Spur Gear Tooth Geometry (Diametral Pitch)
The blank and cutter dimensions of a spur gear, from its tooth count and pitch.
Example
You enter
- Diametral pitch Pd (teeth/in) 10
- Number of teeth N 40
- Mating gear teeth (optional) 20
You get
- Pitch dia (in) 4
- Outside dia (in) 4.2
- Root diameter 3.75 in
- Center distance (with mate) 3
Details, formula, and sources
From the diametral pitch Pd: pitch dia = N/Pd, OD = (N+2)/Pd, addendum 1/Pd, dedendum 1.25/Pd, whole depth 2.25/Pd, root (N-2.5)/Pd, center distance (N1+N2)/(2Pd). Pd 10, N 40, mate 20 -> PD 4.000, OD 4.200, center 3.000 in; a finer Pd 20 halves every dimension. A shop aid; the gear drawing and AGMA govern.
PD = N/Pd; OD = (N+2)/Pd; addendum = 1/Pd; dedendum = 1.25/Pd; whole depth = 2.25/Pd; root = (N-2.5)/Pd; center = (N1+N2)/(2 Pd).
Spur gear tooth proportions in the diametral-pitch system (20-degree full-depth involute; Machinery's Handbook / AGMA), by name.
The diametral-pitch tooth proportions are standard published gear geometry (Machinery's Handbook).
Estimate. AHJ and licensed professional govern.
Field names used by the API: diametral_pitch, teeth, mating_teeth, pitch_dia_in, outside_dia_in, root_dia_in, center_dist_in
- Diametral pitch Pd = teeth per inch of pitch diameter; must match to meshgear geometry
- Full-depth proportions addendum 1/Pd, dedendum 1.25/Pd, whole depth 2.25/Pd20-deg full-depth involute
- Geometry only no tooth-strength, backlash, or undercut checkscope of this tile