Formula to calculate ring inside diameter

What is the correct formula to calculate the Inside Diameter of a
ring in inches.

I have it as “(Ring Size x 0.032) + 0.458”

Best Regards,

I have it as "(Ring Size x 0.032) + 0.458" 

Wouldn’t you just use ring sizes, a dial caliper (or digital if
you’re less romantic) ?

Regards Charles

I have it as 40mm for zero size and 2.5 mm for each size after. Now
the problem is width. As a customary thing I would add 2mm for
anything wider than 4mm. You will always have to file and fit so
better to have a little more than not enough.

Russ H.

Here is a nice chart that shows all different conversions of ring
sizes including diameter and international sizing:


Diameter x Pi (3.14…) + thickness of ring.

Wouldn't you just use ring sizes, a dial caliper (or digital if
you're less romantic) ? 

I want to use the formula in a program

I have it as "(Ring Size x 0.032) + 0.458" 

It starts off OK, but gets less accurate at the larger sizes. A
better formula is (Size x 0.0324) + 0.454, which is accurate to a
couple of thou.

It’s easy to derive.

Size 1 = 0.486; Size 13 = 0.875

Increment/size = (0.875-0.486)/12 = 0.032417 (0.0324 is close

Size 0 would then be 0.486-0.0324 = 0.4536, or 0.454 to the nearest

Regards, Gary Wooding

Diameter x Pi (3.14...) + thickness of ring. 

Adding the thickness of the ring gives you the length of metal to use
to make the ring. For just the inside diameter, you just measure the
diameter of the mandrel at that size. For the inside circumfrence,
multiply by pi.

The question was a formula to get the inside diameter of a ring at a
given size. Since ring sizes, at least U.S. ones, are not based on
any great logical premise, the best way for a program to do it would
be simply to store a table of the established values and work from
there. It’s not a mathematically consistent or logical set of size
values, although the progression from one size to the next is fairly
uniform, but even then, a direct mathematical derivation from just
one starting size won’t be quite as accurate as just storing a table
of the standard sizes in your program. Simple spreadsheet sort of

Some of the several european or international ring size systems,
however, are either direct statements of the metric diameter, or
metric circumfrence of the inside of the ring (depending on which
sizing standard/system you were using). For those size systems, no
calculations are needed. The ring size itself is already the value
you wanted to calculate. Or for those that use the circumfrence of
the ring as the ring size, just divide by pi.


Diameter x Pi (3.14...) + thickness of ring. 

I use two ring thicknesses, one thickness falls short for me.

Regards Charles

I want to use the formula in a program 

Ah, that makes it different then. I think a look up table would be
better if you’re programming an application or a spreadsheet. You
don’t have to re-invent the wheel, especially with a handy forum
like Ganoksin.

Depends on what you are doing really.
Regards Charles

If I have a program that asks for a ring size and I enter 10. It must
then calculate the inside diameter by using a formula. In this case I
have it as (10 x.032) +.458 =.778 which is correct according to my

The problem is it is not always correct.

Size 7 calculates to.682, according to my chart it must be .683

Does anyone have a better formula? OR Is this formula good enough?

Does anyone have a better formula? OR Is this formula good enough? 

If you’re getting within a thousandth of an inch through the whole
size range, then your formula is good enough. That’s much tighter
specification than is normal for ring sizing. I’ve never seen a ring
mandrel, for example, that’s as accurate as that (even the so-called
high accuracy ones). And further keep in mind that both your
formula, and the charts, will be subject to both rounding errors, and
limits to the significant digits. Calculations can show answers with
far more decimal places than are actually valid accuracies, for
example, and you can be sure the same limits applied to the
publishers of your chart. They’re listing that size as .683. But what
if the actual measurement is .6825? They’ve rounded one way, your
program the other. Both, considering that a thousandth of an inch
exceeds usual jewelry accuracy requirements, would be correct.

Peter Rowe

Hi Johan,

Size 7 calculates to .682, according to my chart it must be .683 

Depending on the rounding algorithm used in your program, .682 &
.683 are the same. They are only .001" different. The odds are you
couldn’t measure that amount with anything other than a high quality
micrometer & a little experience. .001" is less than 1/6 the
thickness of the average human hair.


I use two ring thicknesses, one thickness falls short for me.

Possibly because the correct formula for the length of a blank is
diameter + thickness x Pi not diameter x Pi + thickness.

James Binnion

See “The Jeweler’s Bench Reference” by Harold O’Connor, pp.9-11. A
very handy book with lots of formulas and charts. I will not give
specifics since I believe the author deserves royalties. So buy the



HeHe, reminds me of the time I had 3 mandrels. One under, one over
and the middle one close to right. With careful mandrel selection the
boss had to admit everything was sized correctly and find some one
else to blame. Me bad.

I have to agree about.001" as being excessive for jewellery work
(with machine tooled stuff a good challenging goal and desirable). If
I can’t see it or have to bust my buns to measure it then it is not
there. Mikes, loupes and the typical assortment of tools handy.

With a major piece of software I use the author has warned about
floating point errors. They are out there and can’t be avoided :slight_smile:

Demand Designs
Analog/Digital Modelling & Goldsmithing

From the feedback I received I believe my formula is good enough.
Thanks to everyone that replied.


Possibly because the correct formula for the length of a blank is
diameter + thickness x Pi not diameter x Pi + thickness. 

You are very correct Sir, but the 2 metal thickness stands (for me),

The revised formulae :-

(D + (metal thickness x2)) x Pi

Then I rolled a piece of stock using the one metal thickness it fell
short. The teacher knew this, but wanted me to find out for myself
(we think this was a way to keep the class at the same speed).

Regards Charles

See "The Jeweler's Bench Reference" by Harold O'Connor, pp.9-11. A
very handy book with lots of formulas and charts. I will not give
specifics since I believe the author deserves royalties. So buy
the book. 

This is a good book and the chart and formulas O’Connor provides are
very useful. I keep a copy on my bench at all times I’m working with
rings. However, I’ve seen students of mine make the same mistake
using it that James Binnion pointed out earlier. The formula for the
length of a piece of metal stock for a ring shank is (diameter+
thickness of the stock) x Pi, NOT (diameter x Pi) plus thickeness.
And I’ve seen students do it the second way over and over. If
someone is designing a computer program or spreadsheet to calculate
stock lengths for rings, those parentheses are really important. If
someone just writes “D + Thickness x Pi”, the computer will do the
multiplication operation first and then the addition (ie: D +
(Thickness x Pi)), which is wrong.

So, knowing the correct conventional order of mathematical
operations is citical to programming or using a formula. Computers
(and spreadsheets run on them) don’t necessarily read "left to right"
in mathematical calcs; they do multiplication and division first
(reading L to R), then go back and do the addition and subtraction
(reading L to R), UNLESS there are parentheses to specify an order,
starting with the innermost sets of parentheses and working outward
in a formula that contains nested sets of parentheses. (Aren’t
computers cool in that they can do that!?). So be aware of
parentheses.Now on thicker stock, I’ve also seen students cut their
metal correctly and exactly and then find out it is still too short.
“But I cut it exactly to the length from the chart you said to use”.

Why? When I question them it’s usually because when they bend it
into a circle, they use that little trick of filing the ends or
passing a saw blade between the ends to get them to mate up perfectly
for soldering. “Gee, didn’t you think that that process might take a
little off of the length?” Hmmm. So, in practice a little extra on
the length can be helpful. I usually add about 1 mm, sometimes 2,
leaning towards more as the thickness increases, because I know I’m
going to cut/file it out. Or, as Charles Anderson suggests, something
close to 2 times the metal thickness.

It’s not an “accurate” formula that way, but takes into account the
practicalities of joining two ends of metal together. And, as has
been pointed out, if in the end you are off a thousandth of an inch
(or three) or half a millimeter even, it’s close enough for jewelry
work. I’ve never seen an accurate ring mandrel that was tapered. I
don’t own a step-by-step mandrel with a step for each half size;
don’t even know if they make them. And the way most people’s fingers
swell and contract with hydration, weather, and time of the month, a
quarter size is probably close enough for most. And most people’s
fingers aren’t round anyway, they are slightly rectangular in shape,
so I use one of those round-cornered, rectangular cross-sectioned
mandrels anyway for the final shape. People love the way they feel on
their hands as opposed to a round ring shank, so my shanks aren’t
round, so the formula for a perfect circle isn’t completely critical
to me, anyway, even if that’s what I teach students.

Denny Turner