The sheet, then the roll
Two numbers decide everything on this page. The first is the cut sheet: the hoop plus a margin on every side, because a sheet the size of the hoop cannot be gripped and cannot be hooped. A 6.5 inch hoop with a one inch margin needs an 8.5 by 8.5 sheet. The second is how many of those sit across the roll width.
On a 20 inch roll, an 8.5 inch sheet goes across twice with three inches left over. That three inch strip is scrap on every yard you unroll, and over a 100 yard roll it is 300 linear inches of a strip you paid for. Two sheets across at 8.5 inches deep gives 8.5 sheets a yard.
Where turning the sheet helps
When the hoop is square, turning the sheet changes nothing, and the page says so. When it is not — a 5 by 7 hoop, say, or a cap frame — the two orientations give genuinely different yields, and which one wins is not obvious. The page lays the sheet both ways, works out yards per sheet for each, and takes the better one.
The thing to notice is that the better orientation is the one with the lowest pitch divided by the number across, not the one with the most across. Three narrow sheets across a roll that then advances a long way down can be worse than two wide ones that advance a short way.
Margin is a step function
Adding a quarter inch of margin usually costs you nothing at all, and then one day it costs you a third of the roll. That is because the number across the width is a floor division: it does not move at all until the sheet crosses a boundary, and then it drops by a whole sheet. On a 20 inch roll with a 6.5 inch hoop, the sheet fits twice across up to a margin of 1.75 inches, and at 1.8 it fits once.
The page prints the yield at your margin and at half an inch more, so you can see whether you are sitting comfortably inside a band or one hooping habit away from the edge of one. If you are close to a boundary, either trim the margin or buy a width where you are not.
What it costs, and what it does not
On the defaults — 120 garments, one placement, one layer, 8.5 inch sheets off a 20 inch by 100 yard roll at 45 dollars — the backing under one garment is a few cents. Nobody wins or loses a job on that. What the page is actually useful for is the buying decision: how many rolls to have on the shelf before a run starts, and whether the roll width you keep re-ordering is the right one for the hoops you actually use.
It counts only the backing. Topping, whether that is a water soluble film over a pile knit or anything else laid on top, is a second material off a second roll. Run the page again with that roll and add the two.
Questions people ask
How big should a backing sheet be for a hoop?
Bigger than the hoop on every side, by enough that you can hold and grip it while hooping. The page takes your hoop dimensions and your own margin rather than asserting one, because the margin depends on the hoop style and on whether you are hooping the backing with the garment or floating it. A one inch margin on a 6.5 inch hoop gives an 8.5 by 8.5 sheet.
How many sheets do I get from a roll of backing?
The number across the width times the number of rows down the length, both rounded down. On a 20 inch roll, 8.5 inch sheets go two across, and a 100 yard roll gives 423 rows, so 846 sheets. Change the hoop by half an inch and that can drop to one across and half as many, which is why it is worth calculating rather than estimating.
Is a wider roll of stabiliser cheaper?
Only if the sheet fits it well. A wider roll that leaves a wide unusable strip on every yard can work out dearer per sheet than a narrower roll the sheet fits exactly. The comparison field on the form lays your sheet on a second width so you can see the yards each one needs for the same run, and that is the figure to put next to the two prices.
Does this account for cutting the leftover strip into smaller pieces?
No. It assumes a plain grid with no nesting and no use of the offcut strip, which is what cutting by hand with a straight edge produces. If you cut on a plotter or a die and use the strip for small left chest pieces, you will do better than this figure, so treat it as an upper bound on consumption.
How many layers of backing does a knit need?
That is a decision about the garment and the design, and this page does not make it. It counts what the decision consumes once you have made it: set the layers field to what you actually lay in, and the sheets, yards and rolls follow.