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MachineCalcs

Gear Module Calculator

Gear module from pitch diameter and tooth count, with the diametral pitch (1/in), circular pitch, addendum and whole depth. Convert module ↔ diametral pitch. Metric and imperial.

Inputs

mm

Results

Module(m)
2

≈ DP 12.7 (1/in)

mm

Diametral pitch(DP)
12.7

1/in

Circular pitch(p)
6.283 mm

Addendum(a)
2 mm

= module

Whole depth
4.5 mm

= 2.25 × module

  • Module m = pitch diameter ÷ tooth count; diametral pitch DP = 25.4 / m (they are reciprocals scaled by 25.4).
  • Assumes the pitch diameter, not the tip (outside) diameter. From a tip diameter, m ≈ tip ÷ (z + 2).
  • Mating gears must share the same module and pressure angle.

How it works

The module sets a gear's tooth size. It is the pitch diameter per tooth: m = d / z where d is the pitch diameter and z the tooth count. The imperial equivalent is the diametral pitch DP = 25.4 / m (1/in) — module and DP are reciprocals scaled by 25.4, so m = 25.4 / DP. The circular pitch (arc length per tooth along the pitch circle) is p = π · m. For standard full-depth teeth the addendum equals the module (a = m) and the whole depth is 2.25 · m. Mating gears must share the same module (or DP) and pressure angle.

Worked example

A gear with a 40 mm pitch diameter and z = 20 teeth has module m = 40 / 20 = 2 mm — equivalently DP = 25.4 / 2 ≈ 12.7 (1/in). Its circular pitch is π · 2 ≈ 6.28 mm, the addendum is 2 mm, and the whole depth is 2.25 × 2 = 4.5 mm. The calculator returns exactly this.

Frequently asked questions

How do you calculate the gear module?
Module m = pitch diameter d ÷ number of teeth z. Enter the pitch diameter and tooth count above and the calculator returns the module in mm, along with the diametral pitch, circular pitch, addendum and whole depth.
What is the difference between module and diametral pitch?
They are the metric and imperial measures of the same tooth size and are reciprocals scaled by 25.4: module (mm) m = 25.4 / DP, and diametral pitch (1/in) DP = 25.4 / m. So module 2 mm is about DP 12.7, and DP 10 is module 2.54 mm.
How do I measure the module of an existing gear?
Count the teeth z and measure the tip (outside) diameter. For a standard full-depth tooth the tip diameter ≈ m·(z + 2), so module m ≈ tip diameter ÷ (z + 2). Confirm against the standard module series — a 41.8 mm tip with 19 teeth gives m ≈ 1.99, i.e. module 2.
What is circular pitch?
Circular pitch p is the distance from one tooth to the next measured along the pitch circle: p = π · m. It is the arc length per tooth, whereas the module is the pitch diameter per tooth.
What are the standard module sizes?
ISO 54 lists preferred metric modules. Series 1 (first choice) is 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25 mm. Sticking to a preferred module makes mating gears, cutters and replacements easier to source.
Does this work in metric and imperial?
Yes — toggle SI/Imperial in the header to switch the diameters between mm and inches. The module is always shown in mm and the diametral pitch in 1/in, so you get both systems at once.

Method & assumptions

  • Standard full-depth involute proportions (addendum = m, whole depth = 2.25 m). Stub or non-standard tooth systems differ.
  • Uses the pitch diameter, not the tip (outside) diameter. If you only have the tip diameter, module ≈ tip ÷ (z + 2).
  • Module (mm) and diametral pitch (1/in) are reciprocals scaled by 25.4: m = 25.4 / DP.

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