Gear Geometry Calculator
Enter module and teeth to get the full set of spur gear dimensions — pitch, outside and root diameters, circular pitch and tooth depth.
Last updated: 2026-09-15
How the calculation works
- The module is the pitch diameter per tooth — it defines the tooth size. Two gears mesh iff they share it.
- Pitch diameter is module × teeth; outside adds two addendums (2m), root subtracts 2.5m for standard full-depth teeth.
- Circular pitch is the arc spacing between teeth, and whole depth is 2.25m.
Formula
d = m × z da = d + 2m df = d − 2.5m p = π × m
| Symbol | Meaning | Unit |
|---|---|---|
m | Module | mm |
z | Number of teeth | — |
d | Pitch diameter | mm |
da, df | Addendum (outside) / dedendum (root) circle | mm |
Worked example
Interpreting the result
The module system makes gears interchangeable: same module means any tooth counts mesh at center distance (z₁+z₂)m/2. Bigger module = stronger teeth but coarser action. For repair work, measuring the outside diameter and counting teeth recovers the module — that's the standard first step in identifying an unknown gear.
Assumptions
- ISO full-depth involute teeth, 20° pressure angle, no profile shift.
- Standard addendum (1m) and dedendum (1.25m).
Limitations
- Profile-shifted (corrected) gears change outside and root diameters.
- Stub teeth (with 1.8× module depth) and helical gears differ.
- US DP (diametral pitch) system: module = 25.4/DP.
Frequently asked questions
How do I identify an unknown gear's module?
Count teeth, measure the outside diameter, then m = (OD − 2×addendum)/z ≈ OD/(z+2). Verify with the circular pitch against mating gears.
What module should I use?
Match the mating gear exactly — module defines meshing. For new designs, choose from standard series based on torque: bigger loads need bigger modules.