Gear-Tooth Chordal Thickness (Caliper)
The gear-tooth caliper settings: chordal tooth thickness tc = (N/Pd) sin(90/N deg) read across the tooth.
Example
You enter
- Diametral pitch Pd (teeth/in) 10
- Number of teeth N 40
You get
- Chordal tooth thickness (caliper reading) 0.1570 in
- Chordal addendum (caliper tongue depth) 0.1015 in
Details, formula, and sources
The gear-tooth caliper settings: chordal tooth thickness tc = (N/Pd) sin(90/N deg) read across the tooth, and chordal addendum ac = 1/Pd + (N/2Pd)(1 - cos(90/N deg)) set as the tongue depth. Pd 10, N 40 -> tc 0.1570 in, ac 0.1015 in (the arc thickness pi/2Pd is 0.15708). Standard 20-degree full-depth involute, no profile shift or backlash allowance. A shop inspection aid; the gear drawing and AGMA govern.
chordal tooth thickness tc = (N/Pd) x sin(90/N deg); chordal addendum ac = 1/Pd + (N/(2Pd)) x (1 - cos(90/N deg)); arc tooth thickness = pi/(2Pd).
Gear-tooth-caliper (vernier) inspection dimensions for a 20-degree full-depth involute spur gear, the standard Machinery's Handbook / AGMA method, by name.
The chordal-thickness and chordal-addendum relations are standard published gear geometry (Machinery's Handbook).
Estimate. AHJ and licensed professional govern.
Field names used by the API: diametral_pitch, teeth, chordal_thickness_in, chordal_addendum_in
- Chordal thickness tc = (N/Pd) sin(90/N deg), the chord of the arc thickness pi/(2Pd)Machinery's Handbook gear-tooth caliper
- Chordal addendum ac = 1/Pd + (N/(2Pd))(1 - cos(90/N deg)), the caliper tongue depthMachinery's Handbook
- Standard tooth 20-deg full-depth, no profile shift or backlash allowance; subtract the drawing tooth-thinning for a working gearscope of this tile