Narrow Piece First: Does Row Order Change Yardage?
Packing order can change how many pieces a remnant supplies, and that changes how many rows of the wide piece you still need from new fabric. The question is not which order feels tidier. It is whether the narrow piece, packed across the remnant first, leaves a strip that still holds the wide piece, or whether the wide piece should claim the remnant's full width first.
Run the remnant packing twice and compare the wide piece's new-fabric row count. In the supplied example, nine pieces are needed, each cut 24 by 20 inches with allowances already included, the usable width is 45 inches with no rotation, the remnant is 44 inches long, and the shop increment is 6 inches. Assume both fabrics have completed any chosen preshrink treatment before measuring these usable dimensions, so the 45-inch usable width, the 44-inch remnant length, and the 24 by 20 inch cut pieces are all post-wash measurements. Wide-first gives one piece across, two full rows in the remnant, two pieces from the remnant, seven still needed, 140 inches of new cut length, and a rounded purchase of 144 inches. The narrow-first pass is a separate calculation you must run yourself; do not assume it improves the count.
Why packing order is a real variable, not a preference
A remnant is a fixed length you already own. Whatever it absorbs is subtracted from the cut list before you round the purchase. If the narrow piece takes a column of the remnant's usable width, the wide piece may lose the ability to fit across at all, which can push every wide piece onto new fabric. If the wide piece takes the width first, the narrow piece may be squeezed into a side strip that is too narrow for it.
The two orders are not symmetric because the pieces have different widths. Pieces across equals the whole-number result of usable width divided by the piece width. A 45-inch usable width holds one 24-inch wide piece with 21 inches left over, and it holds one 24-inch piece plus one narrow piece only if the narrow piece is at most 21 inches wide. That leftover strip is the whole battleground.
Keep the remnant's usable width separate from its nominal width. Selvage, a printed border, a skewed edge, or a damaged strip all reduce what you can cut. Measure across the remnant at more than one point and use the smallest repeatable width when the fit is tight. The calculation method walks through that measurement discipline, and the same discipline applies to the new bolt you intend to buy.
The wide-first pass, step by step
Wide-first means the wide piece claims the remnant's width before anything else is placed. Pieces across equals floor(45 ÷ 24) = 1. Rows available equals floor(44 ÷ 20) = 2. Remnant pieces equals 1 × 2 = 2, capped at the nine pieces required. Remaining pieces equals 9 − 2 = 7. New cut length equals ceil(7 ÷ 1) × 20 = 140 inches. Rounding 140 inches up to the next 6-inch increment gives 144 inches to purchase.
The inserted table records exactly this pass: one piece across, two full rows in the remnant, two pieces from the remnant, seven still needed, 140 inches of new cut length, and a 144-inch rounded purchase. Read it as the wide-first baseline, not as a universal answer. The table does not contain a narrow-first column, so any narrow-first figure you see elsewhere is a separate calculation.
Note what the leftover strip looks like here. One 24-inch column occupies 24 of the 45 usable inches, leaving a side strip 21 inches wide running the full 44-inch remnant length. A narrow piece up to 21 inches wide and up to 44 inches long could sit in that strip without disturbing the wide piece's two rows. That is the case where narrow-first and wide-first can agree, because the narrow piece never needed the wide piece's column.
Running the narrow-first pass and comparing row counts
Narrow-first means you place the narrow piece across the remnant first, then ask what width remains for the wide piece. Take a concrete narrow piece: 10 inches wide, 12 inches long, three needed, allowances already included, no rotation. Placed first, it occupies 10 of the 45 usable inches, leaving 35 inches. The wide piece still fits across because floor(35 ÷ 24) = 1. The wide piece's row count is unchanged at one across, so the wide piece still needs ceil(7 ÷ 1) = 7 rows and 140 inches of new fabric. The narrow pieces fit in the same side strip: floor(21 ÷ 10) = 2 across and floor(44 ÷ 12) = 3 rows gives 6 pieces against the 3 needed, so this order changes nothing about the wide piece's new cut length.
Now widen the narrow piece to 22 inches, keep its length at 12 inches and its quantity at three, and keep rotation prohibited. Placed first, it occupies 22 of the 45 usable inches, leaving 23 inches. The wide piece no longer fits across because floor(23 ÷ 24) = 0. Every wide piece moves to new fabric: nine pieces at one across needs ceil(9 ÷ 1) = 9 rows, and 9 × 20 = 180 inches of new cut length, 40 inches more than the wide-first 140 inches, and a 180-inch rounded purchase versus 144 inches — 36 inches more.
The comparison you want is the wide piece's new-fabric row count under each order, not the total piece count. Write both passes on one sheet: pieces across for each piece size, rows available in the remnant, pieces supplied, pieces remaining, and the new cut length for the wide piece. If the two orders give the same wide-piece row count, choose the order that leaves the cleaner side strip or the better grain alignment. If they differ, the order that keeps the wide piece across the remnant usually wins, because the wide piece is the one that cannot be squeezed.
Rotation is a separate decision from packing. If the pattern, grain, nap, or one-way print forbids turning a piece ninety degrees, then only the entered orientation counts, and a strip that would fit a rotated piece does not fit at all. Record that restriction before you count anything. The row logic here is the same one described in how to cut repeated rectangles with less waste, applied to two piece sizes instead of one.
Units, tolerances, and the exact inch
The inch is a defined unit, not an estimate. The NIST length page records the 1959 agreement that made the inch exactly 25.4 millimeters, and the NIST conversion-factor appendix lists the inch-to-centimeter factor as 2.54. That matters when a remnant is described in centimeters and your cut list is in inches, or when you compare a metric listing against a 24-inch cut.
Exact conversion does not make your measurement exact. A 24-inch cut piece is 24 inches only if your ruler, your marking, and your cutting are consistent. The remnant's usable length is whatever survives squaring the end, and the usable width is whatever survives the selvage and any defect. Treat the calculated 140 inches as a geometric requirement, then add your own trimming margin before you treat measured fabric as usable.
Rounding belongs at the end. Convert the new cut length into the seller's increment and round up only after the remnant has already absorbed its share. If you round first and subtract later, you can buy a length that no longer matches the pieces you still need.
Failure modes that make the comparison meaningless
The most common error is subtracting more pieces than the project needs. If the remnant supplies more pieces than the cut list requires, cap the remnant count at the total and stop. A second error is treating a fractional row as a whole row. Seven pieces at one across needs seven rows, not six and a half, and ceil(7 ÷ 1) = 7 is what produces the 140-inch figure.
A third error is mixing the two orders in one calculation. If you count the narrow piece in the remnant and then also count the wide piece as if it had the full width, you double-book the same fabric. Run each order as a complete, separate pass and compare the outputs.
A fourth error is ignoring grain and print direction. A side strip that fits a piece dimensionally may still be illegal if the piece must share one orientation with the rest of the project. Grain direction and one-way prints are constraints, not preferences, and they can turn a passing strip into a failing one.
Finally, do not treat the remnant and the new fabric as interchangeable without checking shade and pattern. Place labeled samples together before combining sources, and assign each piece to a planned position. If the difference is unacceptable or still uncertain, exclude the remnant from the count and recalculate every piece from new fabric.
Choosing an order and recording the decision
Choose the order that keeps the wide piece across the remnant whenever the narrow piece can also fit in the leftover strip. That order usually minimizes new-fabric rows because the wide piece is the one that cannot be squeezed into a narrow gap. If the narrow piece is wide enough to displace the wide piece, compare the two new cut lengths directly and pick the smaller one, then check that the chosen order still respects grain, print, and shade.
Record the decision on the cut sheet: piece sizes with allowances already included, usable remnant width and length, rotation status, pieces across for each size, rows available, pieces supplied, pieces remaining, new cut length, and the rounded purchase. A written record lets you re-run the comparison if the remnant measures differently than you assumed, or if the bolt you buy turns out to be narrower than its label.
This is a reproducible row layout, not a claim of globally optimal packing. Other complete layouts may use the remnant differently. The value of the two-pass comparison is that it makes the order an explicit, checkable input instead of a habit.
Sources and method
- NIST: SI units of length — retrieved 2026-09-27
- NIST: conversion factors — retrieved 2026-09-27
AI-assisted writing with automated source, calculation and editorial checks. No hands-on testing or professional certification is claimed. Check the stated assumptions before applying this guide.