Gear module and diametral pitch calculator

Metric spur pitch module from diameter and tooth count.

gears-module.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	modulemm	circularPitchmm
	2	6.28319
	1.6	5.02655

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.

module target2.00 mm✓ passes

BASELINE INPUTS

diameter60 mmteeth30

CALCULATED

module2 mm

circularPitch6.2832 mm

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Gear module and diametral pitch
# Scope: Metric spur pitch module from diameter and tooth count.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

diameter = 60 mm
teeth = 30

module := diameter/teeth [mm]
circularPitch := pi*module [mm]

check module target: module <= 3 mm

scenario alternative: diameter = 48 mm

Calculated from your source · not saved

Baseline · Baseline

module target2.00 mm ✓ passes

alternative · alternative

module target1.60 mm ✓ 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.

module: module = diameter/teeth [mm]
circular pitch: circularPitch = pi*module [mm]

Original worked example

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

Given

diameter: 60 mm
teeth: 30

Calculated

module: 2 mm
circular pitch: 6.28319 mm

Assumptions and limits

Metric spur pitch module from diameter and tooth count.

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 module and diametral pitch. Inputs: pitch diameter; tooth count or diametral pitch. Outputs: module; tooth size; compatible dimensions. 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: pitch diameter, tooth count or diametral pitch
Outputs: module, tooth size, compatible dimensions
Modes: calculate, compare, sweep
Drawing: Animated gear assembly

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