Involute Gear Design Equations and Calculator

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

Notes:

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

Click on the image below to enlarge

Involute Spline Design Calculator
Input Design Data
Number of Teeth	N_t
Diametral Pitch	P		teeth/in.
Applied Torque (in-lb.)	T		in-lb.
Internal diameter (if hollow)	d_i		in.
Pressure angle	f		degrees

Results
Dimensional Relations
Circular pitch	p		in./tooth
Pitch diameter	d		in.
Addendum	a		in.
Base circle diameter	d_b		in.
Circular tooth thickness	t		in.

Diametral Pitch	1 thru 12	16 thru 48
d_oi (Major dia. internal)			in.
d_re (Minor dia. External)			in.
b_1i (Dedendum internal)			in.
b_1e (Dedendum ext.)			in.


Effective Spline Length	L_e		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.

References:

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

Link to this Webpage: