Weight per Metre, Coil Length and Why the Kilogram Is a Moving Target

Steel wire is bought by weight and consumed by length. Those two numbers are linked by the cross-section, and the cross-section is the one part of the order that always carries a tolerance. That is why two coils of the same nominal size can contain measurably different lengths, and why a purchase order that states only a weight leaves the length to chance.

The Only Formula Needed

Mass per metre follows directly from the density and the cross-section:

m = density x pi x d squared / 4

With density in g/cm3 and diameter in mm, the practical form for shop use is a single coefficient: kg/m = 0.00623 x d squared for 304, and a slightly different coefficient for each grade because the densities differ.

Applied to common sizes in 304: 0.5 mm gives 0.0016 kg/m, so 1 kg is about 640 m. 1.0 mm gives 0.0062 kg/m, or about 160 m per kg. 3.0 mm gives 0.056 kg/m, about 18 m per kg. 6.0 mm gives 0.224 kg/m, about 4.5 m per kg. 12 mm gives 0.897 kg/m, about 1.1 m per kg.

The coefficient is worth carrying in a notebook. It converts a coil weight into a length, a length into a weight, and a price per kilogram into a price per metre, which is the number the production planner actually needs.

Why the Kilogram Does Not Fix the Length

Mass depends on the square of the diameter, so the length inside a fixed weight depends on the inverse square. A coil wound from wire at the top of its tolerance band contains less length than one at nominal, for the same weight.

As an example, 6.00 mm wire at plus 1 percent measures 6.06 mm. Its mass per metre rises by about 2 percent, so 1,000 kg of it contains about 2 percent less length than 1,000 kg of nominal wire. On a 3 mm wire held at plus or minus 0.02 mm, the band alone accounts for roughly 1.3 percent of length at each end of the range. None of this is a defect; it is arithmetic, and it becomes a commercial argument only when the basis of the order was never stated.

Three Ways to Establish the Length in a Coil

• From the net weight. The most reliable method, because the length and the mass are the same measurement. Weigh the coil, subtract the carrier and packaging, divide by mass per metre calculated from the measured diameter, not the nominal one.
• From the coil geometry. For a level-wound coil, the length is close to L = pi x (outer diameter squared - inner diameter squared) / (4 x d). It is an estimate, because winding tension compresses the inner layers and the build is never perfectly rectangular, but it is adequate for scheduling and for checking that a delivered coil is plausible.
• From a counter. A measuring wheel or encoder gives length directly, with an accuracy limited by slip. Useful for cutting lines, less so for goods-inward checks unless the wheel is calibrated against a known length.

Do not mix the methods in one calculation. Weighing the coil and then converting with nominal diameter instead of measured diameter reintroduces the tolerance error that the weighing was supposed to remove.

What Has to Be Deducted

Gross weight is not wire weight. Coils on carriers arrive with a spool or a wooden drum, and the packaging adds strapping, wrapping and sometimes a desiccant. On a 25 kg spool the carrier can be a meaningful share of the gross figure. The purchase order should state whether the quantity is gross, net of packaging, or net of carrier, and that single sentence prevents most weight disputes.

Welded Joints Change the Count

A coil is not always one continuous length. Mills join wire to reach a coil weight, and the joint is a real feature that the buyer needs to know about:

• How many. State a maximum number of joints per coil, and per tonne, rather than leaving it to practice.
• How marked. A joint flagged with a tag or a coloured tie lets the operator stop the line before the joint reaches the die, instead of discovering it when the feed jams.
• How made. A butt weld has a local heat-affected zone and a slight diameter increase. On small wire it may fail in a guide bush before it reaches the tool; on drawn wire the joint may also be softer or harder than the parent metal.
• Where permitted. Some processes, pressure-containing parts and food-contact components, do not accept joints at all. Say so explicitly if that applies.

Grade and Size Reference

Wire Specification

Weight is what the invoice measures. Length is what the machine consumes. Converting between them with the measured diameter, and stating the joints and the tare on the order, removes most of the difference between the two.