What is diametral pitch?

Diametral pitch is the number of teeth per inch of pitch diameter: DP = z ÷ d. A 60-tooth, 20 DP gear has a 3.000 in pitch diameter; larger DP means smaller teeth.

Module is pitch diameter in millimeters per tooth: m = d ÷ z. A 24-tooth module 2 gear is 48 mm on the pitch circle; larger module means larger teeth.

How do you convert diametral pitch to module?

Divide 25.4 by the diametral pitch. 20 DP is 1.27 mm, 10 DP is 2.54 mm, and 32 DP is 0.794 mm.

Can a module gear mesh with a DP gear?

Only if the pitch and pressure angle are actually equal, which standard sizes almost never are. Module 1.25 (3.927 mm pitch) and 20 DP (3.990 mm) differ by about 1.6%, enough to bind or run rough.

What is circular pitch?

Circular pitch is the arc distance between neighboring teeth on the pitch circle: p = π·m. Module 2 has a 6.283 mm circular pitch, and 20 DP has 0.1571 in.

Which modules are standard?

ISO 54 lists preferred modules of 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, and 10 mm and larger, with 0.5 and 0.8 common for fine gears. Pick one of these unless you are matching an existing gear.

Power transmission calculator

Module to Diametral Pitch Converter & Chart

Convert gear module to diametral pitch and back, with charts of standard metric modules, common DP sizes, and circular pitch in mm and inches.

Design a laser-cut spur gear

Set the pitch, teeth, and pressure angle, add a mating gear, then choose a bore and plate.

Units

Presets

Pitch system

Module

Pressure angle

Teeth

Profile shiftx · module

Backlash per gearTooth thinning

Mating gear

Preview the mesh, center distance, ratio, and contact ratio.

Mating gear teeth

Mating profile shiftx · module

Hub, holes, and plate

Bore

Bore diameter

Mounting holes

Lightening holes

Fabworks plate material

Plate thicknessMin. feature 0.050 in · 1.27 mm

Gear dimensions

Pitch diameter: 48 mm
Outside diameter: 52 mm
Root diameter: 43 mm
Base circle diameter: 45.105 mm
Circular pitch: 6.283 mm
Tooth thickness at pitch: 3.092 mm
Diametral pitch: 12.7 DP
Mating pitch diameter: 96 mm
Mating outside diameter: 100 mm
Center distance: 72 mm
Gear ratio: 2 : 1
Contact ratio: 1.675

Mesh preview

Involute flanks and trochoid root fillets are generated by rolling a basic rack through each tooth space, the way a hob cuts a gear. Dashed circles are pitch circles.

True generated tooth form

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Spur gear
⌀ 51.7 mm
Mating gear
⌀ 99.9 mm

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Quick answer

How this module and dp chart calculator works

Module and diametral pitch are reciprocal measures of tooth size: m = 25.4 ÷ DP and DP = 25.4 ÷ m, so 20 DP is module 1.27 and module 2 is 12.7 DP. Module is millimeters of pitch diameter per tooth; diametral pitch is teeth per inch of pitch diameter. The charts list standard modules and common DP sizes with circular pitch, and the generator accepts either.

How to use the calculator

1To convert DP to module, divide 25.4 by the diametral pitch.
2To convert module to DP, divide 25.4 by the module.
3Find circular pitch, the tooth spacing on the pitch circle, as π·m or π ÷ DP.
4Enter either value in the spur gear generator to draw the gear.

Key formulas

Module and DP chart formulas

DP to module: m = 25.4 ÷ DP; m in millimeters, DP in teeth per inch of pitch diameter.
Module to DP: DP = 25.4 ÷ m
Circular pitch: p = π·m (mm) = π ÷ DP (in); Distance between teeth along the pitch circle.
Circular pitch to module: m = p ÷ π; For “CP” gears specified by circular pitch.
Pitch diameter: d = m·z = z ÷ DP

Worked example

Converting 20 DP to module

Inputs: An FRC gear specified as 20 DP.
Result: m = 25.4 ÷ 20 = 1.27 mm; circular pitch 0.1571 in (3.990 mm).

Module 1.25 is close but not equal, so a 20 DP gear and a module 1.25 gear will not mesh properly.

Common questions

What to know before using the result

What is diametral pitch?: Diametral pitch is the number of teeth per inch of pitch diameter: DP = z ÷ d. A 60-tooth, 20 DP gear has a 3.000 in pitch diameter; larger DP means smaller teeth.
What is gear module?: Module is pitch diameter in millimeters per tooth: m = d ÷ z. A 24-tooth module 2 gear is 48 mm on the pitch circle; larger module means larger teeth.
How do you convert diametral pitch to module?: Divide 25.4 by the diametral pitch. 20 DP is 1.27 mm, 10 DP is 2.54 mm, and 32 DP is 0.794 mm.
Can a module gear mesh with a DP gear?: Only if the pitch and pressure angle are actually equal, which standard sizes almost never are. Module 1.25 (3.927 mm pitch) and 20 DP (3.990 mm) differ by about 1.6%, enough to bind or run rough.
What is circular pitch?: Circular pitch is the arc distance between neighboring teeth on the pitch circle: p = π·m. Module 2 has a 6.283 mm circular pitch, and 20 DP has 0.1571 in.
Which modules are standard?: ISO 54 lists preferred modules of 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, and 10 mm and larger, with 0.5 and 0.8 common for fine gears. Pick one of these unless you are matching an existing gear.

Reference

Standard metric modules with diametral pitch equivalents

Modules from 1 mm up follow ISO 54 series I; 0.5 and 0.8 are common fine modules. Module 10 equals 2.54 DP with a 31.416 mm circular pitch.

Module m (mm)	Equivalent DP (1/in)	Circular pitch (mm)	Circular pitch (in)	Whole depth 2.25m (mm)
0.5	50.80	1.571	0.0618	1.125
0.8	31.75	2.513	0.0989	1.800
1	25.40	3.142	0.1237	2.250
1.25	20.32	3.927	0.1546	2.813
1.5	16.93	4.712	0.1855	3.375
2	12.70	6.283	0.2474	4.500
2.5	10.16	7.854	0.3092	5.625
3	8.47	9.425	0.3711	6.750
4	6.35	12.566	0.4947	9.000
5	5.08	15.708	0.6184	11.250
6	4.23	18.850	0.7421	13.500
8	3.17	25.133	0.9895	18.000

Common diametral pitches with module equivalents

DP gears and module gears with close but unequal pitch do not mesh correctly. The nearest module is listed only to help pick a family.

Diametral pitch	Equivalent module (mm)	Circular pitch (in)	Circular pitch (mm)	Nearest standard module
48	0.5292	0.0654	1.662	0.5
32	0.7937	0.0982	2.494	0.8
24	1.0583	0.1309	3.325	1
20	1.2700	0.1571	3.990	1.25
16	1.5875	0.1963	4.987	1.5
12	2.1167	0.2618	6.650	2
10	2.5400	0.3142	7.980	2.5
8	3.1750	0.3927	9.975	3
6	4.2333	0.5236	13.299	4

Formula

d = m·z · dₐ = m(z + 2) · d_f = m(z − 2.5) · d_b = d·cos α

Pitch diameter d is module m times tooth count z, with diametral pitch converted by m = 25.4 ÷ DP. Flanks are true involutes of the base circle d·cos α, and the root is the trochoid traced by an ISO 53 rack cutter.

Engineering references

Assumptions and limits

Default tooth proportions follow ISO 53 profile A: addendum 1.0m, dedendum 1.25m, root fillet 0.38m.
Center distance and contact ratio assume rigid, correctly aligned shafts at the working center distance.
Backlash is applied by thinning each gear tooth by the entered allowance at the pitch circle.
Exported flanks are arc approximations within 0.005 mm of the generated tooth form.
Laser-cut gears suit low to moderate speed and load; critical drives need engineering review.

Educational estimate

Use this result for learning and early design exploration. Verify safety-critical or production decisions with the governing standard, material data, real tooling, and a qualified engineer.

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