Enrichment · STEM Explorations

Trade speed for torque,
one gear at a time.

Enter the teeth on each gear and the motor's speed and torque. The page shows the overall ratio, what comes out of every shaft and which way it turns, with the working written out and the train drawn to scale.

Open the calculatorWhat you get

The calculator

The worked example is a made-up robot drive: a small motor at 6,000 rpm through three gear stages. Two more examples are in the menu.

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What you get

Enrichment · STEM ExplorationsFree

What you finish with
The overall ratio of your gear train, the speed, torque, power and turning direction of every shaft, the working written out for a lab report, and the gear sizes that come closest to a ratio you need.
Who it is for
Middle and high school students in physics, engineering and robotics; robotics and maker club teams; anyone building with gears, sprockets or belts.
Format
Browser tool with three tabs: the gear train calculator with a scale drawing, a finder for a target ratio and your saved trains. Prints the train with its drawing and working; downloads the shaft table (.csv) and a file you can import later.
Access
Free. No account or sign-in. It runs in your web browser on a phone, tablet or computer. Everything you type stays in this browser and is saved there as you go; nothing is sent to Caveat.
Where it lives
The STEM Explorations space in Caveat Enrichment.
Support
Questions, a correction or a request: team@caveatacademic.com.

How to use it

  1. Load the robot drive example, or start blank.
  2. Enter the input speed, and the torque if you know it. Add a wheel diameter to get ground speed, or a module to get gear sizes in millimetres.
  3. For each stage, pick gear pair, chain or belt and enter the driver and driven teeth. Add idlers when you need the output to turn the other way.
  4. Read the ratio, output speed and torque, and check the working underneath. Press Turn the gears to watch the speeds.
  5. Need a particular ratio? Use the finder with the gear sizes you have, then load the best train and save it.

Open the calculator

The physics behind the numbers

Ratios multiply; power is conserved, minus losses.

Ratio, speed and torque

Two meshing gears move the same number of teeth past the contact point, so speed falls in proportion to teeth: a 40-tooth gear driven by an 8-tooth gear turns 8/40 as fast. Stages on shared shafts multiply. Power is torque times angular speed, and a gear train cannot create power, so when speed drops by the ratio, torque rises by the same ratio, less what friction takes at each mesh.

Each external gear contact reverses the direction of turning. An idler between two gears changes direction without changing the ratio. A chain or belt keeps both sprockets turning the same way.

The efficiency defaults

Defaults are typical values for well-lubricated parts in good condition: 98% per spur gear mesh, 97% for a roller chain and 96% for a toothed belt. Real values depend on load, speed, lubrication and wear; worm gears, which this page does not model, can be far lower. Change the numbers if you measured or looked up your own.

The module (in millimetres) sets tooth size: pitch diameter = module × teeth, and two gears mesh only if their modules match.

Sources

  1. Budynas, R. G., and Nisbett, J. K. (2020). Shigley's Mechanical Engineering Design (11th ed.). McGraw-Hill. Gear trains, train value, spur gear geometry and mesh efficiency.
  2. OpenStax (2016). University Physics, Volume 1, chapters 10 and 11. Rotational kinematics, torque and power (P = τω).
  3. ISO 54 and ISO 21771. Cylindrical gears: modules and geometry (module, pitch diameter and centre distance definitions).
  4. National Institute of Standards and Technology (2008). Guide for the Use of the International System of Units (SI), Special Publication 811. Conversion of newton metres to pound-force feet.

The examples are made up. Efficiencies are typical values, not measurements of your parts; check gear strength, shaft loads and safety factors before building anything that carries a person or a heavy load. Support: team@caveatacademic.com.