CONSTANT = [1.93335 X (1/PITCH)] - [2.9939 X BALL/WIRE SIZE]

The formula I got from the Threadcheck table, for Acme Screws, is:

E = M -[ 4.9939 G -

__1.933357__]

n

Where E is the Pitch Diameter, M is your "over wires" measurement, G is the wire / ball diameter, and n is threads per inch. Multiplying the minus sign through the brackets you get:

(1.933357 / n) - (4.9939 * G)

which matches your "Constant" formula except for the 4.9939 factor instead of your 2.9939.