Mechanical Engineering

Gear Ratio Calculator

GR = N_driven/N_driver. Output speed and torque calculations

Last updated: How we build & verify
teeth
teeth
RPM
N·m

How it works

Gear ratio is the tooth count of the driven gear divided by the tooth count of the driver. A ratio above 1 is a reduction: the output shaft turns slower and carries proportionally more torque, because an ideal gear pair trades one for the other rather than adding power.

Formula
GR = N_driven / N_driver
Output speed = Input speed / GR
Output torque = Input torque × GR
Variables
  • N_driverteeth on the input gear
  • N_driventeeth on the output gear
  • GRgear ratio, conventionally written as GR:1
  • Powerspeed × torque, conserved across the mesh apart from friction
Worked example
Inputs: 20-tooth driver meshing a 60-tooth driven gear, with 1,500 RPM and 50 N·m at the input
  1. GR = 60 / 20 = 3, written 3:1
  2. Output speed = 1,500 / 3 = 500 RPM
  3. Output torque = 50 × 3 = 150 N·m
  4. Power check: 50 × 1,500 = 75,000 = 150 × 500
Result: 3:1 reduction giving 500 RPM at 150 N·m
Notes
  • Idler gears sitting between the driver and the driven gear reverse the direction of rotation but drop out of the ratio entirely. Their tooth count never appears in the answer.
  • Compound trains multiply rather than add. A 3:1 stage feeding a 4:1 stage on a shared shaft gives 12:1.
  • Efficiency is not free. A spur mesh typically loses 1 to 2%, while a high-ratio worm drive can fall below 60%, and that lost power leaves as heat in the gearbox.
  • Tooth counts sharing a common factor let the same tooth pairs meet repeatedly. A hunting ratio, where the counts are coprime, spreads wear evenly across every tooth.

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Frequently Asked Questions

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Gear Ratio Calc follows the standard method used in textbooks and technical references for this calculation, and we show the formula or approach on the page itself so you can check the working rather than trust a black box. Found an edge case that breaks it? Use the feedback button in the bottom-right corner.

Gear Ratio Calculator | ExaCalc