How to calculate wire length when rolling down from larger gauge

Hi Folks,

I tried to search this but I hardly know how to word the search. So
here’s what I need to do. I’m going to roll down/pull/hammer 8 ga (my
calipers measure 5.2 mm) sterling wire to 3 mm. I want to end up with
about 240 mm of the 3 mm wire, and I don’t want to have much extra 3
mm wire, in order to save as much in the 8 ga length for future
projects. So I calculated the square mm crossection of each and set
up a ratio and multiplied that on my desired length of 3 mm wire, as
follows:

3 mm/5.2mm x 240mm equals length of 5.2 mm to start with

Or

18.849/32.6716 x 240 equals 138.46 mm or 5.45"

This seems like it’s in the ballpark for a bracelet but I don’t
know. Does anybody know if I’ve got this right?

Thanks for all the wonderful sharing from you all.

You’re right in saying that the cross section area is the key to the
problem. You just have to use the ratio of the two areas.

Since the cross section area varies with the square of the diameter,
the ratio you need is (3/5.2)**2 which is 0.3328.

You now multiply this by the length of 3mm wire you need, to get the
length of 5.2mm wire to start with. So, 240x0.3328 = 79.82mm. (This
works for wire of any cross section: round, square, etc PROVIDED
that the sections are similar).

I’d add a bit to allow for the bit that gets mangled by the
draw-tongs, so start with about 85mm of 5.2 wire.

Whoops! I used the wrong formula for finding the area of the
cross-section of a piece of wire. I used 2xpixD instead of Pi x
rsquared.

The calculation should have been:

The area of the 3mm wire divided by the area of the 5.2mm wire x
times the desired length of the 3mm wire. I am hoping this will yield
the proper length of the 5.2mm wire to start with.

Thank you for the formula, but I have a question - What operation is
indicated by **2? I have tried several things and can’t seem to come
up with the 0.3328 from 3/5.2

Thank you for the formula, but I have a question - What operation
is indicated by **2? I have tried several things and can't seem to
come up with the 0.3328 from 3/5.2

**2 means the number is squared (raised to the second power).

2 means “squared”. ie. 32 = 3x3 = 9. (3/5.2)2 =
(3/5.2)x(3/5.2) 0.5769 x 0.5769 = 0.3328 Another way of indicating
"squared" when there is no superscript facility is by using the ^
symbol. So, 3^2 = 32 = 3x3.

Been too busy and resting after a huge Easter party to do much
writing, but like our old Cossack friend, some people just gotta do
it the hard way.

This chart: Society of American Silversmiths - Silver Wire Chart is for round wire
but it was just on a quick search. There aresuch charts all over,
including the back of Metal Techniques for Craftsmen. Obviously,
dividing by 12 gives you weight per inch, if you need that.Why this
one is in inch diameters is one of life’s mysteries, but that’s
easily converted, too.

You want one foot of ten gauge, start with just over 1/2 oz of
sterling. Starting with 4 gauge, that’s about 3 inches but I’m only
roughly calculating here.