Circumference of the middle, not of the hole
Bending a strip into a ring stretches the outside and compresses the inside. Only a line somewhere in between keeps the length it started with, and on plain rectangular stock that line sits close enough to mid-thickness to use it. So the blank you cut is the circumference of a circle drawn through the middle of the metal:
blank length = pi x (inside diameter + stock thickness), which is the same as inside circumference + pi x thickness.
With the defaults on this page — a size 7 on a scale reading 36.48 mm at size 0 with 2.5654 mm per size, in 1.5 mm stock — the inside circumference is 54.44 mm, the thickness adds 4.71 mm, and the blank is 59.15 mm. Cut it at 54.44 instead and the ring lands near a size 5.2.
What the thickness costs in sizes
Divide the thickness allowance by the millimetres per size and you get the answer directly. At 2.5654 mm per size, pi times the thickness is worth roughly 1.22 sizes per millimetre of stock:
| Stock thickness | Added to the blank | Sizes it is worth |
|---|---|---|
| 0.8 mm | 2.51 mm | 0.98 |
| 1.0 mm | 3.14 mm | 1.22 |
| 1.5 mm | 4.71 mm | 1.84 |
| 2.0 mm | 6.28 mm | 2.45 |
| 3.0 mm | 9.42 mm | 3.67 |
This is why the mistake is expensive on heavy stock and forgivable on thin. A 0.8 mm wedding band cut without the allowance is a size small, which is annoying. A 3 mm gents band cut the same way is nearly four sizes small, which is a new blank.
Two constants that are yours, not ours
Ring sizing is a trade convention, not a physical constant, and gauge sets do not all agree. The two numbers that define a scale — the circumference at the bottom of it, and the step between whole sizes — are fields on this page for that reason. If your gauges read a quarter size against somebody else, the difference is in those two numbers. Slide your own gauges onto a mandrel and measure them if you want to know what scale you are actually working on.
The same goes for anything a scale cannot capture. A 8 mm wide band feels tighter on the same finger than a 2 mm one, a domed inside feels looser than a flat one, and knuckles change the whole question. How many quarter sizes you add for those is a bench judgement built out of your own returns, so the page takes it as a number you type rather than pretending to know it.
Where the simple formula stops
Everything above assumes even thickness all the way round and a strip that actually bends. Three common cases break that:
- Tapered shanks. The thickness varies, so the neutral line is not at a constant depth. Develop the heavy and light sections separately or bend a test piece.
- Sections that do not bend. A cast head, a soldered-on setting or a wide flat top does not compress and stretch with the rest of the ring. The bending allowance applies only to the part that bends.
- Forged rings. Anything hammered rather than rolled moves metal instead of merely curving it, and the finished length has nothing to do with what you started with.
Sizing up after the fact
The same arithmetic runs backwards. To open a finished ring by one size you are adding one size worth of circumference at the neutral axis, which is the millimetres-per-size figure on this page — 2.5654 mm on the default scale — and that is the length of the piece you solder in, before any kerf. Stretching on a mandrel gets there by thinning the shank instead, which is why there is a limit to how far it goes before the band is noticeably lighter than it was.
Questions people ask
How much longer than the inside circumference should a ring blank be?
Pi times the stock thickness. On 1.5 mm stock that is 4.71 mm, on 3 mm stock it is 9.42 mm. The reason is that the inside of a bent strip compresses and the outside stretches, so the length that stays put is the one running through the middle of the metal, and that circle is one thickness bigger in diameter than the hole.
What length blank do I cut for a size 7 ring?
It depends entirely on the stock. On the sizing scale in this page, a size 7 has a 54.44 mm inside circumference. In 1.0 mm stock the blank is 57.58 mm, in 1.5 mm it is 59.15 mm, and in 3 mm it is 63.86 mm. The size number alone does not answer the question, which is the single most common way a blank comes out wrong.
Why does my ring come out smaller than the blank suggests?
Two usual causes. Either the thickness allowance was left out, which loses about 1.2 sizes per millimetre of stock, or the calculation was right and the forming shrank it. Sanding a solder seam and truing on a mandrel usually add size rather than remove it, so a ring that ends up small is nearly always a short blank. Bend a scrap in the same stock and measure the result.
Do wide bands need to be cut larger?
Most benches add something, and how much is a judgement rather than a formula. A wide band bears on more of the finger and cannot rock past a knuckle the way a narrow one does, so the same measured size feels tighter. This page takes the adjustment as a field you fill in from your own experience rather than baking in a number, because the right amount depends on the profile, the inside finish and the customer.
How much metal do I add to size a ring up?
One size worth of circumference at the neutral axis for each size, which is the millimetres-per-size figure your scale uses — 2.5654 mm on the default scale here — plus whatever your saw kerf takes. Going up two sizes is a little over 5 mm of shank. Stretching instead thins the shank to get the same circumference, which is why heavily stretched rings feel light.