# How do you calculate the gearing ratio of a gear train?

A gear train is simply a series of gears connected together such that each gear in the series drives the next gear either directly or via another gear on the same axle. The diagram below shows an example of a 3 stage gear train. On the left is the input axle and on the right is the output axle.

The overall gearing ratio between the input axle and the output axle is simply the product of the gearing ratios of all the gear train stages. So in the example:

Stage 1: |
12 tooth driving a 20 tooth gear = 12 / 20 | = 3 / 5 |

Stage 2: |
12 tooth driving a 20 tooth gear = 12 / 20 | = 3 / 5 |

Stage 3: |
8 tooth driving a 24 tooth gear = 8 / 24 | = 1 / 3 |

So the overall gearing ration between the input axle and the output axle is (3 / 5) x (3 / 5) x (1 / 3) = **3 / 25**

This means for every **25** rotations of the input axle the output axle will rotate **3** times.

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