How to calculate torque through a gear reducer

Written by douglas quaid
How to calculate torque through a gear reducer
Interlocking gears turn at different speeds and with different amounts of force. (gears of clock image by jimcox40 from

A gear reducer is a pair of interlocking gears. One of the gears is driven by an input, usually a motor which has a given speed, in revolutions per minute, and torque. Torque is rotational force. The gear reducer translates the input force and speed into a different force and speed at the output. The total amount of power, however, remains the same. The transmission in your car is an example of a gear reducer. In first gear, the fast rotation of the engine is translated into slow rotation with high torque, and in fifth gear the output gear rotates quickly but with low torque. You can calculate the output torque using a figure called the "gear ratio" of the reducer.

Look up the torque of your motor in its specifications.

Look up the gear ratio of your gear reducer if you have documentation for it. If you don't have any packaging or documentation for the gear reducer, count the teeth on each gear. The gear ratio is the number of teeth on the output gear divided by the number of teeth on the input gear, the one attached to the motor. If you don't want to count the teeth, measure the diameter of each gear from the centre to the point of contact between the gears. Divide the diameter of the output gear by the diameter of the input gear.

Multiply the torque of the motor by the gear ratio to get the output torque. For example, a motor that puts out 4.54kg.-feet of torque used with a gear reducer with a 10:1 gear ratio will give you 45.4kg.-feet of torque at the output gear.

Multiply the output torque by the rated efficiency of the gear reducer, if the manufacturer has published this information. The result is the actual output torque of the reducer. The calculation in step three assumes that the gear reducer transmits power completely efficiently, but in reality all gear reducers lose some power due to friction. Lightweight plastic gears are very efficient, and for many applications you can ignore the efficiency rating. However, for very heavy metal gears or critical applications you should take the efficiency of the reducer into account.

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