Involute Gear Design Equations and Calculator

Gear Design and Engineering

The following are equations and engineering design calculator to determine critical design dimensions and features for an involute gear.


  • Number of Teeth: Between 6 and 50)
  • Diametral Pitch Teeth/in. Stndard sizes: 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 24, 32, 40, 48
  • Pressure Angle: Typically 30, 37.5, or 45 degrees

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Spline SPur Gear and Formulas

Involute Spline Design Calculator        
Input Design Data
Number of Teeth Nt
Diametral Pitch P teeth/in.
Applied Torque (in-lb.) T in-lb.
Internal diameter (if hollow) di in.  
Pressure angle f degrees
Dimensional Relations
Circular pitch p in./tooth
Pitch diameter d in.
Addendum a in.
Base circle diameter db in.  
Circular tooth thickness t in.
Diametral Pitch 1 thru 12 16 thru 48  
doi (Major dia. internal) in.  
dre (Minor dia. External) in.  
b1i (Dedendum internal) in.  
b1e (Dedendum ext.) in.  
Effective Spline Length Le in.  
Shear Stress t psi
*Shear stress and spline length are calculated based on the assumption that only 25% of the teeth make contact at any given moment.



Deutschman, Michels, Wilson. Machine Design: Theory and Practice. Macmillan, 1975. Pp. 374-376.

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