Gear Ratio Calculator

About the Gear Ratio Calculator

Gearing is how machines trade speed for torque, and getting the ratio right decides whether a conveyor moves at the correct rate, a winch has the pulling power it needs, or a robot joint holds position. This calculator takes the teeth counts of the driver and driven gears along with the input speed and torque, and returns the gear ratio plus the resulting output speed and output torque. It is aimed at anyone laying out a single gear pair or a belt-and-sprocket stage and wanting to see the tradeoff immediately.

The core idea is conservation: a gear train does not create energy, so whatever speed you lose you gain back in torque, and vice versa, minus friction losses. A reduction that slows the output down multiplies torque by the same factor. This calculator makes that tradeoff explicit by showing output RPM falling and output torque rising together as you increase the ratio.

Enter teeth counts as whole numbers, input speed in RPM, and input torque in pound-feet. The tool treats the pair as ideal with no losses, which is a good first approximation for spur and helical gears that are often 95 percent or more efficient per stage. For worm drives or long chains you would derate the output torque for efficiency separately.

How the Gear Ratio Calculator works

Gear ratio is defined here as the driven gear teeth divided by the driver gear teeth. A 60-tooth driven gear on a 20-tooth driver gives a ratio of 3, written 3:1, meaning the driver turns three times for every one turn of the driven gear. A ratio above 1 is a speed reduction and torque increase; a ratio below 1 is an overdrive that speeds output up and reduces torque.

Output speed is the input speed divided by the ratio, because the slower-turning driven gear rotates fewer times. Output torque is the input torque multiplied by the ratio, reflecting the mechanical advantage a reduction provides. These two relationships are inverse: multiply output speed by output torque and, ignoring losses, you get back the same product as input speed times input torque, which is the power passing through unchanged.

The tool recalculates the moment you change any input, so you can hunt for the teeth combination that hits a target output speed or a required output torque. Because it assumes an ideal lossless pair, real output torque will be slightly lower after friction, but the ratio and speed relationships hold precisely since they depend only on geometry.

Worked example

Consider a motor spinning at 1,800 RPM and producing 50 lb-ft of torque, driving a 20-tooth pinion that meshes with a 60-tooth gear. The gear ratio is driven divided by driver, 60 / 20 = 3, so 3:1.

Output speed is input speed divided by ratio, 1,800 / 3 = 600 RPM. The driven gear turns a third as fast as the motor. Output torque is input torque times ratio, 50 x 3 = 150 lb-ft, so the reduction triples the available torque at the output shaft.

Check the power balance: input is proportional to 1,800 x 50 = 90,000 and output to 600 x 150 = 90,000, confirming no energy was created. If you instead needed the output to spin faster, swapping to a 20-tooth driven on a 60-tooth driver gives a 0.333:1 overdrive, raising speed to 5,400 RPM but cutting torque to about 16.7 lb-ft.

Tips & common mistakes

• A ratio greater than 1 slows the output and multiplies torque; a ratio less than 1 speeds it up and reduces torque. Decide which you need before picking teeth counts, since it is easy to invert driver and driven and get the opposite effect.
• The tool assumes an ideal lossless pair. Real spur and helical stages lose a few percent to friction, so derate the calculated output torque by roughly 2 to 5 percent per stage for planning, and more for worm gears.
• For multiple stages, multiply the individual ratios together. Two 3:1 stages give an overall 9:1 reduction, and the same multiply-then-divide logic applies to speed and torque across the whole train.
• Teeth counts should be whole numbers. Avoid a common factor between driver and driven when you can, since a hunting-tooth combination spreads wear more evenly across all teeth over time.
• Belt and chain sprockets follow the exact same ratio math using their teeth counts, so you can use this tool for timing belts and roller chain drives, not just meshing gears.

Gear Ratio Calculator: frequently asked questions