Gear Ratio Calculator

The gear ratio of a two-gear drive system tells you how many times the driver (input) gear must rotate for the driven (output) gear to complete one full turn. It is calculated by dividing the number of teeth on the driven gear by the number of teeth on the driver gear. A ratio greater than 1 is called a reduction drive: the output shaft turns slower than the input but produces more torque. A ratio less than 1 is an overdrive: the output turns faster but with less torque. This relationship is fundamental to mechanical engineering because it lets you trade speed for torque, or torque for speed, without changing the power source. Gear ratios appear in car gearboxes, bicycle drivetrains, electric motors, industrial conveyors, and any machine where rotational motion needs to be transformed. You enter the number of teeth on the driver gear, the number of teeth on the driven gear, and the input speed in revolutions per minute (RPM). The calculator returns the gear ratio expressed as a decimal and a simple ratio, the output RPM, and the torque multiplication factor (assuming 100% efficiency). For the default values of a 20-tooth driver at 1,000 RPM and a 40-tooth driven gear, the ratio is 2:1, the output speed is 500 RPM, and torque is doubled. These calculations assume a simple two-gear mesh and do not account for friction losses in real gearboxes.

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t
RPM
2.00 : 1
gear ratio (driven : driver)
Output RPM500.00
Torque multiplier2.00x
Drive typeReduction

How it works

Gear ratio = driven teeth divided by driver teeth. Output RPM = input RPM divided by gear ratio. Torque multiplier = gear ratio (assuming 100% efficiency, i.e. no friction losses). If the ratio is greater than 1, the drive type is "Reduction" (slower output, more torque). If less than 1, it is "Overdrive" (faster output, less torque). If equal to 1, it is a 1:1 direct drive. Division by zero is caught and flagged.

Worked example

A driver gear has 20 teeth and spins at 1,000 RPM. The driven gear has 40 teeth. Gear ratio = 40 divided by 20 = 2.00 : 1. Output speed = 1,000 divided by 2 = 500.00 RPM. Torque multiplier = 2.00x. Drive type is Reduction. These match the default values pre-filled above.

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Frequently asked questions

How is gear ratio calculated?

Gear ratio equals the number of teeth on the driven (output) gear divided by the number of teeth on the driver (input) gear. A ratio greater than 1 means the output gear turns slower than the input (reduction drive), and a ratio less than 1 means it turns faster (overdrive). For example, a 40-tooth driven gear and a 20-tooth driver gear gives a ratio of 2:1.

What happens to torque when you increase the gear ratio?

In a simple gear pair, torque is multiplied by the gear ratio (assuming no losses). If the gear ratio is 2:1, the output shaft produces twice the torque of the input shaft but rotates at half the speed. Energy is conserved: higher torque at lower speed equals the same power as lower torque at higher speed.

What is the difference between a reduction drive and an overdrive?

A reduction drive has a gear ratio greater than 1, meaning the output shaft spins slower than the input but with more torque. An overdrive has a ratio less than 1, meaning the output spins faster but with less torque. Gearboxes in vehicles use reduction drives in lower gears for acceleration and overdrive in top gear for cruising efficiency.