Pitch Diameter Calculator
Calculate a gear’s pitch diameter, outside diameter, and circular pitch from its tooth count and diametral pitch or module.
What this calculator does
The pitch diameter calculator finds the pitch diameter of a spur gear — the diameter of the theoretical circle where two mating gears effectively contact each other — along with outside diameter and circular pitch, using either the imperial diametral pitch system or the metric module system.
The formula
In the imperial system, pitch diameter (in) = number of teeth ÷ diametral pitch, and outside diameter (in) = (teeth + 2) ÷ diametral pitch. In the metric system, pitch diameter (mm) = module × number of teeth, and outside diameter (mm) = pitch diameter + 2 × module. Circular pitch (the distance along the pitch circle from one tooth to the corresponding point on the next) equals π ÷ diametral pitch, or π × module.
- Diametral pitch and module are reciprocal-style measures of tooth size from different unit systems — gears must be matched within the same system to mesh correctly.
- Outside diameter formulas here assume standard full-depth gear teeth; specialized tooth forms may differ slightly.
This tool is for general mechanical design reference and educational purposes.