Let’s take a look at math first: Length of the circumference of a
circle is diameter X 3.14. For better precision 3.14158 can be used.
That is the whole math.
In practice however, there are complications. First is thickness to
account for. General recommendation is to add one thickness to
diameter and multiply the resulting sum by 3.14. Sounds easy enough.
The problem is that when we bend something, we increasing it’s
length. By how much? It depends on technique. With very careful
bending, not very thick gage, and good pliers - very little. Heavy
gage; bad bending technique, pliers not suitable for the task, and
etc… and degree of deformation can be striking, so it is not
possible to give any meaningful recommendation.
Personally, I am using diameter + one thickness and the sum is
multiplied by 3, not 3.14. As thickness increases I may use 2.9 or
even less. The difference between 3.14 and actual multiplier is known
as “fudge factor”, and it is different for any goldsmith, and
situation. You simple have to find you own.