning force at a lower shaft speed.
72-tooth driver turning a 24-tooth gear
The exact ratio is 24 / 72 = one third, which displays as 0.333:1. The formula uses the unrounded ratio for speed, so 1,500 divided by one third gives 4,500 RPM. Ideal output torque is one third of input torque.
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 |
Reduction, Overdrive, and Compound Ratios
A reduction uses a driven gear with more teeth than the driver. The output turns more slowly because the smaller driver must rotate several times to move every tooth on the larger gear past the contact point. That lower speed comes with a proportional increase in ideal output torque. Reductions are common where a fast motor needs to move a load slowly, start under resistance, or hold speed under changing load.
An overdrive uses a driven gear with fewer teeth than the driver. The smaller output gear completes more than one revolution during each input revolution, so output RPM rises. The cost is lower ideal output torque. A 48-tooth bicycle chainring driving a 12-tooth rear cog is a clear example. The 0.25 ratio makes the rear cog turn four times per crank revolution, but the rider must apply more pedal force for the same force at the wheel.
Compound gear trains contain two or more stages. Find each stage as driven teeth divided by driving teeth, then multiply the stage ratios. A 3:1 first stage followed by a 2:1 second stage produces a 6:1 overall reduction. Do not round each stage before multiplication if accuracy matters. Idler gears that sit between a driver and driven gear do not change the ratio, although each external mesh reverses rotation direction.
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.
- Using the rounded displayed ratio to reproduce output RPM. The calculator derives RPM from the full tooth-count ratio, then rounds the final speed to one decimal place.
- Treating the ideal torque multiplier as measured shaft torque. Friction, tooth geometry, chain condition, bearings, and lubrication reduce real output.
- Multiplying tooth counts across a compound train instead of multiplying the ratio of each active driver-driven stage.
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