Rack-and-pinion: gear ratio

Updated February 21, 2017

Gear ratio is the relationship between the number of teeth on each gear. This ratio shows the number of revolutions each gear makes. Rack-and-pinion gear ratio is slightly different in that it measures the distance the rack travels.

Calculating Gear Ratio

For two standard round gears, the gear ratio is calculated by counting the number of teeth on each gear and dividing the number of teeth on the driver gear by the number of teeth on the driven gear. For example, a gear with 25 teeth drives a gear with 75 teeth. Dividing 25 by 75 gives you a ratio of 3/1, meaning that for every three rotations the driver gear makes, the larger gear turns once.


A rack-and-pinion gear system consists of a round gear known as the pinion and a flat, toothed component known as the rack. The principle is the same; however, rather than rotations, the ratio determines the linear distance travelled by the rack with each rotation of the pinion.

Calculating Rack-and-Pinion Gear Ratio

Instead of counting the number of teeth in each gear, the distance the rack moves is measured in inches. Measure the distance from the end of the rack to an arbitrary point, turn the pinion one full revolution and then measure the distance again. The difference is the gear ratio.

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About the Author

Mike Goldstein has been writing since 2005 and has been published in "Science" and Boston College's "Intellectual Property and Technology Forum Law Review." He studied Shakespeare at Rutgers University, pursuing a Bachelor of Arts in English literature. Music and photography are two of his specialties.