Gear Identification (Pitch from Teeth and OD)
Identify an unknown spur gear from a counted tooth count and a measured outside diameter.
Example
You enter
- Number of teeth N (counted) 40
- Measured outside diameter (in) 4.2
You get
- Diametral pitch Pd 10
- Pitch diameter 4 in
- Metric module equivalent 2.54 mm
Checked against published worked examples from: Boston Gear (catalog P-1930-BG) / Machinery's Handbook (ANSI B6.1).
Details, formula, and sources
ScopeBecause OD = (N+2)/Pd, the diametral pitch is Pd = (N+2)/OD, the pitch diameter is N/Pd, and the module is 25.4/Pd. Count 40 teeth on a 4.200 in gear -> Pd 10 teeth/in, PD 4.000 in, module 2.54 mm; the measured Pd snaps to the nearest standard so a caliper a hair off still identifies it. 20-degree full-depth involute; confirm against the drawing or a gear gauge.
Formula or tablePd = (N + 2)/OD; pitch dia = N/Pd; module = 25.4/Pd; snap Pd to the nearest standard value.
Source and editionSpur gear identification in the diametral-pitch system (20-degree full-depth involute; Machinery's Handbook / AGMA), the inverse of OD = (N+2)/Pd, by name.
Free accessThe diametral-pitch tooth proportions and the standard Pd series are standard published gear geometry (Machinery's Handbook).
What governsEstimate. AHJ and licensed professional govern.
API field namesteeth, outside_dia_in, pd, pitch_dia_in, module_mm
- Pitch from OD Pd = (N + 2)/OD for a standard full-depth involutegear geometry
- Standard-pitch snap the measured Pd is matched to the nearest standard diametral pitch for identificationMachinery's Handbook Pd series
- Tooth form assumes 20-deg full-depth proportions; a stub/nonstandard form shifts the relationscope of this tile