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Bevel Gear Calculator 

This calculator determines bevel gear and pinion parameters. It assumes 90 degree angle between the gears. The smallest gear is referred to as a pinion and the larger gear is referred to as gear.   Select the diametral pitch with units of teeth per distance, and then select the number of teeth for each gear, and the other parameters are computed. 

Parameter Pinion Gear
Diametral Pitch (P)
Teeth (N)
Pitch Diameter (D)
Whole Depth (Ht)
Addendum (a)
Dedendum (b)
Clearance (c)
Circular Tooth Thickness (T)
Pitch Angle (deg)
Pitch Cone Radius (Rc)
Face wideth (F)
Outside Diameter
Back Cone Radius
Virtual Number of Teeth

Boston Gear has an excellent document on the formulas and geometry at this link.


Pitch Diameter: D= N/P

Diametral Pitch: P= N/D

Number of Teeth: N

Whole Depth:  Ht= 2.188/P+.002

Addendum: a= 1/P

Dedendum : b= Ht-a

Clearance: c= Ht-2*a

Circular Tooth Thickness: T= PI/(2*P)

Pitch Angle:  Lp = atan(Np/Ng),  and Lg= atan(Ng/Np)

Pitch Code Radius:  Rcp= D/(2*sin(Lp)), and Rcg= D/(2*sin(Lg))

Face Width:  F= min(C/3, 8/P)

Outside Diameter:  Dop= Dp+2*a*cos(Lp),  and Dog= Dg+2*a*cos(Lg)

Back Cone Angle:  = 90-L;

Back Cone Radius:  Rbp= Dp/cos(Lp), and Rbg= Dg/cos(Lg)

Virtual Number of Teeth:  Vp= N/cos(Lp),  and Vg= N/cos(Lg)

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