⚙️ Gear Ratio Calculator
By Shihab Mia · Updated 2026-08-03
This gear ratio calculator turns two tooth counts into three numbers you actually need: the gear ratio in simplified X:1 form, the resulting output RPM if you know your input speed, and the ideal torque multiplier. Enter the driving gear (the one connected to the motor) and the driven gear (the one connected to the load), add an optional input RPM, and every value updates instantly.
What is the Gear Ratio Calculator?
A gear ratio describes how the rotational speed of one gear compares to another when two gears mesh together. It is calculated by dividing the number of teeth on the driven gear (the output gear, attached to the load) by the number of teeth on the driving gear (the input gear, attached to the motor or crank). If a small 20-tooth gear drives a larger 60-tooth gear, the gear ratio is 60 divided by 20, which equals 3, written as 3:1. That single number tells you everything about how speed and torque trade off across the mesh.
The reason gear ratio matters so much in mechanical design is the inverse relationship between speed and torque. When a small driving gear turns a larger driven gear, the driven gear completes fewer rotations for every turn of the driving gear, so output speed drops. But because gears are (ideally) frictionless and conserve mechanical power, whatever speed is lost gets converted into torque. A 3:1 gear ratio means the output shaft turns at one third the input speed, but delivers three times the torque. This is why low gears in a car or bicycle feel harder to spin but pull much stronger, while high gears spin easily but push weakly. A gear ratio calculator makes that trade-off instant to check instead of doing the division by hand every time.
Calculating output RPM from a gear ratio is straightforward once you know the input speed. Output RPM equals input RPM multiplied by the ratio of driving teeth to driven teeth, which is the same as dividing input RPM by the gear ratio itself. If a motor spins at 1000 RPM into a 20-tooth driving gear meshed with a 60-tooth driven gear, the gear ratio is 3:1, and the output shaft turns at 1000 divided by 3, or about 333.33 RPM. The torque multiplier works in exactly the opposite direction: output torque equals input torque multiplied by the gear ratio, so that same 3:1 setup triples the torque delivered to whatever the output shaft is driving.
This calculator assumes an idealized, frictionless gear mesh, which is the standard way gear ratio is taught and used for sizing and comparison. Real gearboxes lose a small percentage of power to friction, bearing drag, and lubricant churn, typically 1 to 5 percent per mesh stage for well-made spur or helical gears, a bit more for worm gears. For quick design checks, sprocket and chain sizing, bicycle gearing, or homework, this gear ratio calculator is exactly what engineers, students, and hobbyists reach for first before applying an efficiency factor.
When to use it
- Sizing a gear train for a robotics or 3D-printed project, choosing tooth counts to hit a target output speed or torque.
- Working out bicycle gearing, comparing chainring and cassette tooth counts to understand pedaling effort versus speed.
- Checking automotive or gearbox specifications, confirming a stated gear ratio matches the actual tooth counts.
- Homework and mechanical engineering coursework on simple gear trains, speed ratios, and mechanical advantage.
- Selecting a stepper motor gearbox or planetary reducer to slow a shaft down to a usable speed while boosting torque.
- Verifying that a 3D printer, CNC, or conveyor drive train will deliver the RPM and torque the application actually needs.
How to use the Gear Ratio Calculator
- Enter the tooth count of the driving gear, the one attached to the motor or the input shaft turning the system.
- Enter the tooth count of the driven gear, the one attached to the output shaft or the load.
- Optionally enter the input RPM (the speed of the driving gear) to see the resulting output RPM.
- Read the gear ratio in simplified X:1 form, the decimal ratio, the output RPM, and the torque multiplier, all updated live as you type.
Formula & method
Worked examples
A 20-tooth driving gear meshes with a 60-tooth driven gear. The motor spins the driving gear at 1000 RPM. Find the gear ratio, output RPM, and torque multiplier.
- Gear ratio = driven teeth / driving teeth = 60 / 20 = 3, written as 3:1.
- Output RPM = input RPM x (driving teeth / driven teeth) = 1000 x (20 / 60) = 333.33 RPM.
- Torque multiplier = gear ratio = 3, so output torque is 3 times the input torque.
Result: Gear ratio 3:1, output RPM approximately 333.33, torque multiplied by 3x.
A bicycle chainring (driving gear) has 44 teeth and the rear cog (driven gear) has 11 teeth. The rider pedals at 80 RPM. Find the gear ratio and the rear wheel drive speed.
- Gear ratio = driven teeth / driving teeth = 11 / 44 = 0.25, written as 0.25:1 (or 1:4 the other way).
- Output RPM = input RPM x (driving teeth / driven teeth) = 80 x (44 / 11) = 320 RPM.
- Because the ratio is below 1, this is a speed increaser: the rear cog spins 4 times faster than the pedals, at reduced torque.
Result: Gear ratio 0.25:1 (a 4:1 speed increase), rear cog spins at 320 RPM, torque multiplier 0.25x.
Common gear ratios and what they do to speed and torque
| Driving teeth | Driven teeth | Gear ratio | Effect |
|---|---|---|---|
| 12 | 12 | 1:1 | No change, speed and torque pass through unchanged |
| 10 | 20 | 2:1 | Speed halved, torque doubled (reduction) |
| 20 | 60 | 3:1 | Speed cut to a third, torque tripled (reduction) |
| 15 | 60 | 4:1 | Speed cut to a quarter, torque quadrupled (reduction) |
| 40 | 10 | 0.25:1 | Speed quadrupled, torque cut to a quarter (increase) |
| 60 | 20 | 0.33:1 | Speed tripled, torque cut to a third (increase) |
Typical gear ratio ranges by application
| Application | Typical ratio range | Purpose |
|---|---|---|
| Bicycle gearing | 0.5:1 to 4:1 | Balance pedaling effort against road speed |
| Automotive final drive | 2.5:1 to 4.5:1 | Convert engine speed into usable wheel torque |
| Stepper motor gearbox | 3:1 to 100:1 | Increase holding torque, reduce output speed for precision |
| Worm gear drives | 5:1 to 300:1 | Very high reduction, often self-locking |
| Wind turbine gearbox | 1:60 to 1:120 | Step rotor speed up to generator speed |
Common mistakes to avoid
- Dividing the wrong way around. Gear ratio is driven teeth divided by driving teeth, not the other way around. Flip the division and you will invert speed and torque results, turning a reduction into an increase or vice versa.
- Forgetting the ratio is between mating gears, not the whole train. In a gear train with an idler gear in the middle, the idler does not change the overall ratio, only the direction of rotation. The overall ratio is still (final driven teeth) / (first driving teeth), calculated across the whole chain, not per idler.
- Ignoring real-world efficiency losses. This calculator gives the ideal, frictionless torque multiplier. Real gear meshes lose a few percent of power to friction, so actual output torque will be slightly lower than the ideal figure, especially through multiple stages or worm gears.
- Confusing gear ratio with mechanical advantage in compound gear trains. For a single pair of meshing gears the torque multiplier equals the gear ratio. In a compound train with several gear pairs, the overall mechanical advantage is the product of each stage ratio, not just the first or last pair.
Glossary
- Driving gear
- The input gear connected to the motor, engine, or crank. Also called the driver gear.
- Driven gear
- The output gear connected to the load. Also called the follower gear.
- Gear ratio
- The ratio of driven teeth to driving teeth, describing how speed and torque change across a gear mesh, typically written X:1.
- Torque multiplier
- How many times the output torque is multiplied relative to the input torque under ideal, frictionless conditions. Equal to the gear ratio.
- Speed reducer
- A gear pair or gearbox where the driven gear has more teeth than the driving gear, so output speed drops and torque increases.
- Idler gear
- A gear placed between the driving and driven gears that reverses rotation direction without changing the overall gear ratio.
Frequently asked questions
What is the formula for gear ratio?
Gear ratio equals the number of teeth on the driven gear divided by the number of teeth on the driving gear, usually written as X:1. For a 20-tooth driving gear and a 60-tooth driven gear, the gear ratio is 60 / 20 = 3, or 3:1. This gear ratio calculator applies that exact formula the moment you enter both tooth counts.
How do I calculate output RPM from a gear ratio?
Output RPM equals input RPM divided by the gear ratio, which is the same as input RPM multiplied by (driving teeth / driven teeth). At 1000 input RPM through a 3:1 ratio, output RPM is 1000 / 3, about 333.33 RPM.
Does a gear ratio increase or decrease torque?
It depends on the direction. When the driven gear has more teeth than the driving gear (a ratio above 1:1), speed drops and torque increases, this is a reduction. When the driven gear has fewer teeth (a ratio below 1:1), speed increases and torque drops.
What does a 3:1 gear ratio mean?
A 3:1 gear ratio means the driving gear must turn 3 times for the driven gear to turn once. Output speed is one third of input speed, and under ideal conditions output torque is 3 times the input torque.
Is torque multiplier always equal to the gear ratio?
For a single, ideal, frictionless gear pair, yes, torque multiplier equals the gear ratio. In practice, friction and bearing losses mean real torque output is slightly below the ideal value, typically by a few percent per mesh stage.
How does gear ratio work with more than two gears?
In a gear train, idler gears in the middle change rotation direction but not the overall ratio. The overall ratio across a simple train is still the final driven tooth count divided by the first driving tooth count. In a compound train with multiple meshing pairs, multiply each stage ratio together to get the total.