Coil calculator: weight, length, diameter and PIW
For metal coil: steel, stainless, aluminium, copper and brass. Enter what you know and it gives you the rest, in metric or imperial, plus the two numbers most coil calculators leave out, which are what one slit strip weighs and how many of them fit across the width.
Densities are nominal for the grade, so a weight from geometry is an estimate and not a weighbridge figure. Coating, temper and grade all move it. Length and diameter do not depend on density and are exact for the numbers you typed.
There is only one idea here
A coil is a long flat strip that has been rolled up, and rolling it up does not change how much metal is in it. So the ring of metal you see looking at the end of the coil has exactly the same area as the strip would have if you unrolled it and looked at it edge on.
That gives two ways of writing the same area, and everything else is those two lines rearranged:
Which is why length does not depend on width, and why width does not appear in the length formula at all. It also explains something that catches people out: doubling the outside diameter roughly quadruples the weight, because the diameter is squared.
The formulas
| You want | Formula | Units |
|---|---|---|
| Weight | A x width x density | mm, g/cm³, divide by 1e6 for kg |
| Length | A / thickness | mm, divide by 1000 for m |
| OD from length | sqrt(ID² + 4 x L x t / pi) | L and t in mm |
| OD from weight | sqrt(ID² + 4 x A / pi) | A from weight and density |
| PIW | weight / width | lb and inches |
| Slit strip weight | parent weight x slit width / parent width | same gauge throughout |
Density is the only input that is not a measurement of your coil. It is nominal for the grade, so a weight computed from geometry is an estimate: coating, temper and grade all move it, and a galvanised coil weighs more than the base steel it started as. Length and diameter do not involve density at all and are exact for the numbers you type.
A worked example
Cold rolled steel, 1500 mm outside diameter on a 508 mm mandrel (a 20 inch mandrel), 1250 mm wide, 1.00 mm gauge, density 7.85 g/cm³.
- Area. (pi / 4) x (1500² minus 508²) = 1,564,463 mm²
- Weight. 1,564,463 x 1250 x 7.85 / 1e6 = 15,351 kg
- Length. 1,564,463 / 1.00 / 1000 = 1,564 m
- Check it. Length x thickness x width x density has to give the weight back: 1564.46 x 1000 x 1.00 x 1250 x 7.85 / 1e6 = 15,351 kg. It does, so the two formulas agree.
- PIW. 15,351 kg is 33,844 lb, and 1250 mm is 49.21 in, so 688 lb per inch of width.
- One 152 mm strip. 15,351 x 152 / 1250 = 1,867 kg, and eight of them fit across 1250 mm with 34 mm left for edge trim.
Slit coil weight, and why PIW makes it easy
Slitting changes width and leaves gauge and length alone, so a slit strip is the parent coil scaled by width. That is the whole calculation, and it is why the trade quotes PIW: once you have pounds per inch of width, a strip's weight is just PIW times its width, whatever the coil it came from.
A useful consequence: a slit strip has the SAME PIW as the coil it was cut from. If you work out a strip's PIW and it differs from the parent, one of your numbers is wrong.
The width that is not sold is edge trim plus whatever is left over from the pattern. That leftover is a planning decision rather than an arithmetic one, and it is what the slitting calculator is for: it works out the knife positions and spacer widths that turn this coil into that set of strips.
What this will not tell you
- Whether the coil clears your uncoiler or the crane. Compare the outside diameter against your own limits.
- Whether your tooling can actually build that slit pattern. That depends on the spacers you hold, and it is the question OptiStack Pro answers against your real inventory.
- An exact weight. Nominal density is not your coil's density. For anything commercial, weigh it.
Next
You have the coil. Now work out the knife and spacer stack that cuts it, then check the clearance for the grade on the slitting machine guide.
Open the slitting calculator