Diametral Pitch Calculator (gear P, module, addendum, outside diameter)

Understanding the diametral pitch calculator — concept and principle

Diametral pitch is the inch-system measure of gear tooth size: the number of teeth per inch of pitch diameter. This calculator finds it from the tooth count and pitch diameter and gives the metric module, circular pitch and the standard full-depth tooth dimensions.

Diametral pitch counts teeth per inch of pitch diameter; P = 12 then sets every tooth dimension.

How it is calculated

Diametral pitch P = N ÷ D (teeth per inch).
Module m = 25.4 ÷ P (mm); circular pitch p = π ÷ P.
Addendum = 1 ÷ P; dedendum = 1.25 ÷ P; whole depth = 2.25 ÷ P.
Outside diameter = (N + 2) ÷ P; root diameter = (N − 2.5) ÷ P.
Base circle diameter = D cos φ; circular tooth thickness = π ÷ (2P).

The principle

The pitch circle is the imaginary circle on which two meshing gears roll without slipping. Teeth must be spaced identically on both gears, so meshing gears share the same diametral pitch (or module) and pressure angle. A larger P means more, smaller teeth on the same diameter. Tooth involute profiles are generated from the base circle, whose size depends on the pressure angle.

Worked example

Default inputs: 24 teeth, pitch diameter 2 in, pressure angle 20°.

P = 24 ÷ 2 = 12 teeth per inch; module = 25.4 ÷ 12 ≈ 2.1167 mm.
Circular pitch = π ÷ 12 ≈ 0.2618 in; tooth thickness ≈ 0.1309 in.
Addendum = 0.0833 in; dedendum = 0.1042 in; whole depth = 0.1875 in.
Outside diameter = 26 ÷ 12 ≈ 2.1667 in; root diameter = 21.5 ÷ 12 ≈ 1.7917 in.
Base circle = 2 × cos 20° ≈ 1.8794 in.

Each point is the calculator re-run with only “Pitch diameter D (in)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Pitch diameter D (in)	Diametral pitch P (teeth per inch)
0.5	48
1	24
1.5	16
2	12
2.5	9.6
3	8
4	6

How to read the result

Use the outside diameter for the gear blank and the root diameter to check clearance. To mesh with this gear, a mating gear must also be 12 DP with a 20° pressure angle; its pitch diameter is its tooth count ÷ 12, and the centre distance is the sum of pitch radii.

Common mistakes

Mixing diametral pitch and module systems.
Mixing gears with different pressure angles.
Using the outside diameter as the pitch diameter.
Applying full-depth proportions to stub or special tooth forms.

Keep in mind: Gear design also involves strength, materials, tolerances and lubrication. Follow AGMA or ISO standards and qualified engineering advice.

Frequently asked questions

What is diametral pitch?

The number of teeth per inch of pitch diameter, P = N ÷ D.

How do I convert diametral pitch to module?

Module (mm) = 25.4 ÷ P.

Can a 12 DP gear mesh with a 2 mm module gear?

Not properly; 12 DP equals 2.1167 mm module, so the teeth would not match.

Sources: ANSI/AGMA 1012, Gear Nomenclature, Definitions of Terms with Symbols · Machinery's Handbook, Industrial Press (gearing)

Checked 9 Nov 2026. Gear relations P = N/D, m = 25.4/P, p = π/P and full-depth involute proportions (addendum 1/P, dedendum 1.25/P, base circle D cos φ): standard formula.

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