How do you calculate SAP diameter of Gear?

The SAP (Standard Addendum Profile) diameter of a gear can be calculated using the formula: ( d = \frac{N \cdot P}{\pi} ), where ( d ) is the pitch diameter, ( N ) is the number of teeth, and ( P ) is the diametral pitch. The SAP diameter typically refers to the outer diameter of the gear, which can be determined by adding twice the addendum (the radial distance from the pitch circle to the top of the teeth) to the pitch diameter. Thus, the formula for the outer diameter ( D ) is ( D = d + 2 \cdot a ), where ( a ) is the addendum. Ensure that you use consistent units throughout the calculation.