What is the difference between a reduction and an overdrive?

A reduction (ratio greater than 1) makes the output turn slower than the input while multiplying torque, useful for moving heavy loads. An overdrive (ratio less than 1) speeds the output up at the cost of torque, like a top cruising gear.

Why does torque go up when speed goes down?

Ignoring friction losses, mechanical power (torque times angular speed) is conserved through the gear pair. So if the gears cut the speed by a factor, they must raise the torque by the same factor to keep power constant.

Does the gear ratio depend on tooth count or gear diameter?

Either works because meshing gears share the same tooth pitch, so tooth count is directly proportional to pitch diameter. Using tooth counts is exact and avoids measuring diameters.

How do I find the ratio of a multi-stage gear train?

Multiply the individual stage ratios together. For example, a 3:1 stage followed by a 2:1 stage gives an overall 6:1 reduction; you can chain this calculator stage by stage.

Gear Ratio Calculator

Driving Gear Teeth

Driven Gear Teeth

Input Speed

RPM

Input Torque

N·m

Gear Ratio3.0000 : 1

Output Speed500.00 RPM

Output Torque30.00 N·m

TypeReduction (torque up, speed down)

The Gear Ratio Calculator works out how a pair of meshing gears trades speed for torque. Enter the tooth counts of the driving (input) and driven (output) gears, along with the input shaft speed and torque, and it returns the gear ratio, the resulting output RPM, and the multiplied output torque. A ratio above one is a reduction that slows the shaft while boosting torque; a ratio below one is an overdrive that does the opposite.

Formula

ratio = N_driven / N_driving; RPM_out = RPM_in / ratio; T_out = T_in × ratio

N_driving: Tooth count of the driving (input) gear
N_driven: Tooth count of the driven (output) gear
RPM_in: Rotational speed of the input shaft
T_in: Torque applied to the input shaft

How it works

Enter the number of teeth on the driving gear and on the driven gear, then add the input RPM and input torque you want to transmit.
The ratio is driven teeth divided by driving teeth; output RPM is the input RPM divided by that ratio.
Torque scales the other way, so output torque is input torque multiplied by the ratio, and the tool labels the setup as a reduction or an overdrive.

Worked example

A 12-tooth pinion drives a 36-tooth gear at 1500 RPM carrying 10 N·m of input torque.

Gear ratio = 36 / 12 = 3, written 3 : 1.
Output RPM = 1500 / 3 = 500 RPM.
Output torque = 10 × 3 = 30 N·m.

Ratio 3 : 1, output 500 RPM, output torque 30 N·m (a torque-multiplying reduction).

Frequently asked questions

What is the difference between a reduction and an overdrive?: A reduction (ratio greater than 1) makes the output turn slower than the input while multiplying torque, useful for moving heavy loads. An overdrive (ratio less than 1) speeds the output up at the cost of torque, like a top cruising gear.
Why does torque go up when speed goes down?: Ignoring friction losses, mechanical power (torque times angular speed) is conserved through the gear pair. So if the gears cut the speed by a factor, they must raise the torque by the same factor to keep power constant.
Does the gear ratio depend on tooth count or gear diameter?: Either works because meshing gears share the same tooth pitch, so tooth count is directly proportional to pitch diameter. Using tooth counts is exact and avoids measuring diameters.
How do I find the ratio of a multi-stage gear train?: Multiply the individual stage ratios together. For example, a 3:1 stage followed by a 2:1 stage gives an overall 6:1 reduction; you can chain this calculator stage by stage.

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