Module vs diametral pitch

Module and diametral pitch both describe how big a gear's teeth are. Module is the metric measure and diametral pitch the inch one, and they run in opposite directions: a bigger module means bigger teeth, while a bigger diametral pitch means smaller ones.

Definitions

Module m is the pitch diameter in millimetres divided by the number of teeth: m = d / z.

Diametral pitch P is the number of teeth per inch of pitch diameter: P = z / d, with d in inches.

Since one inch is 25.4 mm, they convert directly:

m = 25.4 / P · P = 25.4 / m

Converter

Module (mm)

Diametral pitch (1/in)

Circular pitch: 3.1416 mm · 0.12368 in
Addendum: 1 mm
Dedendum: 1.25 mm
Whole depth: 2.25 mm

Diametral pitch to module

Diametral pitch	Module (mm)	Nearest standard module
64	0.3969	0.4
48	0.5292	0.5
32	0.7938	0.8
24	1.0583	1
20	1.2700	1.25
16	1.5875	1.5
12	2.1167	2
10	2.5400	2.5
8	3.1750	3
6	4.2333	4
5	5.0800	5
4	6.3500	6

Module to diametral pitch

Module (mm)	Diametral pitch	Circular pitch (mm)
0.5	50.800	1.571
0.8	31.750	2.513
1	25.400	3.142
1.25	20.320	3.927
1.5	16.933	4.712
2	12.700	6.283
2.5	10.160	7.854
3	8.467	9.425
4	6.350	12.566
5	5.080	15.708
6	4.233	18.850
8	3.175	25.133
10	2.540	31.416

Close is not the same. A 20 DP gear has a module of 1.27 mm, about 1.6% larger than a 1.25 module gear. The two will not run together: the spacing error builds with every tooth, so they bind or run rough. Mating gears need the same module (or diametral pitch) and the same pressure angle.

How do you calculate tooth dimensions from the module?

For standard full-depth teeth, every dimension scales with the module. In inch units, replace m with 1 / P.

Dimension	Full depth	Stub (20°)
Pitch diameter	z · m	z · m
Addendum	1.0 · m	0.8 · m
Dedendum	1.25 · m	1.0 · m
Whole depth	2.25 · m	1.8 · m
Outside diameter	(z + 2) · m	(z + 1.6) · m
Circular pitch	π · m	π · m

An internal gear such as a planetary ring has its teeth pointing inward, so its tip diameter is (z − 2) · m and its root diameter is larger than its pitch diameter.

Which pressure angle should you use?

Pressure angle is the other number two gears must share. 20° is the modern standard for both metric and inch gears. 14.5° shows up in older inch designs and replacement parts, and 25° is used where tooth strength matters more than quiet running.

GearStudio works in either system: design in diametral pitch or module, and STEP, STL and DXF files always come out in millimetres.

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