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Gear Train Reduction Calculator

Enter driver teeth, driven teeth, and input RPM to find the output speed.

How it is calculated

For one pair of meshing gears the ratio is the tooth count of the driven (output) gear divided by that of the driver (input) gear: ratio = driven teeth / driver teeth. The output speed is output rpm = input rpm / ratio, and the torque multiplication shown equals the ratio itself, because ideally power is conserved when speed is traded for torque. A ratio above 1 means a reduction (slower output, more torque), below 1 an overdrive (faster, less torque). Tooth counts must be above zero. The tool assumes a lossless pair, so friction, gear efficiency and the direction of rotation are not modelled, and a train of several stages must be multiplied stage by stage.

Worked example

An 18-tooth driver gear on a motor turning at 3,000 RPM drives a 54-tooth gear. Ratio: 54 / 18 = 3, shown as 3.00:1. Output speed: 3,000 / 3 = 1,000, which the tool shows as 1,000.0 RPM. The torque multiplication is ×3.00, so the output shaft can deliver up to three times the input torque, minus losses in a real gearbox. Swapping the two gears, 54 teeth driving 18, would give a ratio of 0.33 and 9,000 RPM.

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Common mistakes

  • Swapping driver and driven. The ratio is driven over driver; reversed, a reduction is reported as an overdrive and the output speed is three times too high instead of three times too low.
  • Entering the pitch diameters or the shaft speeds in the tooth fields. The fields expect tooth counts; diameters give the right ratio only if you keep the same proportion on both gears.
  • Treating the torque multiplication as what you will measure at the output. Friction and meshing losses reduce the real torque below the ideal ×3.00.
  • Using the tool for a multi-stage gearbox in a single step. For stages in series, calculate each pair separately and multiply the ratios, or feed the output RPM of one stage into the next.
  • Expecting the tool to show the output direction. A single external pair reverses the rotation, which is not displayed.

About this calculator

In a simple gear train, the gear ratio is the number of teeth on the driven gear divided by the number of teeth on the driver gear. A larger driven gear turns more slowly than the driver but with proportionally more torque, since (ignoring friction losses) power is conserved: output RPM = input RPM ÷ gear ratio, while output torque = input torque × gear ratio.

This trade-off between speed and torque is the entire point of gearing down — a small motor spinning fast can drive a heavy load slowly but with much greater force, which is why reduction gear trains show up in everything from car transmissions and robotics actuators to power tools and wind turbine nacelles. Count the teeth on the driving and driven gears, add the input speed, and the page gives the gear ratio, the output RPM and how much the train multiplies torque.

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Comments (1)

  • Editorial team

    This handles a single meshing pair. For a compound train, multiply the ratios of each stage: a 12 to 36 pair followed by a 10 to 30 pair gives 3 times 3, a 9:1 reduction, so 1800 rpm in becomes 200 rpm out. Real gears lose some torque to friction, so the torque figure is the ideal. Describe your gear train and the final ratio you need.

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