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Gear ratio

A gear pair or a belt changes the speed and torque between a driving and a driven shaft. The gear ratio is the ratio of the number of teeth (or diameters), and the speed changes opposite to the torque: if the speed drops, the torque rises, roughly by the same ratio.

i = \dfrac{z_2}{z_1} = \dfrac{n_1}{n_2}

gear ratio

Symbols

$i$	gear ratio
$z_1,\ z_2$	number of teeth on driving/driven gear
$n_1,\ n_2$	input/output speed	rpm

Example

A 20-tooth driving gear drives a 60-tooth gear:

$i = 60/20 = 3$ , so the output speed is a third.

Speed down and torque up follow roughly the same ratio

i

– energy is (nearly) conserved.

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Part of Machine Design: Machine elements.