Gears · Browser-based conversion
Gear Module / Diametral Pitch Converter
Convert gear module and diametral pitch in either direction, with equivalent metric and imperial circular pitch values, formulas, and engineering scope notes.
Reference calculator #002
Select a pitch system
Inputs stay in your browser. Values are normalized to canonical units before calculation.
Calculated output
Results
- Module, m
- Diametral pitch, Pᵈ
- Circular pitch, p (metric)
- Circular pitch, p (imperial)
Valid pitch conversion
- Module is expressed in millimetres per tooth and diametral pitch in teeth per inch of pitch diameter.
- The conversion uses one consistent pitch basis, as for a spur gear or a specified transverse plane.
- For helical gears, normal and transverse pitch systems must not be interchanged without accounting for helix angle.
- Pitch compatibility alone does not verify pressure angle, tooth form, profile shift, tolerances, or load capacity.
Calculation engine: gear-pitch/1.0.0
Module and diametral pitch formulas
The constant 25.4 converts millimetres to inches. Module and diametral pitch describe the same basic tooth-size relationship in opposite directions.
| Symbol | Meaning | Unit |
|---|---|---|
m |
Module: pitch diameter divided by tooth count | mm/tooth |
Pᵈ |
Diametral pitch: tooth count divided by pitch diameter | teeth/in |
p |
Circular pitch measured along the reference circle | mm or in |
Circular pitch follows p = πm in the module system and p = π / Pᵈ in the diametral-pitch system.
Worked conversion examples
For a module m = 2 mm/tooth:
Pᵈ = 25.4 / 2 = 12.7 teeth/in.- Metric circular pitch:
p = π × 2 = 6.283185 mm. - Imperial circular pitch:
p = π / 12.7 = 0.247369 in.
For Pᵈ = 20 teeth/in:
m = 25.4 / 20 = 1.27 mm/tooth.- Metric circular pitch:
p = π × 1.27 = 3.989823 mm. - Imperial circular pitch:
p = π / 20 = 0.157080 in.
The calculation engine retains full precision. Rounding is applied only when results are displayed.
How to use the converter
Choose the pitch system shown on the drawing, catalogue, or gear data, then enter its value. Switching the input type converts the current value so the physical tooth size stays unchanged. The share link stores either m or dp in the query string while the page keeps one canonical URL.
Use the primary result for the equivalent pitch designation. The secondary results expose both conventions and their metric and imperial circular pitches for cross-checking.
After a valid conversion, the next-calculation link transfers the canonical module to the Gear Center Distance Calculator. It starts with an editable 20/40-tooth example and does not transfer or infer tooth counts from the pitch conversion.
Engineering scope and compatibility
This is a geometric pitch conversion, not a complete gear interchangeability check. It assumes that both values describe the same pitch basis, such as a spur gear or one explicitly identified plane of a helical gear.
Before selecting or pairing gears, also verify:
- pressure angle, tooth form, addendum system, and profile shift;
- normal versus transverse pitch for helical gears and the associated helix angle;
- tooth thickness, backlash, quality grade, tolerances, and center distance;
- face width, materials, heat treatment, lubrication, speed, load, and life requirements.
An equivalent module or diametral pitch does not by itself prove that two gears will mesh or meet the application duty.
Frequently asked questions
What is the formula for converting module to diametral pitch?
Divide 25.4 by the module in millimetres: Pᵈ = 25.4 / m. To convert in the other direction, divide 25.4 by diametral pitch: m = 25.4 / Pᵈ.
What diametral pitch is module 2?
Module 2 equals 12.7 diametral pitch because 25.4 divided by 2 is 12.7 teeth per inch of pitch diameter.
What module is 20 diametral pitch?
20 DP equals module 1.27 because 25.4 divided by 20 is 1.27 millimetres per tooth.
Are module and diametral pitch the same measurement?
They describe tooth size using reciprocal conventions. Module is pitch diameter in millimetres divided by tooth count; diametral pitch is tooth count divided by pitch diameter in inches.
Can I use this conversion for helical gears?
Only when both values refer to the same pitch plane. Normal and transverse module or diametral pitch are different for a helical gear and require the helix angle for conversion between planes.
References and review status
Reviewed . References provide independent formula checks and context; they do not imply endorsement.
- KHK Gears — Comparison of Gear Pitch — Published comparison table used to cross-check module, diametral pitch, and circular pitch relationships and known-answer values.
- KHK Gears — Calculation of Gear Dimensions — Public technical reference for module-system and diametral-pitch terminology and gear-dimension context.