Gear Ratio Calculator
This gear ratio calculator works out the ratio between two gears and what it does to speed and torque, using the formula for gear ratio. Enter the tooth counts and the input RPM and the gear ratio calculator shows the ratio, the output RPM, and the torque multiplication. It also works as a gear ratio finder and gear ratio RPM calculator.
Results
The Gear Ratio Calculator is part of our Rotation collection. Browse more rotation to size, convert, and check your work alongside this tool.
What the gear ratio calculator does
The gear ratio calculator finds the trade a pair of gears makes between speed and turning force. Put a big gear on the output and you slow things down but gain torque; flip it and you speed up at the cost of torque. Using the formula for gear ratio, this gear ratio finder shows both sides of that trade from the tooth counts, and as a gear ratio RPM calculator it gives the output speed too.
Formula for gear ratio
The formula for gear ratio is the driven teeth over the driver teeth:
Output speed is the input divided by that ratio, so the gear ratio formula RPM version is RPM_out = RPM_in ÷ ratio. Torque climbs by the same factor the speed drops, which is the gear ratio equation the calculator applies in full.
Gear ratio calculator example
A 20-tooth driver turning a 60-tooth driven gear at 1000 RPM, through the formula for gear ratio:
The output turns at 1000 ÷ 3 ≈ 333 RPM, and the torque comes out three times higher than it went in.
How to use the gear ratio calculator
Enter the number of teeth on the driver gear (putting power in) and the driven gear (taking it out), plus the input speed. The gear ratio calculator returns the ratio, the output RPM, and the torque multiplier. As a gearbox ratio calculator RPM tool, the output speed updates the moment you change a tooth count.
Reading the gear ratio calculator result
A ratio above one is a reduction: slower, stronger. Below one is an overdrive: faster, weaker. The torque multiplier tells you how much heavier a load the output can shift, and the gear ratio RPM calculator output shows the exact speed. Real gears lose a few percent to friction, so treat the torque figure as a close ceiling.
When to use the gear ratio calculator
- Designing a gearbox with the gearbox ratio calculator RPM output
- Applying the formula for gear ratio to pick sprockets
- Setting the speed of a conveyor with the gear and RPM calculator
- Working out torque at the output shaft with the gear ratio finder
Common gear ratio mistakes
- Swapping driver and driven. Flip them and a reduction turns into an overdrive.
- Expecting free torque. The gain in torque costs speed; power stays put.
- Ignoring friction. Real sets lose a few percent, so the torque multiplier is a ceiling.
Tips for accurate gear ratio results
- Above 1:1 gives torque, below 1:1 gives speed.
- Use the gear ratio RPM calculator output to check the final shaft speed.
- Choose tooth counts with no common factor for even wear.
Why the formula for gear ratio is about trade-offs
Gears are the clearest example in mechanics of the idea that you cannot get something for nothing. A gear set moves power from one shaft to another, and the power out equals the power in, minus a little friction. What the formula for gear ratio changes is the shape of that power: how it splits between turning force and speed. Choose the tooth counts and you choose the split, which is why a car has several gears rather than one, since a single ratio cannot both launch a heavy vehicle and cruise it efficiently.
Gear ratio, RPM, and tooth choice
The gear ratio RPM calculator ties the ratio to real output speed, which is what most designs care about. But the tooth counts carry a practical detail too: designers avoid ratios where the same two teeth mesh every rotation, because any wear or grit keeps hitting the same partner and both wear unevenly. Picking counts that share no common factor spreads the contact around every tooth. It rarely changes the ratio the formula for gear ratio gives by much, but it is the difference between a gearbox that ages gracefully and one that develops a rough spot.
Gear ratio and RPM chart
Output speed and torque effect at 1000 RPM input, from the gear ratio RPM calculator:
| Ratio | Output RPM | Torque |
|---|---|---|
| 3:1 | 333 | 3× stronger |
| 1:1 | 1000 | no change |
| 1:2 | 2000 | half |
Gear Ratio Calculator FAQ
What is the formula for gear ratio?
The formula for gear ratio is driven teeth divided by driver teeth. The gear ratio calculator applies it, and the gear ratio formula RPM version divides input RPM by the ratio to give output speed.
How do I find output RPM?
Divide the input RPM by the gear ratio. The gear ratio RPM calculator does this, so a 3:1 ratio at 1000 RPM gives about 333 RPM out.
Does a gear ratio change power?
Not in an ideal set. Gears trade speed for torque and keep the product, which is power, about the same. The gear ratio equation shows torque rising as speed falls.
What does 3:1 mean?
The input turns three times for every one turn of the output. The output runs a third of the speed and carries three times the torque, as the gear ratio finder shows.