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 |