gEAR eQUATIONS

Gear Formulae

  Spur Gear

Calculate When Defined Formula
Diametral Pitch (P) Pitch Diameter (D) and the Number of Teeth (N) P = N / PD
Diametral Pitch (P) Circular Pitch (p) P = 3.1416/p
Diametral Pitch (P) Outside Diameter (OD) and the Number of Teeth (N) P = (N+2)/OD
Pitch Diameter (PD) . Number of teeth (N) and the Diametral Pitch (P) PD = N/DP
Outside Diameter (OD) Number of teeth (N) and the Diametral Pitch (P) OD = (N+2)/DP
Number of Teeth (N). Pitch Diameter (D) and the Diametral Pitch (P) N = PD * DP
Addendum (a) . Diametral Pitch (P) a = 1/DP
Dedendum (d) Whole Depth and Addendum d = hw – a
Tooth Thickness (t) at the Pitch Diameter Diametral Pitch (P) t = 1.5708/P
Working Depth (WD). Addendum WD = 2(a)
Center Distance (C) Normal Diametral Pitch (P) and the Number of Teeth in Both Gears C = (N1+N2)/2P
Center Distance (C) Pitch Diameters of both gears C = (PD1+PD2)/2
Circular Pitch (p) Diametral Pitch (P) p = 3.1416 / P
Whole Depth (hw) for 20 Pitch & finer . Diametral Pitch (P) hw = 2.2/P + .002
Whole Depth (hw) for Coarser than 20 Pitch . Diametral Pitch (P) hw = 2.157/P

Helical Gear

Calculate When Defined Formula
Normal D.P. (Pn) Tranverse D.P.(P) and the Helix Angle (A) Pn=P / cos A
Normal D.P. (Pn) Number of teeth (N) and the Helix Angle (A) Pn= N / (D X cos A)
Pitch Diameter (D) Number of teeth (N), the Normal Diametral Pitch and the Helix Angle (A) D = N / (Pn X cos A)
Outside Diameter (OD) Pitch Diameter (D) and the Addendum (a) OD = D + (2 X a)
Outside Diameter (OD) Normal Diametral Pitch (P) and the Pitch Diameter (D) OD = D + 2/Pn
Helix Angle (A) for Parallel Shaft Drive Number of Teeth (N), Pitch Diameter (D) and the Diametral Pitch (P) Cos A = N / (Pn X D)
Addendum (a) Normal Diametral Pitch (Pn) a = 1 / Pn
Lead (L) Pitch Diameter (D) and Pitch Helix Angle L = (pi*D) / Tan

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