Basic ring formula

Jewelry Discussion
1

I think i may have my ring formula muddled up.
Is it: (3.14 x inside diameter) + metal thickness?

Thanks,
Rhonda

2 
I think i may have my ring formula muddled up. Is it: (3.14 x
inside diameter) + metal thickness?

Almost.

The inside diameter plux the metal thickness, the multiply the sum
of those two by pi.

So: 3.141 x (inside diameter + metal thickness) = blank length

You can also use the outside diamber, subtracting the metal
thickness, as in:

3.141 x (outside diamter - metal thickness) = blank length.

Or, if you’re bored and want to play math games, you can also use:

(3.141 x inside diamter) + (3.141 x metal thickness) = blank length

(that’s the same as the first formula, just rearranged.)

The point is that both the inside diameter and the metal thickness
are multiplied by pi, where your version just adds it on without
multiplying it by pi.

Peter Rowe

3 
I think i may have my ring formula muddled up. Is it: (3.14 x
inside diameter) + metal thickness?

No, its 3.14 x (diameter + metal thickness). It makes the
(reasonable) assumption that the neutral axis is in the centre of the
metal.

Regards, Gary Wooding

4

Hi Rhonda,

I think i may have my ring formula muddled up. Is it: (3.14 x
inside diameter) + metal thickness?

You are close. It is Inside diameter + metal thickness x 3.14. If you
wait until you have multiplied by pi to add the metal thickness it
will be too small as the metal thickness also needs to be multiplied
by pi.

Cheers,
Lona

5

Hi Rhonda,

The ring formula is: inside diameter + metal thickness x 3.14. You
can also do: outside diameter - metal thickness x 3.14. It depends
on what you are using as your measurement.

Cassandra.
www.cbjewelrydesigns.com

6

According to my the formula is:
(inside diameter + metal thickness) x 3.14

Good luck
Joel

7 
According to my the formula is: (inside diameter +
metal thickness) x 3.14

This is correct. If you don’t add the metal thickness, the ring
should only connect at the right size on the inside edge of your
metal.

8

Hi cassandra and Lona

Your formula is almost correct. When the formula is written down you
must have brackets (is that the proper English word?) like this:
(inside diameter + metal thickness) x 3.14, otherwise it is not
correct for gettting the length of the ring blank. Without the
brackets you will have a different result.

Per

9

Hi Per,

Your formula is almost correct. When the formula is written down
you must have brackets (is that the proper English word?) like
this: (inside diameter + metal thickness) x 3.14, otherwise it is
not correct for gettting the length of the ring blank. Without the
brackets you will have a different result.

I really don’t understand why the brackets would make a difference
in the result. I have been doing it this way and teaching my students
how to do it for years. I just put the numbers in the calculator and
it always works out fine. But thanks anyway. I guess if you were
writing it down for somebody it would make a difference in their
understanding the formula.

Lona

10

Lona, see what happens to your calculator result if you write it as
3.14 * ID + metal thickness. You will get the wrong result and your
student’s blank will be too short. Do understand why? I’m sad that
calculators are used as not a tool to accelerate processing, but an
alternative to teaching math (which I hated, but understand, sort
of).

11 
I really don't understand why the brackets would make a difference
in the result. I have been doing it this way and teaching my
students how to do it for years. I just put the numbers in the
calculator and it always works out fine.

Parentheses override the order of operations when evaluating an
arithmetic expression (or have highest priority in the order). Not
having the parentheses in the expression (inside diameter + metal
thickness) x 3.14 would yield a very different answer because,
working from left to right, the multiplication would be performed
prior to the addition. Not sure what your calculator is doing or
what you are teaching students.

Robert

12 
really don't understand why the brackets would make a difference in
the result. I have been doing it this way and teaching my students
how to do it for years. I just put the numbers in the calculator
and it always works out fine. But thanks anyway. I guess if you
were writing it down for somebody it would make a difference in
their understanding the formula.

Some calculators perform their calculations in the order the buttons
are pressed. EG. 3+42 is calculated as 3+4 (which is 7) times 2 =
14. Other calculators do multiplication and division before addition
and subtraction, so 3+42 is calculated as 3 plus 4*2 (which is 8),
which comes to 11. Most modern calculators do it this way, so you
use brackets to remove the ambiguity. (3+4)*2 says; add 3 and 4, then
multiply the result by 2.

IHTH
Regards, Gary Wooding

13 
I really don't understand why the brackets would make a difference
in the result. I have been doing it this way and teaching my
students how to do it for years. I just put the numbers in the
calculator and it always works out fine.

You’re calculator may be just by accident doing it the right way.
But brackets make a big difference. Brackets determine what gets done
first.

In the case of this formula, (diameter+ metal thickness) x pi, which
is the correct formula, whether you add the two numbers together and
then multiply the whole by pi is quite different from without the
brackets, or the other position of the brackes, which would multiply
pi by one number and then add the second number to the result.

For example: Just numbers for this, not realistic ones, but to
illustrate the math.

diameter = 5
metal thickness = 5

with pi x (5+5) you have the equivalent of pi x 10, or 31.4159.

if you had the brackets around pi and the diameter instead, then the
formula would be (pi x 5) + 5. That is (15.707) +5, which equals
20.707. Very different result, depending on the position of the
brackets.

It’s a question of what the order of operation is. If you multiply
first, then pi gets multiplied by only one of the measurements. If
you add first, then pi gets multiplied by both.

With your calculator, you’re probably entering:

diameter + thickness x pi. No brackets. The calculator is simply
performing the operations in the order you entered them, which ends
up correct.

If you entered the same numbers as:

pi x diameter + thickness, you’d get the wrong result.

But it’s intuitive in this situation to enter the measurements
first, so you got lucky and did it right by accident.

Adding brackets to the equation means there is then no longer any
ambiguity as to which operation (multiplication or addition) is done
first (within the brackets is always done first), so the results no
longer vary according to which direction you write or enter the
equation. Simpler calculators don’t have bracket keys, though, so
then you simply have to enter the numbers in the right order.

Peter Rowe

14

You need the brackets to force the “order of operations” (good old
BEDMAS - Brackets, Exponents, Division, Multiplication, Addition,
Subtraction) without the brackets the first step is multiplying the
metal thickness by pi, THEN adding the inside diameter

example:

2.5 + 0.2 x 3.14
2.5 + 0.628
= 3.128

But with the brackets the addition happens first:

(2.5 + 0.2) x 3.14
2.7 x 3.14
= 8.478

A considerable difference, I’m sure you’d agree. The first one is
barely over the diameter of the ring, certainly not the
circumference. And here I thought that I’d never need math in the
’real world.’

Cheers,
Mark Wells

15 
I really don't understand why the brackets would make a difference
in the result. I have been doing it this way and teaching my
students how to do it for years. I just put the numbers in the
calculator and it always works out fine

There is such a thing as precedence of operations. Depends on a
calculator it may make a difference. Besides, some people do not use
calculators, so brackets are very important.

Leonid Surpin

16

Hi Lona

I am certain that you are getting the right length of ring blanks
when you are working. You add inside diameter and material thickness,
and multiply that sum with 3.14. You are in fact using the formula
(inside diameter+thickness)x3.14

I’m having a little trouble in explaining this in English. Perhaps
someone can help me out? I just wanted to show you that there IS a
difference in these formulas. There is a difference in the order of
operations without the brackets.

I’ll give you an example when we compare the two different formulas:

Let’s say we have a ring with inside diameter, Di= 20 mm, and
material thickness, t=1mm

(Di + t) x 3.14 =(20+1) x 3.14 = 21 x 3.14 = 65.94 mm --> length of
ring blank

and the other formula without brackets:

Di + t x 3.14 = 20 + 1x3.14 = 23.14 mm

or if it is written down in this order:

t + Di x 3.14 = 1 + 20x3.14 = 1 +62.83 = 63.83 mm

I just wanted to make the point that the brackets are important if
the formula is written down in a instruction manual for example. I
hope I made it clearer now.

Per

17

Hi Per,

You are right. This formula needs brackets. I am confused myself too
because Carles Codina in book "The Complete Book of Jewelry Making"
p.31 made the same mistake.

Irwan

18

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.

Hoping for a simple and elegant solution!
Tamizan

19

Well, I have certainly learned something today about brackets but
would just like to say that my calculations always get me the result
that I need. But I would just like to say “thanks” to everybody who
gave me a math lesson today. This is one I won’t forget very soon.

Lona

20

Finally, a use for my mathematics degree :slight_smile:

(inside diameter + metal thickness) x 3.14

The parens are a signal to perform the action within them FIRST,
THEN the action(s) outside the parens. If you have always been
getting the correct results without considering this fact then you
have been lucky - both you and your calculator are performing the
addition BEFORE the multiplication, which the parens are indicating.
Of course to anyone who has not been made aware of this usage, parens
don’t mean anything.

To those familiar with the terminology it is a clear message NOT
to multiply metal thickness by 3.14 and THEN add inside diameter,
which would yield the wrong result (too short).

Mary Partlan
White Branch Designs