Module vs diametral pitch

Andrew Prestridge · 9 November 2026

Module and diametral pitch are two ways to write the same tooth size. Mix them up and the gear will not mesh with anything you intended.

Module, used on metric drawings and in ISO practice, is the pitch diameter divided by the tooth count, in millimetres: m = d / z. A module 2 gear with 30 teeth has a pitch diameter of 60 mm. Circular pitch, the arc from one tooth to the next at the pitch circle, is p = π m.

Diametral pitch, used on inch drawings and in AGMA practice, is the tooth count divided by the pitch diameter in inches: P_d = z / d. A 10-diametral-pitch gear with 40 teeth has a pitch diameter of 4 inches. Circular pitch is p = π / P_d inches. For a standard full-depth tooth the outside diameter is (z + 2) / P_d and the root diameter, with a 1.25 dedendum, is (z − 2.5) / P_d.

The conversion

m = 25.4 / P_d

when m is in millimetres and P_d is in teeth per inch. Module 2.54 is 10 DP. The conversion is exact. The mistakes are unit mistakes: feeding a module into a formula that expects diametral pitch, or forgetting that an inch blank’s outside diameter adds two teeth worth of addendum, not two millimetres.

The toggle on the designer keeps the same physical gear. Module mode reports millimetres. Diametral-pitch mode reports inches, using a working module of 1/P_d. The other system is printed under the input so a mixed drawing package is easy to check. The SVG is 1:1 in whichever unit you are in.

What has to match

For two external spur gears to run together:

• The same module, or the same diametral pitch. A module 2 gear will not mesh with a 12 DP gear.
• The same pressure angle. A 20° hob and a 14.5° hob cut different base circles on the same pitch diameter, so the base pitches differ. See the involute.
• Compatible addendum, so the contact ratio is real and each tip clears the mate’s root. A stub tooth and a full-depth tooth of the same module can be designed to mesh. They will not mesh if you assume both have the standard outside diameters.

Tooth count does not have to match. That difference is the ratio. Profile shift does not have to match either. It changes thickness and center distance. The pair still meshes if the base pitch is shared and the centers are the ones that shift calls for.

Preferred sizes, without the table

ISO 54 lists a preferred series of modules so hobs stay standard. AGMA practice clusters around common diametral pitches for the same reason. This tool will draw a 3.75 module gear — the geometry is valid — and a shop will ask why you did not pick a hob they already own. Stub-tooth systems also exist in inch practice. They are a different addendum, not a different involute. Change h_a* and h_f* if that is the tooth you mean, and say so on the drawing.