If you do it another way, and you know the inside circumference
and the metal thickness, how do you work out the length to cut? You
could divide the circumference by pi, but is there a shortcut to
this method?

Just add pi times metal thickness to the inside circumference. The
length to cut is the inside circumference + (pi x metal thickness).

If you do it another way, and you know the inside circumference
and the metal thickness, how do you work out the length to cut? You
could divide the circumference by pi, but is there a shortcut to
this method? With very basic equipment you can measure your finger
with a strip of paper.

If the inner circumference and the material thickness is known, the
formula for the ring blank will be:

inner circumference + (material thickness x pi) = length of ring
blank

Ya got it right, eyeball it a little long and cut, or get fancy
and use a strip of paper. Most jewellers I have known were much
better at making little scraps of metal than mathematics

Or get really fancy and use a 1/4" wide strip of sticky masking
paper. Best method for sizing bezel length too; especially for
irregulary shaped cabs; overlap paper and cut in center of overlap,
but add thickness of bezel.

Most jewellers I have known were much better at making little
scraps of metal than mathematics

Since I do not belong to the above described category, I would like
to explore the subject a bit.

The formula (diameter + thickness) * Pi has build in correction for
metal stretching while bent. If our metal would be of unstretchable
kind ( not that it exist ), the formula would be ( inner diameter + 2
thicknesses ). When working in reverse, it would appear that metal is
already of the right length, so the formula should be length / Pi. No
correction is required. But, if we bend our strip, the ring will be
smaller than calculated.

This appear to be a paradox, which need not to be if we realize that
a nonsensical question was asked! Measuring finger with a strip of
paper will not give the desired length for the following reasons:

Paper is not stretchable.

When ring is put on a finger, finger is conforming to the shape of
the ring due to ring rigidity. Paper strip is not rigid enough to
recreate the condition.

Paper is thinner than prospective metal.

We have to remember that formula was created to determine the length
of a metal strip needed to arrive at predictable diameter, taking
into consideration metal properties. This applies to all other
similar recommendation of measuring stones with the string and etc.

âThe Jewelerâs Bench Referenceâ by Harold OâConnor available at Rio
Grande has a chart for ring sizes thatâs very convenient and easy to
use along with conversion tables that I would suggest checking out.
$17.75 spiralbound.

"The Jeweler's Bench Reference" by Harold O'Connor available at Rio
Grande has a chart for ring sizes that's very convenient and easy
to use

An example: I just did a show where a woman wanted a size three ring
composed of four discrete round wire bands to go with another ring
which was 5.5 mm in width.

I went to page 11 of Harold OâConnorâs book âTable of ring blank
widthsâ to the column U.S. size 3 across to B & S ga. 16 (1.3)
length 48 mm which is the length of wire to fabricate a size 3 times
four 192 mm yields 4 rings total width 5.2 mm. Close enough!