Gear Ratio Calculator

Gear ratio: 3 : 1
Output speed: 500 rpm
Output torque: 29.4 N·m
Effect: Reduction: slower output, more torque

Convert 21.68 lbf·ft

The gears turn in opposite directions

What it does

Find the ratio between two meshing gears from their teeth, and what it does to speed and torque. Enter the teeth on the driving and driven gears, the input speed and torque, and see the output speed, the output torque allowing for losses, and whether it's a reduction or an overdrive.

How to use it

Driving gear teeth: Teeth on the gear connected to the motor or input shaft. For pulleys or sprockets, use the diameter or tooth count the same way.
Driven gear teeth: Teeth on the gear being turned, on the output shaft.
Input speed: How fast the driving gear turns, in revolutions per minute. A typical 4-pole motor runs at about 1,450 to 1,500 rpm.
Input torque: The turning force at the input shaft, from the motor's data plate or specification.
Efficiency: How much power gets through. A good spur gear pair is about 97 to 99%; worm gears can be much lower. Use 100 for the ideal figure.

Common uses

Choosing gears or sprockets for a motor, conveyor or machine.
Working out pulley or belt drive speeds (use the pulley diameters).
Checking bicycle or go-kart sprocket ratios.
Working out the current a motor draws. Try the Ohm's Law Calculator

The formula

Ratio = driven teeth ÷ driving teethOutput speed = input speed ÷ ratioOutput torque = input torque × ratio × efficiency

Where:

Ratio above 1: a reduction: the output turns slower with more torque
Ratio below 1: an overdrive: the output turns faster with less torque
Efficiency: the share of power that gets through, as a fraction (98% = 0.98)

For a gear train, multiply the ratios of each pair. An idler gear between two others changes the direction but not the ratio.

Worked example

A driving gear with 12 teeth turning one with 36 teeth:

Ratio: 36 ÷ 12 = 3 : 1
Output speed: 1,500 rpm ÷ 3 = 500 rpm
Output torque: 10 N·m × 3 × 98% = 29.4 N·m (ideal 30 N·m)

Questions people ask

What does a 3:1 gear ratio mean?

The driving gear turns 3 times for every turn of the driven gear. The output is 3 times slower but has about 3 times the torque, less a little for friction.

Does this work for pulleys and chains?

Yes. For sprockets, use the tooth counts. For belt pulleys, use the diameters instead of teeth: the ratio is the driven pulley's diameter divided by the driving pulley's.

Why is the output torque less than the ratio suggests?

Some power is lost to friction in the teeth and bearings. Spur and helical gears lose only 1 to 3% per pair, but worm gears can lose 30% or more, so set the efficiency to match.

Last checked 26 October 2026