When more than one pair of gears are used together, that is called a compound gear train. The gear ratios for each individual gear pair are multiplied together to compute the overall compound gear ratio for the gear train.


Let's look at an example. The gearbox on the right has two pairs of gears. The first pair of gears has an input gear with 8 teeth and an output gear with 40 teeth. The gear ratio of this gear pair is 40 to 8 or, by simplifying, 5 to 1.

The second pair of gears has an 8 tooth input gear meshed with a 24 tooth output gear. The gear ratio of this pair is 24 to 8 or, again simplifying, 3 to 1. Notice that the 8 tooth gear of the second gear pair is on the same axle as the the 40 tooth gear of the first gear pair. The output axle from the first gear pair becomes the input axle for the second gear pair.


Let's compute the gear ratio for the entire compound gear train. This is the ratio between the last output axle and the first input axle. To do this, we multiply the gear ratios of the individual gear pairs.

The total gear ratio is 15 to 1. That means the input axle must make 15 revolutions for the output axle to make 1.

You can combine as many gear pairs as you want in a compound gear train. There is no limit. By combining gears you can make almost any gear ratio that you want!


What is the overall gear ratio for the gearbox shown on the left? Notice that there are 4 pairs of gears including a worm gear.

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See also: Gears, Spur gear, Bevel gear, Worm gear, Idler gear, Gearbox, Belts and Pulleys