Pi is the whole of the strip width
A welt strip wraps the cord completely. It comes up one side, over the top, down the other side, and the two raw edges finish up lying together where they get caught in the seam. That means the fabric has to cover the full circumference — pi times the diameter — and then carry a seam allowance on each edge as well.
For the 5/16 in cord in the form, the wrap is 0.982 in. Add half an inch of allowance on each edge and the strip is 1.982 in, which rounds to 2 in on the cutting table. That is the entire calculation and it is worth internalising, because the common errors both come from ignoring it: cutting to a remembered number that suited a different cord, and treating the diameter as if the fabric only had to go halfway round.
Round up rather than down. A strip an eighth narrow is a welt that sits proud of the seam and cannot be pulled in, and there is no fixing it afterwards.
Adding up the run
The run is boring and it is where the yardage actually comes from. Two cushions welted top and bottom is four seams, and each seam is the cushion perimeter plus a few inches for the corners and the tails. On the default 22 by 20 in cushion that is 84 in round plus 4 in of ease, so 88 in a seam and 352 in for the pair. Add 96 in of arm and back welting and the job is 448 in — a bit over 37 feet.
Corner ease is a real allowance rather than padding. Welt shortens as it turns a corner because the cord is on the inside of the turn, and you want enough tail at each end to bury the join. Four inches over four corners is a working figure and it is a field because your corners are not the ones in this example.
Strips, and why they are cut across
A crosswise strip is as long as the goods are wide. On 54 in goods with an inch of selvage off that is 53 in a strip, and 448 in of welt with a 2 in join allowance takes nine of them. Eight joins.
Cut the strips the other way, along the length of the goods, and twenty-six of them fit across the width. The cloth you need drops from 18 in to 17.2 in — under an inch of difference. What changes completely is the strips: twenty-six of them, 17.2 in long each, against nine at 53 in. Crosswise wins because a 53 in strip carries a whole cushion side without interruption, and that is the point of welting.
Where this flips is on very wide goods or a very short run. A 118 in sheeting gives crosswise strips nearly ten feet long, which is why railroaded goods and welt get along well. And if the whole job is 30 in of welt, none of it matters.
Joins are a placement problem
Eight joins on this job is eight places where the cord ends are trimmed back and the strip is overlapped, and every one of them can be seen if it lands on the front edge of a seat cushion. Experienced work does not leave that to chance. The front run of each cushion gets cut from a whole strip, the joins are placed at the back corners, and the leftover is what gets used on the parts nobody looks at.
That is a decision the calculator cannot make, because it does not know which edge of your job faces the room. What it gives you is the count, and the count is the thing to plan around.
Straight grain, and when it will not do
Everything above is straight-grain welt, which is what a boxed cushion with square corners normally gets. It turns a corner by being clipped and it lies flat down a straight run.
A curve is a different problem. Round a scroll arm, a round cushion or a tight radius, straight grain either pleats on the outside or drags on the inside, and the answer is bias strip cut at 45 degrees, which eases round the curve without either. Bias costs more cloth to produce than straight grain does, and getting a long continuous run of it out of a square is its own piece of arithmetic. This page does not attempt it and points at the one that does.
Questions people ask
How wide do I cut welt strips?
Cord circumference plus twice the seam allowance. For 5/16 in cord that is pi times 0.3125, which is 0.982 in, plus half an inch on each edge, giving 1.982 in — cut at 2 in. Round up rather than down, because a strip cut narrow makes a welt that stands proud of the seam and cannot be pulled back in.
How much welt cord does a chair take?
Add up every welted seam. Two cushions welted top and bottom, 22 by 20 in each, plus 96 in of arm and back welting comes to 448 in — 37 feet — before any take-up. The page adds whatever take-up and tail percentage you enter on top of that, because how much cord shortens as it is stitched in is a matter of your cord and your machine.
Should welt strips be cut on the bias?
Only where the welt has to turn a curve. Straight grain is normal for boxed cushions with square corners and it clips round them cleanly. Round a scroll arm or a round cushion, straight grain pleats on the outside of the curve and drags on the inside, and bias cut at 45 degrees is what eases through it. Bias costs noticeably more cloth to produce.
Why cut welt strips across the fabric rather than along it?
Because a crosswise strip is as long as the goods are wide, and long strips mean fewer joins. On 54 in goods that is 53 in a strip, so 448 in of welt takes nine strips and eight joins. Cutting the same amount lengthwise off the same piece of cloth gives you far more, far shorter strips, which is the same yardage and many more visible joins.
Where should welt joins go?
Wherever they will not be looked at, which usually means the back corners. The calculator gives you the count — eight on the default job — and the count is what you plan around: cut the front run of each cushion from a whole strip, put the joins at the back, and use the leftovers on the parts facing the wall.