Maximum error e of putter face angle from square at impact can be closely approximated by a much simpler formula versus the arctan formula. Maximum allowable error of putter face angle at impact:

e = 10/Length of Putt

e is the maximum allowable deviation from square of the putter face in degrees

Lenth of Putt is in feet

Table comparing the simple e =10/putt length in feet formula versus the e = arctan(2/put length in inches):

Lenth of putt in feet e=10/putt length in feet e=arctan(2/putt length)

5 feet putt: 2 degrees versus 2 degrees

10 feet putt: 1 degree versus 0.96 degree

15 feet putt: 0.66 degree versus 0.64 degree

20 feet putt: 0.50 degree versus 0.48 degree

25 feet putt: 0.40 degree versus 0.38 degree

30 feet putt: 0.33 degree versus 0.32

The above table shows that the simple formula of e=10/length is a very close approximation, as well as it provides more understandable results of 1 degree for 10 feet putt, half degree for 20 feet putt, and a third degree for 30 feet putt.