How to calculate gear ratios and torque

Updated March 23, 2017

The torque acting on the first gear in your gearbox depends on the force acting on it and the size of the gear. As with all torque systems, the gear consists of a rotational arm and a perpendicular force. In this case, the gear's radius is the system's arm. The torque is a product of the force and its distance from the central pivot point. The gearbox then multiplies the torque by applying it to a second, larger gear. The gear ratio describes the ratio between these two gears' sizes.

Multiply the force acting on the first gear by the first gear's radius. If, for instance, a force of 4,000 newtons acts on the gear, and it measures 0.15 meters in radius, 4,000 x 0.15 = 600. The gear turns with 600 newton-meters of torque.

Divide the second gear's radius by the first gear's. If the second gear, for instance, measures 0.3 meters in radius: 0.3 / 0.15 = 2. The system's gear ratio is 2-to-1.

Multiply the gear ratio by the input torque that you calculated in Step 1: 2 x 600 = 1,200 newton-meters. This is the gearbox's output torque.

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About the Author

Ryan Menezes is a professional writer and blogger. He has a Bachelor of Science in journalism from Boston University and has written for the American Civil Liberties Union, the marketing firm InSegment and the project management service Assembla. He is also a member of Mensa and the American Parliamentary Debate Association.