Why the square yields what it yields
The continuous bias method takes a square, cuts it corner to corner, offsets the two triangles and sews them into a tube with the cutting lines marked on it, then cuts the tube in one long spiral. What comes off is a single strip with one seam in it rather than a dozen joined pieces.
The yield is easy to reason about because nothing is thrown away in the middle: the strip is the square, rearranged. Area divided by strip width gives the length. An 18 inch square is 324 square inches; divided by a 2 inch strip that is 162 inches, or four and a half yards. That figure matches the yield tables printed in quilting references, which is a useful check that the reasoning is sound rather than a coincidence.
It is an approximation in one direction only — it is optimistic. Three things eat into it. The corners of the square end in tapers that are not full width. The tube seam takes a seam allowance out. And the beginning and end of the spiral are usually trimmed square. The yield loss percentage on this page is what accounts for all three, and ten percent is a reasonable working figure that gets worse on small squares, where the corners are a larger share of the area. Under about 15 inches, use 15 percent.
Working backwards to the square
If you know the length you need, the square side is the square root of length times strip width. Four yards of 2.5 inch strip is 144 inches; times 2.5 is 360; the square root is just under 19 inches. Gross that up for the yield loss first and it comes out closer to 20. The calculator does that ordering for you, which matters: taking the square root before applying the loss allowance understates the square by several percent.
One practical limit: the square has to fit across the goods. A 46 inch square cannot be cut from 44 inch fabric. Past that point you either cut two smaller squares and join the strips, or switch to cutting individual bias strips across a wider rectangle, where the same area rule applies but the strips come off as separate pieces to be joined.
When bias is worth the extra fabric, and when it is not
Bias strip is cut at 45 degrees to the grain, which is the direction a woven fabric stretches. That is the whole reason it exists:
- Curves. A cross-grain strip will not go round an outside curve without rippling or an inside curve without pulling. A bias strip eases round both.
- Welt and piping cord. Wrapping cord means the strip has to spiral slightly and shape round the corners. On the straight grain it fights you and crumples at every corner.
- Stripes, plaids and checks. Cut on the bias they become a diagonal, which is a design decision people make on purpose. On the straight grain they either line up perfectly or look like a mistake.
- Wear. Bias binding on an edge that gets handled distributes the strain across the weave instead of along one thread line.
Against that, bias costs more fabric for the same length of strip, takes more work, and stretches while you sew it, which can leave a wavy edge if you pull. On a straight-edged quilt with square corners, cross-grain strips are the normal and entirely defensible choice, and the quilt backing and binding calculator works those out directly. Save the bias for the edges that actually need it.
Cutting the square accurately
Everything about this method depends on the square being square and the first cut being at a true 45 degrees. Tear or pull a thread to find the grain before you measure, because the cut end off the bolt is rarely on grain and a square measured from a crooked edge is a rhombus. Mark the strip lines on the wrong side of the tube with a ruler before you cut, not as you go. And handle the finished strip gently: it is entirely bias, so it will grow several inches if you let it hang under its own weight, and that growth comes back out of the width.
Press with the iron lifted and set down rather than dragged. Dragging an iron along a bias strip stretches it, and a stretched binding applied to an unstretched edge produces ripples that no amount of pressing will remove afterwards.
Questions people ask
How much bias binding does an 18 inch square make?
About 162 inches of 2 inch strip in theory, which is four and a half yards, and roughly 145 inches once you allow around ten percent for the corner tapers, the tube seam and the trimmed ends. At 2.5 inches wide the same square gives about 130 inches theoretical and about 116 usable. The rule behind both figures is the same: area divided by strip width, then a deduction for the parts that do not come off as full-width strip.
What size square do I need for 5 yards of bias?
Five yards is 180 inches. At 2.5 inches wide that is 450 square inches before losses; gross it up ten percent to 500 and the square root is about 22.4 inches, so cut a 22.5 inch square. At 2 inches wide the same length needs 360 square inches, about 400 grossed up, and a 20 inch square. Note that the answer changes with the strip width, which is the field people most often forget to set before reading off the square.
Is the area formula exact?
No, and it should not be presented as one. It is the theoretical maximum: it assumes every square inch of the square ends up as usable full-width strip, which cannot happen because the corners taper and the tube has a seam in it. Treat the area figure as the ceiling and the yield loss percentage as the honest correction. If you cut continuous bias regularly, measure what you actually get from one square and use your own percentage from then on.
Can I use cross-grain strips instead of bias?
For straight edges with square corners, yes, and most quilt binding is made that way. Cross-grain strips are cheaper in fabric, easier to cut and do not stretch while you sew. What they will not do is go round a curve, wrap a cord neatly, or turn a stripe into a diagonal. If any edge on the piece curves at all, that edge needs bias even if the rest does not, and it is normally simpler to cut all of it on the bias than to change halfway round.
How much bias do I need for welt cord?
Measure the run of the seam the cord goes into, add generously for going round corners and for the join where the two ends meet, then work out the strip width from the cord diameter: the strip has to wrap the cord and leave two seam allowances. A rough guide is cord circumference plus twice your seam allowance, and the reliable method is to wrap a scrap round the actual cord and measure it. Corners eat more cord than people expect, so add ten to twelve inches over the bare perimeter.