Wire per ring, and why it is not pi times the mandrel
A ring wound on a mandrel bends round its own centreline, not round its inside face. So the length of wire in one ring is:
wire per ring = pi x (inside diameter + wire diameter)
On a 4 mm mandrel in 1 mm wire that is pi times 5, or 15.71 mm. Using pi times 4 instead gives 12.57 mm and undercounts the wire by exactly 20 percent, which on a thousand-ring project is three metres you did not order.
The proportion of the error goes with the wire diameter against the mandrel, so it gets worse for heavy wire on small mandrels. On a 2 mm mandrel in 1.5 mm wire, the mandrel-only figure is short by 43 percent.
Aspect ratio
Aspect ratio is the inside diameter divided by the wire diameter, and it is how weaves are specified because it is scale-independent. A weave that works at AR 4 works at AR 4 whether the rings are 2 mm or 8 mm across. Below a weave working ratio the rings will not pass through each other; well above it the weave goes loose and drapes differently.
What ratio a particular weave wants is a property of that weave and comes from whoever wrote it up. This page is not going to tell you, because it does not know, and a number pulled out of the air here would be worse than useless. What it will do is convert in both directions: what ratio your current mandrel and wire give, and what mandrel would give a ratio you have been handed.
| Wire | Mandrel for AR 3 | AR 4 | AR 5 | AR 6 |
|---|---|---|---|---|
| 0.6 mm | 1.8 mm | 2.4 mm | 3.0 mm | 3.6 mm |
| 0.8 mm | 2.4 mm | 3.2 mm | 4.0 mm | 4.8 mm |
| 1.0 mm | 3.0 mm | 4.0 mm | 5.0 mm | 6.0 mm |
| 1.3 mm | 3.9 mm | 5.2 mm | 6.5 mm | 7.8 mm |
That table ignores springback, which is real: rings wound on a mandrel open a little when they come off, and how much depends on the alloy and its temper. Dead soft copper barely moves. Hardened sterling moves enough to matter. The only way to know is to wind ten, take them off and measure, which is why springback is a field rather than a constant.
What the saw takes
Cutting a coil into rings with a jeweller saw removes a kerf of metal per ring — call it 0.3 mm, though blade and technique both move it. Against 15.71 mm of wire per ring that is 1.9 percent, which is small. Against a 2.5 mm ring in 0.6 mm wire, where the wire per ring is 9.7 mm, it is 3.1 percent. It scales the wrong way: the smaller the rings, the more of the wire the saw eats.
Flush cutters take almost nothing but leave a pinched end that has to be dressed, so the metal comes off at the file instead. Neither way is free and neither is worth agonising over next to the coil ends, which on a short coil can be more waste than every cut put together.
Turning a chain length into a ring count
Links per inch is where formulas stop being useful. For a simple round-link chain hanging under its own weight, the pitch is somewhere between the inside diameter and the outside diameter depending on how the links sit, and any weave more complicated than that has no simple relationship at all. So this page takes links per inch as a measurement.
Get it by closing twenty rings into a length, hanging it the way the finished piece will hang, and measuring. Twenty is enough that the end effects wash out. A 20 inch chain at 6 links an inch is 120 rings, and at 4 mm ID in 1 mm sterling that is 1.9 m of wire and about 15 g of metal before the clasp.
The number that decides whether it is worth making
Ring count is a proxy for time, and weaves multiply it. A byzantine or a persian chain uses several times the rings of a simple one for the same finished length, and every one of them is opened, threaded and closed by hand. At twelve rings a minute — a reasonable working pace, not a sprint — 120 rings is ten minutes and 1,200 rings is a solid afternoon.
Time your own rate over five minutes of ordinary work rather than a burst, put it in the field, and the page will do the multiplication. It does not include winding, sawing, annealing, tumbling or the ones that spring open at the wrong moment, so treat what comes out as the floor.
Questions people ask
How much wire does one jump ring use?
Pi times the inside diameter plus the wire diameter, because the wire bends round its own centreline. A ring with a 4 mm inside diameter in 1 mm wire uses 15.71 mm, not the 12.57 mm you get from pi times the inside diameter alone. That is a 20 percent difference, and it gets worse for heavy wire on small mandrels.
What is aspect ratio in chainmaille?
Inside diameter divided by wire diameter. It is scale-independent, so a weave specified at AR 4 behaves the same whether the rings are 2 mm or 8 mm. What ratio any particular weave needs comes from whoever documented that weave, not from arithmetic. This page converts between a mandrel size and a ratio in both directions and takes no view on which ratio is right.
How many jump rings are in a 20 inch chain?
It depends entirely on the weave and how the links sit, which is why links per inch is a measurement rather than a calculation. At six links an inch a 20 inch chain is 120 rings. Close twenty rings into a length, hang it the way the piece will hang, and measure — a figure derived from geometry will not survive contact with a real weave.
What size mandrel do I need for a given aspect ratio?
Aspect ratio times the wire diameter, adjusted for however much your rings spring open coming off the mandrel. AR 4 in 1 mm wire wants a 4 mm mandrel if there is no springback. Springback depends on the alloy and its temper — dead soft copper barely moves, hardened sterling moves enough to matter — so wind ten and measure rather than assuming.
How much does jump ring chain weigh?
A 20 inch chain of 120 rings at 4 mm inside diameter in 1 mm sterling wire is about 15 g, ignoring the clasp. Each ring is 15.71 mm of wire with a 0.785 sq mm cross-section, which at 10.36 g per cm3 is 0.128 g. Wire diameter dominates: the same chain in 1.3 mm wire weighs about 80 percent more per ring at the same inside diameter.