Gear Module & Pitch
Compute pitch diameter D, addendum da, root df, circular pitch t and centre distance C from module m and teeth Z; also diametral pitch Pd.
Inputs
Formula
Fundamentals
Module is the basic size parameter of a gear: pitch diameter divided by tooth count, setting tooth size and load capacity.
Module $m=d/z$, with $d$ the pitch diameter and $z$ the tooth count. Standard module series (1, 1.25, 1.5, 2 …) ensure interchangeability; tooth thickness and height scale with $m$.
History
The module concept was introduced by Robert Willis in the 19th c. to standardise tooth size; the 1920s ISO/R 111 defined the first module series, enabling globally interchangeable gears.
Engineering applications
Module is the common basis for gear design, cutting tools (hob, shaper) and inspection (gear caliper, three-wire method), and decides whether a pair will mesh correctly.
Glossary
| Pitch diameter $d$ | Theoretical circle where tooth thickness equals space, $d=mz$. |
| Circular pitch $p$ | Arc distance between adjacent teeth, $p=\pi m$. |
| Standard module | National standard values guaranteeing gear interchangeability. |
How to use
- Fill in Module m, Teeth Z, Mate teeth Z₂ in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Pitch diameter, Addendum dia., Root dia., Circular pitch, Centre distance, Diametral pitch in the results area.
Formula · Worked Example · Knowledge
Formula
Worked Example
Key Points
- Only equal-module gears mesh; standard pressure angle 20°.
- Addendum dia $d_a=d+2m$, root dia $d_f=d-2.5m$.
- Diametral pitch $P_d=25.4/m$ for inch-system gears.
Parameters
Inputs
| Parameter | Symbol | Unit | Default |
|---|---|---|---|
| Module m (mm) | m | mm | 2 |
| Teeth Z | Z | 20 | |
| Mate teeth Z₂ | Z2 | 40 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Pitch diameter | D | mm |
| Addendum dia. | da | mm |
| Root dia. | df | mm |
| Circular pitch | t | mm |
| Centre distance | C | mm |
| Diametral pitch | Pd | 1/in |
Applications
- Common engineering use cases