What is the pitch circle diameter of a 50-tooth spur gear having a circular pitch of 0.375 inch

Pitch circle diameter = 5,66 inch

Explanation:

According to the pitch circle diameter formula

Dc = Dp - 2b; where Dp = primitive diameter, b = dedendum of the tooth and also the dedendum formula is b = 1,25 Pc/π.

The definition of primitive diameter is equal to (Pc*Z) / π; Pc = circular pitch and Z = number of teeths.

Replacing in the formula

⇒ Dc = (Pc*Z) / π - 2 * 1,25 Pc/π, Pc = 0,375; Z=50

In conclusion the pitch circle diameter is equal to:

Dc = 5,66 inch.