Gear ratio calculator

Single stage or compound. Ratio, output speed and torque.

The formula

ratio = driven teeth ÷ driver teeth, multiplied across stages.

Output speed is input ÷ ratio. Output torque is input × ratio × efficiency, in whatever torque unit you entered, because the ratio is dimensionless.

Idlers, and what compounding actually means

An idler gear between two others changes the direction of rotation but not the ratio, so leave idlers out of the calculation entirely. Its tooth count cancels: it is driven by the first gear and drives the second in equal measure.

Compounding means two gears sharing one shaft, so the second stage starts from the first stage's output. Two 3:1 stages give 9:1, not 6:1. This is how a small gearbox reaches a large reduction without one enormous gear.

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