It looks like the CONSTANT in your formula is the same as what I found in the table from Threadcheck, just formatted differently. I assume that you take your constant and subtract it from your "over wires" measurement to get the pitch diameter.
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.
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.