How do I convert diametral pitch to module?

Module = 25.4 ÷ DP. So DP 8 is 25.4/8 = 3.175 mm and DP 20 is 25.4/20 = 1.27 mm. The conversion is exact because both describe the same tooth size in reciprocal units — but the results rarely land on a standard module, which is why inch and metric gears do not interchange.

What is the difference between diametral pitch and circular pitch?

Diametral pitch is teeth per inch of pitch diameter; circular pitch is the distance from tooth to tooth along the pitch circle. They are related by CP = π/DP, so DP 20 has a circular pitch of 0.1571 in. Circular pitch is what a tooth caliper actually measures.

What is a common gear pitch?

DP 20 (module 1.27) is the most common fine pitch for small machinery and instruments, and DP 8 (module 3.175) is common for general power transmission. In metric practice, module 1, 1.25, 1.5, 2, 2.5, 3 and 4 cover most general gearing.

How do I identify an unknown gear's pitch?

Count the teeth and measure the outside diameter. For an inch gear, DP = (teeth + 2) ÷ outside diameter in inches. For metric, module = outside diameter in mm ÷ (teeth + 2). The result will land on a standard value in one system and between standards in the other, which identifies the system.

Can I mesh a module 1.25 gear with a DP 20 gear?

No, although they are only 1.6% apart in tooth size and will physically mesh. The pitch mismatch means the teeth do not roll correctly, so they slide rather than roll, generating heat and rapid wear. Every near-equivalent pair between the two systems has the same problem — identify the system before ordering.

Gear Pitch Chart

Diametral pitch converted to circular pitch and module for 19 standard pitches, from coarse DP 1 to fine DP 120.

Data verified 2026-09-29 · based on ISO 54:1996

Quick Answer

Diametral pitch and module are reciprocally related: module = 25.4 ÷ DP. So DP 8 is module 3.175 mm and DP 20 is module 1.27 mm. Inch gears are specified by diametral pitch (teeth per inch of pitch diameter), metric gears by module (pitch diameter in mm per tooth).

Find a pitch

Diametral Pitch, Circular Pitch and Module

Diametral pitch, DP teeth/in^[1]	Circular pitch in^[2]	Module mm^[2]	Circular pitch mm^[2]	Pitch dia for 20 teeth mm^[2]
1 #	3.1416	25.400	79.796	508.000
1.5 #	2.0944	16.933	53.198	338.667
2 #	1.5708	12.700	39.898	254.000
2.5 #	1.2566	10.160	31.919	203.200
3 #	1.0472	8.467	26.599	169.333
4 #	0.7854	6.350	19.949	127.000
5 #	0.6283	5.080	15.959	101.600
6 #	0.5236	4.233	13.299	84.667
8 #	0.3927	3.175	9.975	63.500
10 #	0.3142	2.540	7.980	50.800
12 #	0.2618	2.117	6.650	42.333
16 #	0.1963	1.587	4.987	31.750
20 #	0.1571	1.270	3.990	25.400
24 #	0.1309	1.058	3.325	21.167
32 #	0.0982	0.794	2.494	15.875
48 #	0.0654	0.529	1.662	10.583
64 #	0.0491	0.397	1.247	7.938
96 #	0.0327	0.265	0.831	5.292
120 #	0.0262	0.212	0.665	4.233

Diametral pitch is teeth per inch of pitch diameter; module is pitch diameter in millimetres per tooth. They describe the same tooth size in reciprocal units, which is why a large DP is a small tooth and a large module is a large tooth — the two scales run in opposite directions, and confusing them is the usual error.

Circular pitch is the distance from one tooth to the next measured along the pitch circle: π ÷ DP in inches, or π × module in millimetres. It is the dimension a gear tooth caliper or a span measurement actually checks, which is why it appears alongside the other two. Addendum is 1 ÷ DP and whole depth is 2.157 ÷ DP for standard full-depth inch teeth; for metric gears addendum is 1 × module and whole depth is 2.25 × module.

Inch and Metric Gears Do Not Interchange

The two systems describe the same geometry with reciprocal units, and they do not produce matching tooth sizes at convenient numbers. DP 8 is module 3.175 mm — not module 3. DP 20 is module 1.27 mm — not module 1.25, which is a standard metric module.

The near misses are the problem. Module 1.25 mm and DP 20 are 1.6% apart, which is close enough that the gears will mesh and wrong enough that they will wear rapidly, run hot and fail early. Every metric module has a near-equivalent diametral pitch, and none of them is exact.

The practical rule: identify the system before ordering. Measure the outside diameter and count the teeth. For an inch gear, DP = (teeth + 2) ÷ outside diameter in inches. For a metric gear, module = outside diameter in mm ÷ (teeth + 2). The answer will land close to a standard value in one system and between values in the other, which identifies it.

Pitch Sets the Whole Tooth Proportions

Once the pitch is known, every other tooth dimension follows from it, which is the point of the system. For standard full-depth inch teeth: addendum is 1/DP, dedendum is 1.157/DP, whole depth is 2.157/DP, and tooth thickness at the pitch line is π/(2·DP).

For metric gears the same relationships use the module: addendum is 1 × module, dedendum is 1.25 × module, whole depth is 2.25 × module. The 0.25 difference between the two systems is the inch system's clearance allowance expressed differently — both are the standard proportions for their respective standards, and neither is a universal rule.

Stub-tooth and other modified proportions exist and change these ratios. Where a gear is being replaced, the proportions matter as much as the pitch, and the safest identification is a measurement over pins or a span measurement rather than a dimensional guess.

Frequently Asked Questions

How do I convert diametral pitch to module?: Module = 25.4 ÷ DP. So DP 8 is 25.4/8 = 3.175 mm and DP 20 is 25.4/20 = 1.27 mm. The conversion is exact because both describe the same tooth size in reciprocal units — but the results rarely land on a standard module, which is why inch and metric gears do not interchange.
What is the difference between diametral pitch and circular pitch?: Diametral pitch is teeth per inch of pitch diameter; circular pitch is the distance from tooth to tooth along the pitch circle. They are related by CP = π/DP, so DP 20 has a circular pitch of 0.1571 in. Circular pitch is what a tooth caliper actually measures.
What is a common gear pitch?: DP 20 (module 1.27) is the most common fine pitch for small machinery and instruments, and DP 8 (module 3.175) is common for general power transmission. In metric practice, module 1, 1.25, 1.5, 2, 2.5, 3 and 4 cover most general gearing.
How do I identify an unknown gear's pitch?: Count the teeth and measure the outside diameter. For an inch gear, DP = (teeth + 2) ÷ outside diameter in inches. For metric, module = outside diameter in mm ÷ (teeth + 2). The result will land on a standard value in one system and between standards in the other, which identifies the system.
Can I mesh a module 1.25 gear with a DP 20 gear?: No, although they are only 1.6% apart in tooth size and will physically mesh. The pitch mismatch means the teeth do not roll correctly, so they slide rather than roll, generating heat and rapid wear. Every near-equivalent pair between the two systems has the same problem — identify the system before ordering.

Value Sources

Each data column on this page is tied to the source it came from. The numbers in square brackets correspond to the table headers above.

#	Source	Type	Revision / method
[1]	ANSI/AGMA 201.02 — Tooth Proportions for Coarse-Pitch Involute Spur Gears	standard	ANSI/AGMA 201.02 (R2014)
[2]	Value computed from the standard's defining relationship	derived	Computed at build time from the defining formula stated on the page, then verified against every row and anchored by known standard values.
[3]	ISO 54 — Cylindrical gears for general engineering and for heavy engineering, modules	standard	ISO 54:1996

Data Sources

Standard	Revision	What it covers on this page
ISO 54 — Cylindrical gears, modules	ISO 54:1996	the standard metric module series
ANSI/AGMA 201.02 — Tooth Proportions for Coarse-Pitch Involute Spur Gears	ANSI/AGMA 201.02 (R2014)	the inch tooth proportions derived from diametral pitch
ANSI/AGMA 1003 — Tooth Proportions for Fine-Pitch Involute Spur and Helical Gears	ANSI/AGMA 1003-G01	the fine-pitch proportions

Cross-checked against:

Module recomputed from diametral pitch at build time as 25.4 ÷ DP for every row
Circular pitch recomputed as π ÷ DP and cross-checked in both unit systems
Six rows held as known-value checks covering the coarse, common and fine ends of the series
The 20-tooth pitch diameter column used as a second independent check on the module relationship

Derived values — the following values on this page are calculated, not taken directly from the standard:

Value	How it is derived
Circular pitch in mm and module	Circular pitch = π ÷ DP (inches) and π × module (millimetres); module = 25.4 ÷ DP. All recomputed at build time for every row and checked against the 25.4 relationship.

Only standard full-depth tooth proportions are implied. Stub teeth, profile-shifted gears, helical gears and modified addenda change the proportions without changing the pitch. Where a gear is being replaced, confirm the system and the proportions by measurement rather than by pitch alone.

Accuracy and use. The values on this page are compiled from the published standards and cross-checked sources listed above. Where values are derived, the derivation is stated. No warranty, express or implied, is made as to the accuracy or completeness of this information, and no liability is accepted for any loss or damage arising from its use. Engineering reference data is provided for guidance in preliminary work — before a value is used for design, fabrication or acceptance testing, verify it against the current revision of the governing standard and against your own inspection. The user assumes all risk and responsibility in connection with the use of this information.

Cite This Page

Every value on this page is traceable to the sources listed above. If you use the data in a document, paper or report, cite it as:

Plain text

Engineering Reference. "Gear Pitch Chart." https://refmanual.com/charts/gear-pitch/ (accessed 2026-09-29). Data from ISO 54 — Cylindrical gears, modules, ISO 54:1996.

BibTeX

@misc{gear-pitch,
  title        = {Gear Pitch Chart},
  author       = {{Engineering Reference}},
  howpublished = {\url{https://refmanual.com/charts/gear-pitch/}},
  note         = {Accessed: 2026-09-29},
  source       = {ISO 54 — Cylindrical gears, modules, ISO 54:1996}
}

RIS (EndNote, Zotero, Mendeley)

TY  - ELEC
TI  - Gear Pitch Chart
AU  - Engineering Reference
PB  - Engineering Reference
UR  - https://refmanual.com/charts/gear-pitch/
PY  - 2026
DA  - 2026-09-29
N1  - Source: ISO 54 — Cylindrical gears, modules, ISO 54:1996
ER  -

Each row in the tables above also has a permanent link — hover a row and use the # link to cite a single value rather than the whole page.