ConverterHub

Gear Ratio Calculator

Enter the tooth counts of both gears to find the gear ratio.

How it is calculated

The ratio is ratio = driven teeth ÷ driver teeth. The driver is the gear connected to the power source (the input) and the driven gear is the one it turns (the output). Both inputs are plain tooth counts, so there are no units, and both must be greater than zero. The tool shows the ratio in the form x : 1 to 3 decimals, and also as a plain number to 4 decimals. A ratio above 1 means the output turns slower than the input but with more torque; a ratio below 1 means it turns faster with less torque; exactly 1 means same speed. Only one pair of gears is handled, so for a gear train multiply the ratios of each pair. Friction losses are ignored.

Worked example

A small motor gear has 17 teeth and drives a larger gear with 45 teeth. Step 1: divide the driven teeth by the driver teeth: 45 ÷ 17 = 2.6471. Step 2: the tool shows this as 2.647 : 1. The driver must turn about 2.65 times for the driven gear to turn once, so the output shaft runs at roughly 38% of the input speed while delivering about 2.65 times the torque (before losses).

Try this example →

Common mistakes

  • Swapping driver and driven. With 45 teeth on the driver and 17 on the driven gear you get 0.378 : 1, a speed-up, instead of the 2.647 : 1 reduction.
  • Counting teeth of a compound or idler gear. An idler between two gears changes only the direction of rotation, not the ratio, so use just the first driver and the last driven gear.
  • Using pitch diameters or pulley sizes in a field meant for tooth counts. This works only if they are in true proportion, so check the actual teeth where you can.
  • Reading the ratio as a speed. A bigger ratio means a slower output, so a 4 : 1 reduction runs at a quarter of the input speed.
  • Applying the result to a multi-stage gearbox. The tool covers one meshing pair, so multiply the results of each stage to get the total.

About this calculator

The gear ratio between two meshing gears is simply the number of teeth on the driven gear divided by the number of teeth on the driver gear (Teeth_driven ÷ Teeth_driver); because gear speed is inversely proportional to tooth count, this ratio also tells you how much the output speed drops (or torque increases) compared with the input.

Mechanical and automotive engineers, machinists, and hobbyists building drivetrains — from car transmissions and differentials to bicycle cassettes and 3D-printer extruders — use this calculation to predict how a gear pair will trade speed for torque, and to match a new replacement gear to an existing one without altering the overall ratio of a gearbox.

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