See "The Jeweler's Bench Reference" by Harold O'Connor, pp.9-11. A
very handy book with lots of formulas and charts. I will not give
specifics since I believe the author deserves royalties. So buy
This is a good book and the chart and formulas O’Connor provides are
very useful. I keep a copy on my bench at all times I’m working with
rings. However, I’ve seen students of mine make the same mistake
using it that James Binnion pointed out earlier. The formula for the
length of a piece of metal stock for a ring shank is (diameter+
thickness of the stock) x Pi, NOT (diameter x Pi) plus thickeness.
And I’ve seen students do it the second way over and over. If
someone is designing a computer program or spreadsheet to calculate
stock lengths for rings, those parentheses are really important. If
someone just writes “D + Thickness x Pi”, the computer will do the
multiplication operation first and then the addition (ie: D +
(Thickness x Pi)), which is wrong.
So, knowing the correct conventional order of mathematical
operations is citical to programming or using a formula. Computers
(and spreadsheets run on them) don’t necessarily read "left to right"
in mathematical calcs; they do multiplication and division first
(reading L to R), then go back and do the addition and subtraction
(reading L to R), UNLESS there are parentheses to specify an order,
starting with the innermost sets of parentheses and working outward
in a formula that contains nested sets of parentheses. (Aren’t
computers cool in that they can do that!?). So be aware of
parentheses.Now on thicker stock, I’ve also seen students cut their
metal correctly and exactly and then find out it is still too short.
“But I cut it exactly to the length from the chart you said to use”.
Why? When I question them it’s usually because when they bend it
into a circle, they use that little trick of filing the ends or
passing a saw blade between the ends to get them to mate up perfectly
for soldering. “Gee, didn’t you think that that process might take a
little off of the length?” Hmmm. So, in practice a little extra on
the length can be helpful. I usually add about 1 mm, sometimes 2,
leaning towards more as the thickness increases, because I know I’m
going to cut/file it out. Or, as Charles Anderson suggests, something
close to 2 times the metal thickness.
It’s not an “accurate” formula that way, but takes into account the
practicalities of joining two ends of metal together. And, as has
been pointed out, if in the end you are off a thousandth of an inch
(or three) or half a millimeter even, it’s close enough for jewelry
work. I’ve never seen an accurate ring mandrel that was tapered. I
don’t own a step-by-step mandrel with a step for each half size;
don’t even know if they make them. And the way most people’s fingers
swell and contract with hydration, weather, and time of the month, a
quarter size is probably close enough for most. And most people’s
fingers aren’t round anyway, they are slightly rectangular in shape,
so I use one of those round-cornered, rectangular cross-sectioned
mandrels anyway for the final shape. People love the way they feel on
their hands as opposed to a round ring shank, so my shanks aren’t
round, so the formula for a perfect circle isn’t completely critical
to me, anyway, even if that’s what I teach students.