Gear Ratio Calculator
Enter any three of driver teeth, driven teeth, input speed and output speed to get the fourth, with the gear ratio and what it does to speed and torque.
Answer
N₁ × T₁ = N₂ × T₂
- Given (in base units): T₁ = 12 teeth, T₂ = 36 teeth, N₁ = 157.08 rad/s
- N₂ = N₁ × T₁ ÷ T₂ = 52.3599 rad/s
Gear ratio 3:1: the output turns 3 times slower than the input, and — losses aside — with 3 times the torque. It turns the other way, unless an idler gear sits between them.
Values
Fill in any 3; leave the one to work out empty.
How is this calculated?
N₁ × T₁ = N₂ × T₂, so N₂ = N₁ × T₁ ÷ T₂. Gear ratio i = T₂ ÷ T₁ = N₁ ÷ N₂. Output torque ≈ input torque × i, less friction losses.Runs in your browser — nothing you enter leaves this device.
About this tool
What it does
Gear Ratio Calculator works out what a pair of meshing gears does to speed. The same number of teeth passes the meeting point on both gears every second, so the input speed times the driver’s teeth equals the output speed times the driven gear’s teeth. Enter any three of driver teeth, driven teeth, input speed and output speed and the fourth is worked out, with the formula and working shown. Below the answer it gives the gear ratio — driven teeth over driver teeth, written as 3:1 for a reduction or 1:2 for an overdrive — and says what it means: how many times slower or faster the output turns, and how the torque changes the other way. Speeds can be in revolutions per minute, revolutions per second, radians per second or degrees per second. The same relation holds for a chain on two sprockets and a toothed belt on two pulleys.
How to use it
- Enter the teeth on the driving gear (the one turned by the motor) and the driven gear.
- Enter the input speed, and leave the output speed empty — or fill any three and leave the fourth.
- Read the gear ratio and what it does under the answer.
- Change the speed unit if you need rad/s for a power calculation.
Limits and your data
- It is one pair of gears. For a gear train, multiply the ratios of each pair: a 3:1 stage followed by a 4:1 stage is 12:1 overall. Idler gears in between change the direction but not the ratio.
- Torque multiplication is the ideal value. Real spur gears lose a few per cent to friction; worm gears can lose half or more.
- Two gears mesh only if they have the same tooth size (module or diametral pitch); the calculator does not check that.
- A worked-out tooth count that is not a whole number is flagged: round it, then work out the speed it actually gives.
- For belts on smooth pulleys, use diameters in place of teeth; the ratio is the same idea, though belts slip a little.
- The calculation runs in your browser. Nothing is sent or stored.
Questions
How do I calculate gear ratio?
Divide the teeth on the driven gear by the teeth on the driving gear. A 12-tooth pinion driving a 36-tooth gear is 3:1 — the output turns three times slower with about three times the torque.
What is the output rpm?
Input rpm × driver teeth ÷ driven teeth. A motor at 1,500 rpm through 12:36 gives 500 rpm, the example the page opens with.
Does a bigger gear make it faster?
A bigger driving gear makes the output faster; a bigger driven gear makes it slower and stronger. That is why a bicycle’s low gear uses a small chainring and a big rear sprocket.
Which way does the output turn?
Two external gears turn in opposite directions. An idler gear between them makes the output turn the same way as the input, without changing the ratio.