Gear Ratio Calculator

How to use the gear ratio calculator

Choose the drive: a single gear pair, a compound gear train of two to four stages, or a belt running over two pulleys. Count the teeth on the driver (the gear on the motor or input shaft) and on the driven gear (on the output shaft). For a chain drive, count the sprocket teeth the same way. Add the input speed in revolutions per minute and, if you need it, the input torque; the output torque comes out in the same unit, whether that is N·m or lb·ft. Leave the efficiency at 100% for the ideal figure, or enter a real value to see the torque you actually get.

The gear ratio formula

The gear ratio is driven teeth ÷ driver teeth. Meshing gears move the same number of teeth past each other, so the speed falls by that ratio and the torque rises by it:

• Output speed = input speed ÷ ratio
• Output torque = input torque × ratio × efficiency

A ratio above 1 (written 3 : 1) is a speed reduction: slower, stronger output, as in a gearbox reducer, a winch or a car's first gear. A ratio below 1 (written 1 : 3) is a speed increase or overdrive: faster output with less torque. Power stays the same apart from losses, which is why speed and torque change in opposite directions.

Worked example

A 20-tooth pinion on a motor turning at 1,500 rpm drives a 60-tooth gear. The ratio is 60 ÷ 20 = 3 : 1, so the output turns at 1,500 ÷ 3 = 500 rpm. With 10 N·m of input torque the ideal output torque is 10 × 3 = 30 N·m; at 95% mesh efficiency it is 28.5 N·m. Swap the gears (60 driving 20) and the output turns three times faster, at 4,500 rpm, with a third of the torque.

Gear trains with several stages

In a compound gear train, the driven gear of one stage shares a shaft with the driver of the next. The overall ratio is the product of the stage ratios: 60/20 × 45/15 = 3 × 3 = 9 : 1, and four such stages give 81 : 1. That is how compact gearboxes reach large reductions without one enormous gear. Efficiency multiplies too: four stages at 98% each pass on about 92% of the power.

Each external gear mesh reverses the direction of rotation, so one pair turns the output the opposite way, two stages turn it the same way as the input, and so on. An idler gear placed between two gears also reverses direction but does not change the ratio — leave it out of the calculation. Internal (ring) gears and planetary sets follow different rules and are not covered here.

Belt and pulley drives

For a belt, the ratio is driven pulley diameter ÷ driver pulley diameter: a 100 mm pulley driving a 250 mm pulley gives 2.5 : 1, so 1,500 rpm becomes 600 rpm. Both pulleys of an open belt turn the same way; a crossed belt reverses the direction. V-belts and flat belts slip slightly under load, so the real output speed is usually a little lower than calculated. Toothed (timing) belts do not slip; for them you can enter the tooth counts as a gear pair.

Tips

• Teeth counts must be whole numbers. If you know only diameters of two gears with the same tooth size (module or diametral pitch), the ratio of the pitch diameters is the same as the ratio of the teeth.
• Gear manufacturers and motor catalogs publish efficiency figures; worm gears in particular can be far below spur gears.
• Check that the output torque stays within the rating of the gears, shafts and bearings, and leave a safety margin.

Frequently asked questions

Last updated: October 19, 2026