Pitch Diameter Calculator

teeth
teeth/in
in/mm
Construction

Calculate the pitch diameter of gears (by tooth count and diametral pitch) or threaded fasteners.

Formula

Gear: PD = N / DP; UN thread: PD = OD − 0.649519/TPI; Metric: PD = OD − 0.649519×pitch
  • Gear: N = number of teeth; DP = diametral pitch (teeth per inch of pitch diameter).
  • OD = (N+2)/DP; Root diameter ≈ (N−2.5)/DP.
  • UN thread: 1/2-13 → PD = 0.5 − 0.649519/13 = 0.4500 in.

24-tooth spur gear, DP=8

Inputs
  • Application: gear
  • Number of Teeth (N): 24 teeth
  • Diametral Pitch (DP): 8 teeth/in
  • Major Diameter (OD): 0.5 in/mm
  • TPI (UN) or Pitch in mm (M): 13

PD = 24/8 = 3.000 in. OD = 26/8 = 3.250 in.

Frequently asked questions

What is diametral pitch?
Diametral pitch (DP) is the number of teeth per inch of pitch diameter. Higher DP = finer (smaller) teeth. DP = N / PD. Standard gear pitches: 4, 6, 8, 10, 12, 16, 20, 24, 32, 48, 64.