Sources and scope for this page: ISO 54:1996, covering the standard metric module series; and ANSI/AGMA 201.02 (R2014), covering the inch tooth proportions derived from diametral pitch (one more source is tabulated below). No independent source check is recorded for this page: the content rests on the sources listed and on the working shown on the page. Full sources, values and limits on this page.
Page last changed 2026-10-19 · based on ISO 54:1996
Quick Answer
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.
Related
Value Sources
References and calculation methods used for this page are listed below. Numbered markers connect table columns where present. A reference listing does not itself establish that every value has been independently checked.
| # | Source | Type | Revision / method |
|---|---|---|---|
| [1] | ANSI/AGMA 201.02 — Tooth Proportions for Coarse-Pitch Involute Spur Gears | reference | 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 | reference | 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 |
Verification scope
No page-specific independent source review is recorded here. The listed references and formulas explain the basis of the compilation; automated consistency checks do not verify the original sources or establish product conformity.
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.
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