Pitch diameter comes straight from the tooth count
The pitch diameter is the effective rolling circle of a gear, and it depends only on the number of teeth and the tooth size. Use the module in the metric system (mm per tooth) or the diametral pitch in the inch system (teeth per inch). Two gears mesh only if they share the same module or diametral pitch.
Pitch diameter by teeth and module
| Teeth | Module 1 | Module 1.5 | Module 2 | Module 3 |
|---|---|---|---|---|
| 12 | 12 mm | 18 mm | 24 mm | 36 mm |
| 18 | 18 mm | 27 mm | 36 mm | 54 mm |
| 24 | 24 mm | 36 mm | 48 mm | 72 mm |
| 36 | 36 mm | 54 mm | 72 mm | 108 mm |
| 48 | 48 mm | 72 mm | 96 mm | 144 mm |
The center distance between two meshing gears is the average of their two pitch diameters: a 24-tooth and a 48-tooth gear at module 2 sit (48 + 96) ÷ 2 = 72 mm apart.
Module against diametral pitch
- They run opposite ways. A large module means large teeth; a large diametral pitch means small teeth. Do not read one scale as if it were the other.
- Convert with 25.4. module = 25.4 ÷ DP. A diametral pitch of 10 is roughly module 2.54, and the two are not directly interchangeable in a single gear train.
- Outside diameter is bigger. Add two modules (or 2 ÷ DP) to the pitch diameter to reach the tips of the teeth, which is what you measure with calipers.
Common questions
How do I find a gear pitch diameter?
In the metric system, multiply the tooth count by the module: 20 teeth at module 2 gives a 40 mm pitch diameter. In the inch system, divide the tooth count by the diametral pitch instead.
What is the difference between module and diametral pitch?
They measure the same thing from opposite ends. Module is millimeters of pitch diameter per tooth, so bigger module means bigger teeth. Diametral pitch is teeth per inch of pitch diameter, so bigger DP means smaller teeth. They are inverses: module is about 25.4 divided by the diametral pitch.
Why is the pitch diameter smaller than the gear itself?
The pitch diameter is the imaginary circle where two meshing gears effectively roll, partway up the teeth. The outside diameter is larger because it reaches the tips of the teeth, roughly two modules more than the pitch diameter.
