How the backing is worked out
The backing has to be bigger than the quilt top. Quilting draws the layers in a little, and a longarm machine needs fabric to clamp onto, so most longarm quilters ask for 4″ extra on every side: 8″ added to the width and to the length. If you quilt it yourself you may manage with less, but the calculator assumes whatever you enter on all four sides.
Standard quilting cotton is 42–44″ wide, and about 40″ is usable once the selvages are trimmed, so most backings are pieced from two or three lengths. Each join is sewn with a 1/2″ seam pressed open, which takes 1″ off the width.
The calculator tries both ways: lengths running top to bottom (seams lengthwise) and lengths turned to run across the quilt (seams crosswise), and shows the one that needs less fabric. Turn it the other way if your print has a direction. Wide backing, 108″ or 118″ on the bolt, often covers a whole bed quilt in one piece.
Assumptions: the backing is centred under the top with the same extra on every side; fabric is bought by length and rounded up to the next 1/8 yard or 10 cm; shrinkage from prewashing is not included.
Worked example
A 60 × 72″ quilt top with 4″ extra needs a 68 × 80″ backing. Two 40″ widths sewn together make 79″, so cut two 80″ lengths: 160″, or 4 1/2 yards. Turned crosswise it would take three 68″ lengths, 204″, so lengthwise wins.