Gear Ratio and Reduction Ratio Calculator

How is a gear ratio calculated?

For two meshing gears the ratio is the ratio of tooth counts: i = z₂ / z₁, where z₁ is the driver and z₂ the driven gear. The same ratio links the speeds: i = n₁ / n₂, so the output speed is n₂ = n₁ / i.

When the ratio is above 1 the output turns more slowly and torque goes up: T₂ = T₁ × i × η. A small gear driving a large one is a reduction, a large gear driving a small one is a speed increase.

Gearbox reduction ratio

A high ratio in one stage makes the gears very large, so gearboxes usually have two or three stages. The total ratio is the product of the stage ratios: i = i₁ × i₂ × i₃. If you know the motor speed and the speed the machine needs, the required ratio is simply i = n₁ / n₂, and the closest gearbox is picked from the catalogue.

Example

A 20 tooth pinion drives a 60 tooth wheel, so the ratio is 60 / 20 = 3. With 1450 rpm at the input the output turns at 483 rpm. If a second stage has an 18 tooth pinion driving a 72 tooth wheel, that stage has a ratio of 4, the total ratio is 12 and the output speed is 121 rpm.

Limits

The tool gives speed and torque ratios only. Whether the gears can carry that torque is a separate strength calculation. When selecting a gearbox, the rated torque and service factor in the manufacturer's catalogue govern.