Sold by weight, used by length
Music wire comes in coils described by weight. Strings are cut to a length. The bridge between the two is the weight of a foot of wire, which is the density times the cross sectional area, and area is where the trouble starts, because it follows the square of the diameter.
At 0.283 lb per cubic inch, a pound of 0.0290 in wire runs to about 446 feet. The same pound of 0.0475 in wire runs to about 166 feet. That is 2.68 times as much wire out of an identical coil, and 0.0475 divided by 0.0290, squared, is also 2.68. The two facts are the same fact.
The practical version is that intuition built on one end of the plain section is wrong at the other end. A coil that comfortably covered a treble run will not cover the same number of notes further down, and it is not close.
Strings per coil, not pounds
Total weight tells you what the job consumes and almost nothing about what to order, because you cannot buy a fraction of a coil and a leftover of one gauge does nothing for another. What decides the order is how many complete strings come out of one coil of each size.
Run the defaults and the whole plain section weighs about two pounds, spread over ten gauges. Nobody buys two pounds. Every run needs a coil of its own gauge, and one 1 lb coil of any of these sizes covers its run several times over — the heaviest run, at 0.0475 in with 41 in strings, still gets thirty nine complete strings out of a pound while only needing fifteen. So the order is ten coils, the total weight never enters into it, and the 7.9 lb left over is stock on the shelf rather than waste.
The number that would change that is strings per coil falling below the strings a run needs. On a small coil size, on a long-scaled instrument, or on a run covering a lot of notes, it does, and then the second coil is decided by a handful of strings at the end of the run. The page prints strings per coil beside every run so it is visible before the order goes in rather than afterwards.
The extra per string
Speaking length is the part that vibrates. It is not the part you cut. Between the tuning pin and the hitch pin there is the becket, several turns on the pin, the run past the agraffe or under the capo, and the wrap at the hitch, plus whatever gets trimmed. The allowance for all of that is a single field on this form and it deserves more respect than it usually gets.
Nine inches is a placeholder. Get your own by pulling one old string, straightening it against a tape, and subtracting the speaking length you measured on the instrument. Be three inches out across two hundred strings and you are fifty feet of wire adrift, which on the heavier gauges is a whole coil.
What the mean length hides
Each line of the form covers a run of notes with one mean speaking length. Real lengths change note by note, and near a break they change quickly. Using a mean is fine for the total weight, because the errors above and below cancel, and it is not fine when a run lands near a coil boundary, because there it is the last string that decides whether a second coil has to be ordered.
Where a run comes out close, split it into two or three shorter lines with their own lengths and run it again. Nothing else in the arithmetic changes and the answer gets sharper exactly where sharpness is worth having.
None of this covers the wound bass strings. Those are a core wire with a wrap over it, made to a length and a mass for one specific note, and they are ordered or made individually. They are a separate list with a separate lead time, and the plain wire arithmetic here says nothing about them.
Questions people ask
How many feet of piano wire are in a pound?
It depends entirely on the diameter, and on the square of it. At 0.283 lb per cubic inch a pound of 0.0290 in wire runs to about 446 feet and a pound of 0.0475 in wire to about 166 feet — the same coil weight giving 2.68 times the length, because 0.0475 over 0.0290, squared, is 2.68. Enter your own density from the supplier data sheet and the page prints the figure for every gauge in your scale.
Why does the calculator order by gauge instead of by total weight?
Because leftover wire of one diameter does nothing for a run of another diameter. The rounding up to a whole coil happens separately for each size, so a job in ten gauges rounds up ten times and the total weight decides nothing. What the weight total is good for is knowing what the job consumes; what decides whether a run needs a second coil is strings per coil against strings in the run, which is printed beside every line.
What should I use for the extra wire per string?
A measurement rather than a guess. Pull one old string out, straighten it against a tape, and subtract the speaking length you measured on the instrument — the difference is the becket, the pin turns, the hitch wrap and the trim for that instrument. The nine inches sitting in the field is a placeholder to replace. It is the input people are furthest out on, and being three inches wrong across two hundred strings is about fifty feet of wire.
Does this cover the wound bass strings?
No, and it says so in the results. A wound string is a steel core with a wrap over it and it is made or ordered for one note, to a length and a mass, rather than cut from a coil. The plain wire arithmetic here applies only to the notes you list in the form as plain. The bass section is a separate order, usually with a separate and longer lead time, and it is worked from the old strings or from the scale rather than from a coil count.
Can I trust the gauge numbers instead of measuring?
Gauge numbering for music wire is a supplier convention rather than a standard, and half a thousandth of disagreement between two suppliers using the same number is not unusual. Half a thousandth on a thirty thousandth wire is about three percent of the weight and three percent of the length out of a coil, which matters for the order and matters much more for the tension the string will end up carrying. A micrometer settles it, and the field on this form takes a diameter rather than a gauge number for that reason.