Gear Pitch Diameter Calculator
Find a gear's pitch diameter from module and tooth count — or work backwards from a known pitch diameter to check module.
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How this calculator works
Pitch diameter is the diameter of the theoretical circle on which two gears' pitch circles are tangent, and it's directly proportional to module and tooth count:
Where m is module in mm and z is the number of teeth. Rearranged, module can be found from a known diameter and tooth count: m = d / z.
Why pitch diameter matters
Pitch diameter sets the effective gear ratio between meshing gears and, together with tooth count, determines center distance. It's the reference dimension used to derive outside diameter, root diameter, and other gear-cutting dimensions.
Frequently asked questions
How do I get outside diameter from pitch diameter?
For a standard full-depth external gear, outside diameter is approximately pitch diameter plus two times the module (do = d + 2m). This gives the blank stock size before cutting teeth.
Does this work for helical gears?
This formula applies to the normal module of a helical gear in the plane perpendicular to the tooth. For the transverse (front-view) pitch diameter, divide the normal module by the cosine of the helix angle first.