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CALCULATORS / GEARS AND GEAR TRAINS

Gear ratio, speed and torque calculator

Ideal external gear pair: no loss, backlash or tooth strength

gears-gear-ratio.napkin / editable
✓ checks pass

SCENARIO COMPARISON

Compare the numbers.

This source describes an analytical model. Its quantities and checks are the view.

ScenarioratiooutputSpeedrpm
3400
3600

All calculated quantities are listed with the inputs. Switch to Source to inspect the equations.

SCENARIOS / CALCULATED VALUESSAME SOURCE

Change an input to see the consequences.

ratio requirement3.00 ✓ passes

BASELINE INPUTS

CALCULATED

ratio3
outputSpeed400 rpm

Edits change the baseline source.

Calculated from your source · not saved
Baseline · Baseline
ratio requirement3.00 ✓ passes
faster · faster
ratio requirement3.00 ✓ passes

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

ratio
ratio = drivenTeeth / driverTeeth
output speed
outputSpeed = inputSpeed / ratio [rpm]

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

driver teeth
20
driven teeth
60
input speed
1200 rpm

Calculated

ratio
3
output speed
400 rpm

Assumptions and limits

Ideal external gear pair: no loss, backlash or tooth strength

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Gear ratio, speed and torque. Inputs: tooth counts; input speed and torque; efficiency. Outputs: ratio; output speed and torque. Model scope: Rigid involute-gear kinematics; qualified stress approximations. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

  • Inputs: tooth counts, input speed and torque, efficiency
  • Outputs: ratio, output speed and torque
  • Modes: calculate, compare, sweep
  • Drawing: Animated gear assembly

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS

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