I’m looking for a formula to find the correct length of metal to
make a bangle taking into account the gauge of the sheet. I can find
many ring blank charts, but nothing for bangles.

I’m working with a 2mm thick piece of sterling that’s 8mm wide and
would like to end up with a bangle with an inside diameter of 2.5"

I’m not particularly good at math and would like to get this right
the first time.

When you bend something with a thickness, the inside of the bend is
compressed and the outside is stretched. Somewhere between these two
sides is a thin layer that retains its original length - this is
known as the “neutral axis”. Although not precise, it is the usual
practise to assume that the neutral axis is half way between the
inside and outside faces, and this gives pretty good results. The
width is irrelevant.

In your case, the metal is 2mm thick and you want an ID of 2.5", or
63.5mm. Assuming the neutral axis is 1mm into the thickness, the
diameter of it after bending will be 63.5+2mm = 65.5mm (the 2mm is
because its 1mm on each radius). This gives a total length of pi x
65.5 = 205.77mm. So you want a strip 8mm x 2mm x 205.77mm.

Can you get a dowel 2.5" and wrap a string around it then measure
the string? Or,

Formula for the Circumference of a Circle

Mathematicians have discovered a special number, called pi
(represented by PI ), which is the ratio of the circumference of any
circle to the length of its diameter. PI is roughly equal to
3.14–most scientific calculators have a “PI” button that will
produce more digits. PI is a non- terminating, non- repeating
decimal; thus, PI is an irrational number.

Since PI is the ratio of the circumference to the diameter, PI =c/d;
c PI xd; and d = c/PI ; wherec and d are the circumference and the
diameter, respectively. The most important equations to remember are
the last two.

Hope this helps.

Mary A.
Chief Design Officer
Jewelry for the Journey

Pam, I’m not much good at math either - I almost died when I first
realised just how many equations and formulas jewellers use all the
time, but decided to live on when I was introduced to the several
pages of invaluable formulas for just about anything a jeweller needs
to calculate in Alan Revere’s book ‘Professional Goldsmithing.’

The formula for a ring blank - inside diameter + thickness of metal

pi (which is 3.1416) will work for a closed bangle.

You do need to calculate everything in either millimetres OR inches,
you can’t mix and match! 2.5" = 6.35cm or 635mm.

So - 635+2*3.1416 = 20001.19mm (20cm) - and that’s the length of 2mm
thick sheet that you need for your bangle.

If the bangle is not closed, you decide how big a gap you need to
slide the bangle over the thinnest side of the wrist and still have
it sit comfortably and cut a shorter length accordingly.

How about a mandrel that has a diameter of 2.5 inches? No math...

Richard has a great point here. One of the things I learned doing
blacksmithing was that often, the inches or millimeters is not the
important part, it’s that sizes match, or that the volume of the raw
billet matches the volume of the end product, no matter what forging
steps were taken, etc… so measuring with a ruler is sometimes not
the best way.

For example… to measure a bangle blank… draw a circle 2.5 inches
in diameter, using a compass or a circle template or even a properly
sized can or bottle to trace around. Then take a piece of string and
wrap it around, mark the overlap point and then measure it. Done!

Or, for forging… Sometimes it’s really hard to estimate how much
raw material you need in order to form a forged part - you change
every single dimension, length, width, thickness, while forging, how
much of “this” was in “that” ?

This was one of the best tricks for that problem that I ever
learned. Take very firm modeling clay, and model the piece you want
to make. Then, smash the model you made, and roll it into the size
stock you have available. So if I wa= nt to make a a big, long forged
earring out of 6 mm silver rod, I first model the earring in clay,
quite carefully - then I smash it and roll up the clay so it’s a
round rod 6 mm in diameter.

The length of that clay rod tells me exactly how much silver rod I
need to start with to forge the earring I want!

Hope that helps, and good luck with your bracelet project.

Something this thick is not the easiest to bend smoothly, especially
at the free ends if you cut to precise length beforehand. IMO its
better to start with an extra long piece then bend the blank around
the mandrel first, crisscrossing the ends so that the ends have at
least a close bearing to the finished curvature. Then simply cut thru
the overlap at the point you need. This allows you to fix the
diameter from reality, instead of theory, and you may not need to
hammer at all.

While its true you ‘can’ mallet the free ends to a curve before you
bend the main body, it takes a lot and you’d need a pretty solid base
upon which to hammer, when dealing w a 2x8mm cross section. The less
hammering, the less finishing, especially on the inside.

You do need to calculate everything in either millimetres OR
inches, you can't mix and match! 2.5" = 6.35cm or 635mm. So -
635+2*3.1416 = 20001.19mm (20cm) - and that's the length of 2mm
thick sheet that you need for your bangle

Err… Jane, 6.35cm = 63.5mm, not 635mm. So your calculation should
have been 63.5+2*3.1416 = 205.77.