Bias binding calculator
Binding is cut two ways, and the arithmetic differs. Straight-grain strips run across the roll, so the count is the length needed divided by the usable width, and the fabric bought is that many strip widths. Continuous bias seams a square into a tube and cuts round it, producing one unbroken strip: a square of side S yields about S² divided by the strip width, so the square needed is the square root of the length times the width. Only bias will go round a curve.
Your binding
Joins and finishing
0.5 m
4 strips of 4.8 cm. Rounded up to nearest 10 cm.
- Strip needed
- 430 cm400 cm to bind, plus 30 cm
- Cut each strip at
- 4.8 cmdouble fold (binds an edge)
- Strips to cut
- 43 joins between them
- Continuous bias would take
- 45.4 cmoff the same roll
Woven cloth stretches on the 45° diagonal and almost nowhere else, which is the entire reason bias binding exists. Straight-grain strips are fine on straight edges and square corners, and will ripple or pull on a curved hem, a neckline or a round cushion.
A strip runs the full width of the roll; the square uses only its own side and leaves the rest of the width bought and uncut. That is true at almost every run, so choose bias for what it does — going round curves, and giving one unbroken strip — rather than to save fabric. If you are cutting from a piece you already own rather than buying by the metre, the square is the more efficient of the two.
How we got this
- Strip width to cut — 4.8 cm1.2 cm finished × 4 for a double fold (binds an edge)
- Strip length needed — 430 cm400 cm to bind + 30 cm for joins and corners
- Strips across the roll — 4 strips430 cm ÷ 109 cm usable per strip
- Fabric off the roll — 19.2 cm4 × 4.8 cm strip width
Two ways to cut a binding strip
Binding is a long narrow strip, and there are two ways to get one out of a piece of cloth. They are not variations on a theme — the arithmetic is genuinely different, and so is what the strip can do.
Straight grain cuts strips across or along the roll and seams them end to end. Each strip is as long as the usable width, so the count is the length you need divided by that, rounded up, and the fabric you buy is that many strip widths. Simple, quick, and it will not go round a curve.
Continuous bias seams a square into a tube, offset by one strip width, and cuts round it in a spiral — which yields one unbroken strip with no joins you did not choose. Because it conserves area, a square of side S gives about S² ÷ strip width of binding, so the square you need for a given length is √(length × strip width). That is an identity rather than a rule of thumb, which is why it can be calculated exactly.
Why the strip is wider than the binding
A double-fold binding wraps the raw edge and folds back on itself, so the cloth has to go round four times its finished width. A single fold turns once and takes twice. Those are constructions, not conventions — the strip is doing the folding, and the arithmetic follows the geometry.
| Construction | Cut at | For 1.2 cm finished |
|---|---|---|
| Double fold (binds an edge) | 4× finished width | 4.8 cm |
| Single fold (turned once) | 2× finished width | 2.4 cm |
| Cut width entered directly | 1× finished width | 1.2 cm |
A worked example
400 cm of binding at 1.2 cm finished, double fold, cut on the straight grain from 112 cm cloth. These are the calculator's own starting values, so the table below is the arithmetic the tool runs rather than a retelling of it.
| Step | Working | Result |
|---|---|---|
| Strip width to cut | 1.2 cm finished × 4 for a double fold (binds an edge) | 4.8 cm |
| Strip length needed | 400 cm to bind + 30 cm for joins and corners | 430 cm |
| Strips across the roll | 430 cm ÷ 109 cm usable per strip | 4 strips |
| Fabric off the roll | 4 × 4.8 cm strip width | 19.2 cm |
Which method uses less cloth
There is a rule of thumb that bias costs 41 per cent more than straight grain. It describes cutting bias strips flat from a rectangle, where the triangular corners at each end of the cloth cannot be used — and avoiding exactly that loss is why the continuous-tube method was invented. The honest answer depends on what you are counting, so here are both.
| Binding needed | Straight: off the roll | Bias: square side | Straight: cloth used | Bias: cloth used |
|---|---|---|---|---|
| 100 cm | 9.6 cm | 25 cm | 11 dm² | 6 dm² |
| 200 cm | 14.4 cm | 33.2 cm | 16 dm² | 11 dm² |
| 400 cm | 19.2 cm | 45.4 cm | 22 dm² | 21 dm² |
| 800 cm | 38.4 cm | 63.1 cm | 43 dm² | 40 dm² |
| 1600 cm | 72 cm | 88.5 cm | 81 dm² | 78 dm² |
The two columns disagree, and both are true. By cloth consumed the bias square is the more efficient of the two at every run in the table: the tube wastes almost nothing while straight strips throw away both ends of every strip on joins. By metres off the roll — which is what you actually pay for — straight grain wins throughout, because a strip runs the full 112 cm of the roll while the square uses only its own side and leaves the rest of the width bought and uncut.
Those two only cross around the point where the square stops fitting the roll at all, which is not a usable answer. So the practical rule is the opposite of the folklore: if you are buying cloth by the metre, straight grain is the cheaper cut; if you are cutting from a piece you already own, the bias square gets more binding out of it.
None of which decides the question on a curve. Woven cloth stretches on the 45° diagonal and almost nowhere else — that is what the bias is — so a bias strip goes round a neckline, an armhole, a curved hem or a round cushion and lies flat, while a straight-grain strip ripples on the outside of the curve and pulls on the inside. Where the edge curves, cost is not the deciding input.
How to measure for this
- Measure the edge. The full perimeter of what you are binding. On a quilt that is twice the width plus twice the length; on a neckline, run a tape along the seam line.
- Decide the finished width. What will show once the binding is sewn down. Narrow binding suits a curve; wide binding suits a straight edge and a heavy cloth.
- Pick the fold. Double fold encloses a raw edge and is cut four times the finished width. Single fold is turned once and cut twice.
- Choose the grain. Bias for anything curved, straight grain for straight edges and square corners. The calculator costs both either way.
- Add for corners and joins. Mitring each corner and closing the run both take a little. 30 cm covers a quilt; more if there are many corners.
If the square the calculator asks for is wider than your fabric, cut two smaller squares and make two strips, joining them once — two squares of about seven-tenths the side hold the same area between them, and the extra join is a small price for a strip that would otherwise not exist.
What this assumes
- The continuous-tube method for bias, not strips cut flat and seamed. Flat cutting wastes the corners and needs roughly a third more cloth.
- One square, if it fits. The calculator warns when the square is wider than the roll rather than silently assuming you can find one.
- Diagonal joins on straight-grain strips, which is why each strip loses a little at both ends. A straight join is bulkier and shows more.
- No shrinkage or pre-wash allowance. Binding is narrow enough that shrinkage rarely decides anything, but pre-wash it with the thing it is binding.
- Rounding is always up, at every step. Running out of binding two-thirds of the way round a quilt is the worst possible time to discover a dye-lot change.
For piping on a cushion, which is the same strip round a cord, the cushion fabric calculator includes it in the piece list and packs it with everything else. For the cut-versus-finished arithmetic behind any of this, see the seam allowance calculator.
Common questions
- How big a square do I need for continuous bias binding?
- The square root of the strip length times the strip width. For 5 metres of binding cut at 5 cm, that is √(500 × 5) = 50 cm square. The method conserves area almost exactly, which is the whole reason it exists — cutting bias strips flat from a rectangle wastes the triangular corners at each end.
- How wide should I cut binding strips?
- Four times the finished width for a double fold that encloses an edge, twice for a single fold turned once. So a 1.2 cm finished double-fold binding is cut at 4.8 cm. These are the constructions rather than conventions: the cloth has to go round the edge and back on itself.
- Is bias binding really more expensive than straight grain?
- It depends what you are counting, and the calculator shows both. Measured in metres off the roll — what you pay for — straight grain wins throughout, because a strip runs the full roll width while a bias square uses only its own side. Measured in cloth consumed, the square wins, which is what matters when you are cutting from a piece you already own. The old 41-per-cent rule describes cutting bias strips flat, which is exactly what the continuous-tube method avoids.
- When do I have to use bias rather than straight grain?
- Whenever the edge curves. Woven cloth stretches on the 45° diagonal and almost nowhere else, so a bias strip goes round a neckline, an armhole, a curved hem or a round cushion and lies flat. A straight-grain strip on the same curve ripples on the outside and pulls on the inside.
- My bias square is wider than my fabric. What now?
- Cut two smaller squares and make two strips, joining them once. Two squares of about seven-tenths the side give the same total area, and one extra join is a small price. Alternatively cut on the straight grain if every edge you are binding is straight — there is no advantage to bias on a square corner.
Related tools
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