How to use the pieces per sheet calculator
- Choose your units, then enter the sheet width and height and the piece width and height. Add the space between pieces if you cut with a saw or leave a gap, and the unused edge if part of the sheet cannot be used.
- Decide whether pieces may be turned 90 degrees. Turning often fits more, but it is not always acceptable for patterned or grained material.
- Read Pieces per sheet at the top, the share of the sheet used, and the table of layouts: pieces as entered, all turned, and the best layout found. To count whole sheets, enter how many pieces you need.
- Use Copy, Print or CSV to keep the result.
Formula
Across = floor((width + space) / (piece width + space))
Down = floor((height + space) / (piece height + space))
Pieces = across x down, with width and height reduced by the unused edge on both sides
Floor means rounding down to a whole piece. The best layout also tries one straight cut at every place where a whole number of pieces ends, and fills each side with its better grid.
Business cards on a letter sheet
Cards measuring 3.5 by 2 inches on an 8.5 by 11 inch sheet fit 2 across and 5 down as entered, which is 10 cards. Turned, they fit 4 across and 3 down, which is 12 cards, using an 8 by 10.5 inch block. That leaves an unusable half inch at the side and at the bottom, so 12 is the answer, and 100 cards need 9 sheets.
With a half inch space between pieces, a plain grid gives only 8 cards as entered or 6 turned. A better layout exists: a block of 2 across by 3 down (7.5 by 7 inches), then half an inch of space, then 3 turned cards across the remaining 3.5 inches. That gives 9, so 100 cards need 12 sheets.
How the best layout is found
A plain grid is the first answer: whole pieces that fit across, whole pieces that fit down, with the space between them counted. The tool compares the grid as entered with the grid turned 90 degrees, and then looks for a layout with two blocks side by side or one above the other, each filled with its own best grid. This catches the common case where a strip left beside a block of pieces is just wide enough for a few turned ones.
This is a good practical answer, but not a proof that no better arrangement exists. In 60 test sheets compared against an exhaustive search of every sequence of straight cuts, the two-block layout matched the best possible in 56 cases when turning was allowed and in all 60 when it was not, and never exceeded it. Irregular nested layouts that need non-straight cuts are not considered.
Space between pieces and edges
The space between pieces covers the width of a saw blade or cutter, or a gap you leave on purpose. It is added between neighbors but not at the outer edges. The unused edge is removed from all four sides of the sheet before the pieces are counted, so a printer margin or a damaged border is handled by one number. All sizes are used to four decimal places.
The units setting only changes the labels, so the numbers must all be in the same unit. For paper sizes and conversions, see the paper size converter, and for ready-made sheets of labels, the label sheet maker. To spread a large print over several sheets instead, use the poster printer tiler.
Assumptions and limits
- All pieces are the same size and rectangular, and all sizes are in the unit you choose.
- Layouts are plain grids and layouts with one straight cut. More complex arrangements are not tried.
- Turning a piece 90 degrees is assumed to be acceptable only when you allow it.
- Sizes are used to four decimal places, and the share of the sheet used is measured against the full sheet area.
Frequently asked questions
Why does turning the pieces change the count?
A piece that is long and thin can sit along either side of the sheet. One direction usually leaves less wasted space than the other, and the tool checks both.
Does the space between pieces count at the outer edge?
No. It is added only between neighboring pieces. Use the unused edge setting for a border that you cannot use.
Is the result always the most pieces possible?
No. It is the best of plain grids and layouts with one straight cut, which is usually the best, but a more complicated arrangement can occasionally fit one more piece.
Can I use it for fabric or wood?
Yes, as long as the pieces can be placed in any direction you allow. For grain or pattern direction, switch off turning.