Gear Train Calculator

A calculator for designing a multi–stage compound gear train. It can also do a reverted gear train.

Provides teeth counts from any given overall ratio.

Free. Nothing else to download and install. Works on home computers (PC or Mac) as well as smartphones and tablets. JavaScript needs to be enabled in your browser.

Click either calculator type below. You can switch from one type to the other later as well.

Compound CalculatorReverted Calculator

This calculator is designed to be a practical tool for the hobbyist, machinist, woodworker, engineering student or mathematics enthusiast. It is intended for people who fabricate custom gears with a number of teeth that may not be commercially available. It is NOT for finding ratios from existing gears such as from bicycle gears or car transmissions. Nor is it for selecting from a set of existing gears for thread cutting lathes.

  • Select a wide range of teeth counts from 3 to 400.
  • Multi–stage compound gear trains — choose number of stages from 1 to 6 (2 to 12 gears). Practical limit is 5 stages.
  • Allow tolerance or get the most accurate result possible.
  • Optional high reduction ratio pre-stage. Examples are pendulum/escape–wheel, pawl/ratchet or worm gear. The teeth count of that driving wheel is incorporated.
  • Reverted gear train mode. This is where driver and final driven gear are collinear and their pitches are required to be equal.


- Finds the most accurate gear ratio.

- Lowest total teeth count.

- Error is shown in percentage as well as other flexible comparisons e.g. parts–per–million, seconds per year, etc.

- Fast! It completes 6 gears (3–stage) in under one second on a smartphone.

- You may enter a formula into the Ratio field including math functions "sqrt", "pow", "exp", "log", "sin", "cos", "tan", "asin", "acos", "atan". The constant "pi" is also available.

Please leave comments on forum.

Revised 18 Apr 2015