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CalcChef

Gear Ratio Calculator

Gear ratio, output RPM and speed change for one pair of gears or sprockets, from the driver and driven tooth counts and the input RPM. How it works

Use the Gear Ratio Calculator

Gear Ratio
1:3.00
Output RPM 333.3 · Speed change -66.7%

How It Works

Gear Ratio

GR = Driven ÷ Driver

Output RPM

RPMout = RPMin ÷ GR

Speed Change

Δ% = (RPMout − RPMin) ÷ RPMin × 100

Output torque (ideal, no losses)

Tout = Tin × GR

Ratio convention

reduction 1:x, overdrive x:1

About the Gear Ratio Calculator

Gear ratio = driven teeth ÷ driver teeth, and output RPM = input RPM ÷ that ratio. A driven gear with more teeth than the driver slows the output and multiplies torque; one with fewer teeth speeds it up. This gear ratio calculator takes the two tooth counts and the input speed and returns the ratio, the output RPM and the percentage change in speed, plus the ideal output torque when you enter an input torque.

How to use this tool

  1. Enter the teeth on the driver, the gear or sprocket on the motor or input shaft.
  2. Enter the teeth on the driven gear, the one being turned.
  3. Enter the input speed in RPM, and pick Both, Ratio Only or Speed Only to choose what the result shows.
  4. Optionally enter an input torque and its unit (N·m, lb·ft or lb·in), and choose how the ratio is written under Ratio shown as.

Frequently asked questions

Which gear is the driver?
The one turned by the power source: the gear on the motor, crank or input shaft. The driven gear is the one it turns. Swapping the two turns a reduction into an overdrive.
How do you calculate a gear ratio from tooth counts?
Divide the driven gear's teeth by the driver's teeth. The output speed is the input speed divided by that ratio, and in an ideal pair the torque rises by the same factor the speed falls: 10 N·m into a 20-tooth driver turning a 60-tooth gear gives 30 N·m out.
Why does the result say 1:x instead of x:1?
On Automatic, the default, the calculator writes a reduction as 1:x, one turn of the driven gear for x turns of the driver, and keeps x:1 for a pair that speeds up. Many gear and axle references write the same reduction the other way round, as x:1: choose Driven : driver under Ratio shown as to match them, or Driver : driven to always put the driver first. The output RPM and speed change are the same in every convention.
Does it work for chain sprockets and toothed belts?
Yes. Sprockets and toothed pulleys follow the same rule by tooth count, so enter the front sprocket as the driver and the rear one as the driven gear.
How do I work out a gear train with more than two gears?
The calculator handles one meshing pair. For a compound train, work out each pair and multiply the ratios. An idler gear between two others reverses the direction but leaves the overall ratio unchanged.

Speed and ratio for a gear pair

Enter both tooth counts and the input speed to get the ratio, output RPM and change in speed. A 20-tooth pinion driving a 60-tooth gear at 1,000 RPM gives 333.3 RPM and −66.7%; swap them, 60 driving 20, and it gives 3000.0 RPM and +200.0%.

Read the ratio with care. Many gear and axle references write the 20 → 60 pair as a 3:1 reduction (driven ÷ driver). On Automatic, the default, this tool writes it as 1:3.00, one turn of the driven gear for three of the driver, and keeps x:1 for a pair that speeds up. Ratio shown as switches that: Driven : driver reads 3.00:1 and Driver : driven reads 1:3.00 for every pair.

Fill in Input torque (N·m, lb·ft or lb·in) to see the ideal output torque: 10 N·m through the 20 → 60 pair gives 30 N·m. Mode limits the result to Ratio Only or Speed Only, and your values stay in this browser until you clear them.

How the ratio is calculated

ratio = driven teeth ÷ driver teeth

output RPM = input RPM ÷ ratio

speed change = (output − input) ÷ input × 100

output torque = input torque × ratio

On Automatic a reduction (a ratio of 1 or more) is written 1:x and an overdrive x:1, both to two decimals; output RPM and the speed change are shown to one decimal. Teeth are whole numbers from 1 to 10,000 and input speed a whole number of 0 or more; at 0 RPM the speed change is 0%. For a compound train, work out each pair and multiply the ratios. The output torque is the ideal figure, in the same unit as the input: real gears lose part of it to friction, and the tool does not compute efficiency or tooth strength.

Fun Fact: An idler gear placed between the driver and the driven gear reverses the direction of rotation but leaves the overall ratio unchanged, because its own tooth count cancels out.

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