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Diametral Pitch Gear Calculator
Diametral pitch (P) is the number of teeth per inch of pitch diameter — the standard imperial (AGMA) gear tooth size. Compute P from tooth count & pitch diameter, find an unknown diameter or tooth count, convert P ↔ metric module, plus automatic circular pitch, addendum, dedendum, and whole depth.
1Diametral pitch from N & D
Formula: P = N ÷ D — N is an integer, D in inches.
P = 5 teeth/in
2Pitch diameter from N & P
Formula: D = N ÷ P — result in inches.
D = 4 inches
3Tooth count from P & D
Formula: N = P × D — N must be an integer; non-integer results are flagged as inconsistent.
N = 16 teeth
4P ↔ metric module conversion + circular pitch
m = 25.4 ÷ P (m in mm) and P = 25.4 ÷ m. Circular pitch p = π ÷ P.
⚑Reference table: standard diametral pitch
Commonly published values (reference only — the calculator does not reject non-standard values).
| P | Module (mm) | Circular pitch (in) | Circular pitch (mm) | Class |
|---|
How the calculation works
- Diametral pitch
P = N ÷ D— N = tooth count (integer), D = pitch diameter (inches). Example: 20 teeth, D = 4 inches → P = 5. - Pitch diameter
D = N ÷ Pand tooth countN = P × D(N must be an integer). - Metric module
m = 25.4 ÷ Pmm — example: P = 5 → m = 5.08 mm. ConverselyP = 25.4 ÷ m. - Circular pitch
p = π ÷ P— example: P = 5 → p ≈ 0.6283 inches (≈ 15.9593 mm). - Full-depth tooth proportions: addendum
1/P(0.2 in), dedendum1.25/P(0.25 in), whole depth2.25/P(0.45 in), clearance0.25/P(0.05 in) for P = 5. - Outside diameter
Do = (N+2) ÷ P(4.4 in) and root diameterDr = (N−2.5) ÷ P(3.5 in) for N = 20, P = 5.
All example figures above were recomputed from the formulas (not from memory) and match the calculator engine.
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Diametral pitch FAQ
What is diametral pitch?
Diametral pitch (P) is the gear tooth size in the imperial system: number of teeth per inch of pitch diameter. Its units are "teeth per inch". A large P means small/fine teeth (e.g. P=48); a small P means large/coarse teeth (e.g. P=2). It is the American (AGMA) standard way of specifying tooth size, the imperial counterpart of the metric module.
How do you calculate diametral pitch?
The formula is P = N ÷ D, where N = tooth count (must be an integer) and D = pitch diameter in inches. Example: a 20-tooth gear with a 4-inch pitch diameter → P = 20 ÷ 4 = 5. The calculator above computes it automatically along with all derived geometry.
How do you convert diametral pitch to metric module (and back)?
The relationship is m = 25.4 ÷ P with m in millimeters, or conversely P = 25.4 ÷ m. Example: P = 5 → m = 25.4 ÷ 5 = 5.08 mm. Conversely, a 2 mm module → P = 25.4 ÷ 2 = 12.7. Mode 4 of the calculator above converts both ways while also showing circular pitch.
What is circular pitch and how is it calculated?
Circular pitch (p) is the tooth-to-tooth distance measured along the pitch circle arc, in inches (or mm). The formula is p = π ÷ P. Example: P = 5 → p = π ÷ 5 ≈ 0.6283 inches (≈ 15.9593 mm). The practical relationship: p (mm) = π × m, so from a 5.08 mm module you directly get p ≈ 15.9593 mm.
What are addendum, dedendum, and whole depth?
These are the standard full-depth tooth proportions (in inches), all derived from P: addendum = 1 ÷ P (tooth height above the pitch circle), dedendum = 1.25 ÷ P (depth below the pitch circle), whole depth = 2.25 ÷ P (total tooth height), and clearance = 0.25 ÷ P. Example with P = 5: addendum 0.2 in, dedendum 0.25 in, whole depth 0.45 in, clearance 0.05 in.
How do you find pitch diameter from tooth count and diametral pitch?
Invert the formula: D = N ÷ P (result in inches). Example: 20 teeth with P = 5 → D = 20 ÷ 5 = 4 inches. From this the calculator also derives outside diameter Do = (N+2) ÷ P and root diameter Dr = (N−2.5) ÷ P — for this example Do = 4.4 inches and Dr = 3.5 inches.
How do you find tooth count from diametral pitch and pitch diameter?
Use N = P × D. Because tooth count must be an integer, a non-integer result means the P/D pair is physically inconsistent. Valid example: P = 8, D = 2 inches → N = 16 exactly. Invalid example: P = 5, D = 4.13 inches → 20.65 → rounds to 21 but the calculator shows an inconsistency warning.
What are the standard diametral pitch sizes?
Commonly published sizes: coarse teeth 0.5–2 (heavy loads, industrial machinery), general 3–12 (general transmissions), and fine 16–120 (precision instruments; 48 and 64 are popular in hobbies like slot cars). This list is reference only — the calculator does not reject non-standard values, it only shows the nearest standard.
When should you use diametral pitch vs module?
Use diametral pitch for components, engineering drawings, and American/AGMA-style catalogs (inch units). Use metric module for ISO/DIN standards and metric manufacturing (mm units). Both describe the same tooth size and convert into each other with 25.4 — what matters is that mating gear pairs must use the same tooth size.
Is diametral pitch the same as "pitch" on bolt threads or LEDs?
No — the word "pitch" is used for different things. Thread pitch is the distance between bolt threads (e.g. M10×1.5 means 1.5 mm per thread; see thread pitch identifier), pixel pitch is the distance between LEDs (e.g. P2.6), and propeller pitch is the distance a propeller travels per revolution. Diametral pitch is specifically for gear tooth size: P = N ÷ D. For 48 vs 64 toy gear pitch, see slot car gear ratio lab.
Is this diametral pitch calculator free?
Yes. Free, runs offline, and all calculations happen in your browser — the tooth and diameter data you enter is never sent to any server.
Free tool by NRTechStudio