# Formula to calculate bracelet sizes

Good day,

I am a self taught silver smith artist. While I have a sizing chart
for ring depending on thickness of wire, etc… Please tell me how
or what formula is used when calculating bracelet sizes? I have been
estimating bracelet sizes for years and very weary of this method.
Is there a mathematical way of calculating? I normally use either
8x2mm. 6x2mm rectangular wire for my bracelets plus clasp hook or
latch, which can easily be figured into a formula.

``````Please tell me how or what formula is used when calculating
bracelet sizes? I have been estimating bracelet sizes for years and
very weary of this method. Is there a mathematical way of
calculating?
``````

Yes, there is. In mathematical lingo, to find the size of a bracelet
is to find circumference of an ellipse. In case of circle the task is
trivial, but ellipse is unexpectedly difficult. The method of taking
length plus width, dividing it by 2 and using result as diameter of a
circle, - works in creating oval settings. In case of bracelet, this
method will be off by few millimeters. So better way is needed.

There are 2 ways to go, - to use approximation which is good enough
for our purposes, or to calculate precisely. I am not going to
explain precise method, because it involves computing infinite
series. Precision gained is meaningless for working with metal. It
will be a lot of work with very small yield. I am not going to
mention it here.

Very good approximation is given by Ramanujan. Let C be
circumference; a - one half of ellipse length and b - one half of
ellipse width. The formula then becomes -

C = 3.14159*[ 3a + 3b - sqrt( (3a + b) * (a + 3b) ) ]

Let’s check it out. Ellipse 60 mm long and 40 mm wide. Computing by
circle method = 3.14159*((60 + 40)/2) = 157mm. Let’s try Ramanujan
way -

C = 3.14159 * [ 330 + 320 - sqrt( (330 + 20) * (30 + 320))]
simplifying - 3.14159 * [ 150 - sqrt( 110 * 90 ))] = 3.14159 * ( 150

• sqrt(9900)) = 3.14159 * ( 150 - 99.5) = 3.14159 * 50.5 = 158.7

The difference is 1.7mm. Large dimensions would produce larger
errors.

Leonid Surpin
www.studioarete.com

``````C = 3.14159 * [ 3*30 + 3*20 - sqrt( (3*30 + 20) * (30 +
3*20))]simplifying - 3.14159 * [ 150 - sqrt( 110 * 90 ))] =
3.14159 * ( 150- sqrt(9900)) = 3.14159 * ( 150 - 99.5) = 3.14159 *
50.5 = 158.7
``````

Standard lady’s bracelet is 7 1/2" long, standard men’s is 9". That’s
for a bracelet with a catch - a full circle. If it’s a slip-on cuff
then take an inch off of that for the opening. For more custom sizes
you can pretty much take or add a half inch. Easiest way is to put a
bracelet on the customer’s wrist and check the fit. It’s not a ring
that needs to actually fit, it’s a thing that flops around on the
wrist.

There is much latitude.
http://www.donivanandmaggiora.com

``````Let's check it out. Ellipse 60 mm long and 40 mm wide. Computing
by circle method = 3.14159*((60 + 40)/2) = 157mm. Let's try
Ramanujan way - C = 3.14159 * [ 3*30 + 3*20 - sqrt( (3*30 + 20) *
(30 + 3*20))] simplifying - 3.14159 * [ 150 - sqrt( 110 * 90 ))] =
3.14159 * ( 150 - sqrt(9900)) = 3.14159 * ( 150 - 99.5) = 3.14159 *
50.5 = 158.7
``````

Or you could just order a “Jewelry Maker’s Gauge” from Stuller, part
number 35-5115. Figure how long you need the bracelet by measuring
the wrist, add three times the thickness of the metal to the
measurement on the gauge. Cut it, finish it and deliver it, never
look at a calculator except to figure the sales tax. Rio and Otto
Frei probably have the same thing. Works well for rings too.

It is possible to over-engineer this whole thing; It’s not really
rocket science, no matter how much some may want it to be.

Dave Phelps

My family has been making heavy twisted, forged and fabricated
silver and gold bracelets for seventy years. See my website below for
examples. There are 1,000s of them all over the world. Cuff bracelets
have to fit or they aren’t worn. If they don’t fit, they aren’t
comfortable and can become a safety hazard. Our system of sizing is
kind of like shoes. We use the flat length of the bracelet prior to
bending as a reference and then increase or decrease the length in
1/4" increments. Once bent with a slightly less than 1" gap except
for larger sizes, the only other variable is the thickness of the
bracelet material. Its impact on size is basic geometry and has
already been discussed. Whatever the length of the bracelet was
before bending is stamped into the inside of the bracelet ( 50 3D 5",
51 3D 5.25", 52 3D 5.5" and so on). Once a customer figures out what
size fits, they remember the number and that is how we communicate.
The challenge comes from a new customer who can’t try on bracelets to
meets the hand. Subtract about an inch for the gap and add a bit
(1/4’ - 1/2") so that it is not too tight. If it fits, remember the
flat length prior to bending and that is the size. Remember also that
the wrist is tapered. If a customer wears more than one bracelet (we
encourage this), they may have to be graduated in size as the stack
grows up the wrist. I have one customer who wears ten silver
bracelets on one wrist and ten gold bracelets on the other. Our
system is a mixture of math, anatomy and lots of experience and it
usually works. If a bracelet doesn’t fit, we exchange it with another
until it does. In the end, everyone is happy and you hopefully have a
customer for life.

Rob Meixner - Jewelry

``````Or you could just order a "Jewelry Maker's Gauge" from Stuller,
part number 35-5115. Figure how long you need the bracelet by
measuring the wrist, add three times the thickness of the metal to
the measurement on the gauge.
``````

It is quite amazing how much disdain some carry towards others, and
this is such a perfect example. A simpleton solution for the problem
that the author of above quote does not even begin to understand. To
write something like that, the author has to believe that only he
knows about Jewelry Maker’s Gauge. Another things that author has to
believe is that all bracelets start as flat strips of metal. But
nothing can be further from the truth.

Let’s take such a popular item like bangle bracelet. It is made by
shaping bottom part and the top separately, and then the two parts
are soldered together. Metal is quite thin, 0.3mm. Fit must be
perfect for soldering pieces so large and so thin. The shaping is
done on specially made rollers, but the size is controlled by length
of starting strip. Strip to form the top is longer, because it has to
form larger ellipse. When top and bottom put together the ends must
coincide and they must be perpendicular to ellipse major axis.

I am sure that some reading this would say “not a big deal, just
make it longer and trim it as required”. It is not going to work.
First it is only possible to form half of ellipse or smaller. So
trimming would actually take away some portion of ellipse. If that
is to happen, the clasp would not operate smoothly if operate at all;
hinge would be put under excessive loads which could cause it to
fail; and there will be very unsightly gaps between clasp walls.
There was some interest expressed in jewellery mechanisms, so here
is first lesson. Alway consider geometry of fulcrum and angle of
insertion of tang into clasp enclosure. They are always
interdependent.

There is only one way to meet all the requirements. The length of
the bottom and the top must be precisely calculated to form exactly
half of the ellipse. Additional difficulty lies in that both parts
must have the same coefficient of eccentricity, which computed by the
formula C_of_e = sqrt( a^2 + b^2 ) / a ( a and b are half major and
minor axis correspondingly ).

I am going to finish by citing Einstein who said " Things must be as
simple as possible, but no simpler". The key of not falling into the
trap of ever-simplification is to have good understanding of the
process, which some apparently lacking.

Leonid Surpin
www.studioarete.com

Or you could just order a “Jewelry Maker’s Gauge” from Stuller,
part number 35-5115. Figure how long you need the bracelet by
measuring the wrist, add three times the thickness of the metal to
the measurement on the gauge.

``````It is quite amazing how much disdain some carry towards others,
and this is such a perfect example. A simpleton solution for the
problem that the author of above quote does not even begin to
understand. To write something like that, the author has to believe
that only he knows about Jewelry Maker's Gauge. Another things that
author has to believe is that all bracelets start as flat strips of
metal. But nothing can be further from the truth.
``````

statements. As no apology for rudeness from Mr. Surpin is expected,

Mr. Surpin is a very talented and knowledgeable jeweler. We are
fortunate that he takes the time from his busy schedule and shares
his knowledge with this group. There is no sarcasm meant or implied
with the above two sentences.

However, what he lacks in manners he also lacks in logical deduction
skills.

Let’s explore the simpleton logical deduction skills he has just
displayed.

``````the author has to believe that only he knows about Jewelry Maker's
Guage.
``````

Really? HAS to believe that, and nothing else? Let’s explore.

Possibility One: He could believe that the original poster does not
know about a Jewelry Maker’s Gauge.

might not know about a Jewelry Maker’s Gauge and desire to be helpful
to them. The list has people of many different skill levels on it.

Possibility Three: He could believe that some expert jewelers like
Mr. Surpin don’t know about it either, since they seem to use Guages
instead of Gauges. Or maybe he just knows how to spell the word.

What other simpleton logical deduction skills has Mr. Surpin
demonstrated in his diatribe?

``````author has to believe is that all bracelets start as flat strips
of metal.
``````

Really? HAS to believe that and nothing else? Let’s explore.

Possibility Four: The author might know about bracelets that do not
start with a flat strip of metal, but might not have experience
making them. Therefore, the author might not know their method does
not work for other bracelet types.

Possibility Five: The author thought the bracelet type the original
poster was trying to make was based on flat strips of metal and
mentioned a simpler method than Mr. Surpin put forward. Being in a
hurry, the author forgot to mention the limitations on the method.

Let’s suppose that Mr. Surpin is correct and the author actually
does believe what Mr. Surpin believes they do.

How could Mr. Surpin have communicated the same without
being so rude?

Well, if we ignore the first paragraph in his reply, Mr. Surpin has
given an excellent example in the rest of his reply.

Regards

I feel really blessed to be a center of such an outpouring of emotion
masquerading as analysis. Only true love can be the driving force
behind it. Alas, I have been already taken and regretfully cannot
respond in kind.

Leonid Surpin
www.studioarete.com

90% of the bracelets that I make are flat before they are bent. Using
the length as the variable in sizing bracelets was the subject of one
of my previous posts. The post that I am replying to mentions that
some bracelets aren’t flat when they are made. This is true, at least
in my case, for bracelets that are thick and forged into their final
shape. I have found it helpful to measure the inside circumference
(end to end) as this is the dimension that will actually fit the
wrist and compare it to the total circumference of the wrist where
the bracelet will be worn. Adjust for the gap and add a bit so it
will be loose and it should fit. In the end, having the final
customer try them on is the best way to go, but you can’t always get
there. I am new to The Orchid, but not new to working in silver. I
enjoy these post each morning with my coffee. Thanks and keep them
coming, I will jump in where I feel that I have something to offer.

Rob

Rob Meixner - Jewelry

Leonid - I have an question. Is English your first language? Where
were you born? I have found that sometimes people who appear a
little rough around the edges actually have come from a rough
background. I find myself sometimes saying and doing things that had
I the benefit of hindsight, I might have done differently. But we
don’t and we move on. You have great skills as a jeweler and you make
beautiful jewelry; whoever were your teachers taught you well. I
would be willing to bet they had big egos!

Barbara on a little island in a rainstorm

``````It is quite amazing how much disdain some carry towards others,
and this is such a perfect example. A simpleton solution for the
problem that the author of above quote does not even begin to
understand.
``````

And you contend that my post was a demonstration of disdain for
others?

I guess I must have hit a nerve or something. But maybe you’re
right, Leonid. Perhaps very few (myself included) are clever enough
to ever understand and implement the geometrical nuances of achieving
the correct solution for the length of a bracelet using nothing but a
set of eyeballs and a ruler. Maybe that’s why there are so few hand
made bracelets in the world. I guess I better quit making bracelets
and attempting to solder and leave them both to the professionals. I
might hurt myself.

Someone recently and kindly posted this concerning Leonid’s absence
from Orchid -

``````Hopefully Leonid is fine. His upper level skill tutorials can only
be appreciated by those who recognize his talent and intent. IMHO
negative comments come from the lesser skilled, with large egos.
``````

While I agreed with the poster’s sentiment concerning Leonid’s health
the context and meaning of the last sentence. Now I wonder if she
wasn’t right. Maybe contempt for the opinions, knowledge and
techniques of others sometimes does come from a large ego that isn’t
entirely backed up by skill and not just from a disagreement about
something that both parties know about, but approach differently, as
is what I thought most disagreements on Orchid are all about. Maybe
sometimes that negativity is driven by nothing more than someone’s
need to be viewed as the smartest person in the room.

Oh, by the way Leonid, in your last post in which you state
categorically that “there is only one way to meet all the
requirements” for figuring the length needed for the components of a
hollow bangle, you were kind enough to include in our "first lesson"
in “jewellery mechanisms” the proper operation of the fulcrum and the
angle of insertion of the clasp. But you neglected to mention the
need to make an allowance for the length of the hinge as determined
by it’s size and position and whether it’s to be an integral lap
joint or a tubular watch case style hinge. And then there’s the
issue of whether to limit it’s travel or not and how exactly that
might affect the length of the inside and outside blanks in the
mathematical equations. But take heart. Einstein missed a detail or
two occasionally and as you know, he was a pretty smart fellow too.

Dave Phelps

``````But you neglected to mention the need to make an allowance for the
length of the hinge as determined by it's size and position and
whether it's to be an integral lap joint or a tubular watch case
style hinge. And then there's the issue of whether to limit it's
travel or not and how exactly that might affect the length of the
inside and outside blanks in the mathematical equations.
``````

Hollow bangle is made exactly to size without any allowance for hinge
and clasp. The reason is that after bangle is soldered, the cutouts
are made in the body of the bangle to accommodate the hinge and the
clasp. So their dimensions are automatically integrated into intended
size. Traveling limit is controlled by tang extension spring hidden
inside the bangle. Fully open, it allows for bangle to be put on,
without stressing the hinge, and at the same time it prevent hinge to
be open to such a degree, that marks are left on opposite side. It is
rather tedious trying to explain hinge geometry, so It should not be
very difficult to find someone specializing in bangles and ask him
for demonstration of hinge mechanics.

Leonid Surpin
www.studioarete.com

``````Leonid - I have an question. Is English your first language? Where
were you born? I have found that sometimes people who appear a
little rough around the edges actually have come from a rough
background.
``````

I was born and educated In Russia. So english is my second language.
However, I do not want to use my background as an excuse for the way
I express myself. I find that we spend way to much time worrying how
other people would react, rather than concentrating on actual
Progress is impossible without accurate and concise
exchange of ideas. Trying to candy-coat criticism, in order to make
it more palatable for overly sensitized egos is a wast of time, and
almost without exceptions obfuscates the intent of criticism in the
first place. Criticism is a bitter pill, no questions about it. But
if object of criticism can take it constructively, it will be a
learning experience. On the other hand if object of criticism would
take a path of indignation than nothing good would come out of it.
In a way, harsh criticism is a mechanism of separating those who can
learn, from others that could not. I do want to help the former and
not really interested in the later.

Leonid Surpin
www.studioarete.com

I’m not a jewelry expert, but I have a lot of expertise in
communication. So I’d like to suggest that we offer "feedback"
instead of “criticism.” The difference, for me, is not
sugar-coating, and “feedback” is not a euphemism for "criticism,"
either. Feedback is my response to what I am responding to. It’s not
about the person I am responding to. It is based on observation (“I
disagree with [specific thing I disagree with] because [reason I
disagree]”. It doesn’t include my generalized judgments like “Any
jeweler worth his salt knows…” It is not disrespectful, but it may
totally challenge what is being responded to. And it is not
necessarily any easier for the person being responded to to take in.

Putting in my two cents, I want to say that IMHO there is a shortage
of courtesy and consideration in the way people talk to one another
in our society (This is my generalization and judgment). Since I am
confident that everyone in this forum wants to learn and/or
contribute, I welcome more respectfulness in the way we post.

Ronnie Hausheer

Ronnie,

I think you are right here in some instances. Too many of us get
confused with criticism, and feedback. There are those that have a
professional “difference of opinion” and they get locked up in “my
way is better” I have been in this industry over 37 years and I have
learned, and still do, from other people who are doing this craft.
There are many ways to “skin” the cat and I believe you have to do
things the way it works best for you in a professional way. Now, there
are certain methods in making jewelry that have withstood the test of
time and are still being used today without conflict of opinion.

Russ Hyder

``````Progress is impossible without accurate and concise exchange of
ideas.
``````

I agree.

Trying to candy-coat criticism, in order to make
it more palatable for overly sensitized egos is a wast of time,
and almost without exceptions obfuscates the intent of criticism in
the first place.

I agree.

Constructive, useful criticism is appropriate. Facts are facts, and
if people don’t like them, too bad for them. If someone is wrong, say
so and explain why. Keep it simple and to the facts.

Here is where we disagree:

It is possible, without any particular effort, to completely
disagree with someone, tell them they are wrong and exactly how they
are wrong, WITHOUT calling them stupid, dumb, or a simpleton.

I know you are capable of this because you have demonstrated this.

Gratuitous insults are pointless and only get in the way of the
educational process.

I am in total agreement Ronnie. I don’t usually feel compelled to get
involved but I was just thining this very thing a few days ago and
you have compelled me to speak up.

This is a forum in which to give advice, input, ideas etc. Rudeness
and rough criticism (from one individual in particular) should not be
apart of this. Leave your egos at the door, if you will. I think it
is a wonderful place for much needed help and advice from experienced
and not so experienced metalsmiths/jewelers. I commend all who
participate in this forum and give out there tid bits of knowledge
and experiences to all in need. It is truely a generous act when so
many artists today charge for giving advice and input. I for one
cannot afford to pay someone \$125/hr for their advice. So I sincerely
thank everyone here who participates and gives their time and
knowledge. It is a wonderful learning place!

Peace
Carol

Russ,

Disagreement, and even conflict, are part of everyday life. I would
not change that. They broaden my perspective. I am responding to the
way that we disagree. It’s possible to disagree without insulting
anyone. It’s possible to present an expert’s view without belittling
anyone. Respect for one another permits us to keep coming back to
ridicule.

Case in point: I really enjoyed the responses to Sabra’s “use
cardboard” post on raising a stone in a bezel. So many different
solutions to one problem. And Leonid’s response made me laugh. (I
hope that was the intention). Let’s disagree, please.

Ronnie Hausheer

In the dark ages when I was teaching at the high school level we had
a principal tell the faculty "Sarcasm is the mark of a bad teacher."
He went on to say, "It’s very nature is that you say the opposite of
what you mean.

If you are sarcastic with your students, you will not last long at
this school." About forty-five years later, I still appreciate and