Plywood sheet cut optimizer

How to use it

Put the sheet's length (the long side, and the grain direction on veneered sheets) and width in the first two boxes, in inches or, with the decimal display, in millimetres. Then list the parts one line each: quantity, length, width, and a name if you want one. 2 x 72 x 11 1/4 side means two sides, each 72" long and 11 1/4" wide. Tick the grain box for veneered plywood where the face grain has to run the length of each part.

Edge trim is removed from all four edges before layout. Factory edges on cheaper sheet goods are often chipped or out of square, and many cabinetmakers take 1/4" to 1/2" off each edge first. Leave it at zero if you trust the edges.

The method

The optimizer is a guillotine rectangle packer. It keeps a list of empty rectangles on each sheet. Each part, largest first, goes into the empty rectangle it fits most tightly, across all open sheets; a new sheet is opened only when no rectangle can take it. The space left around the part is split into two new rectangles with a single straight cut, so the finished layout can always be cut with through-cuts.

There are several reasonable choices at each step: which parts go first (largest area, longest side, length, width or perimeter), how "tightest" is judged (least leftover area, or least leftover on the short side), which way the leftover is split, and whether parts are turned freely or only when they must be. The optimizer tries all forty combinations and keeps the one with the fewest sheets. On a tie it keeps the one with the largest single offcut, since that is the piece most likely to be useful later. The combination that won is printed under the diagram.

Kerf is handled by growing each part and the sheet by one kerf: two parts that touch in the plan are then exactly one blade width apart, and a part flush with the far edge needs no cut beyond it.

Worked example

The default list is a 72" bookcase carcase in 3/4" plywood: two 72 × 11 1/4" sides, five 34 1/2 × 11 1/4" shelves and a 34 1/2 × 3 1/2" toe kick, cut from one 96 × 48" sheet with a 1/8" kerf. The parts total 3,681 square inches; the sheet is 4,608, so the area bound is one sheet and the parts cover 80% of it.

It fits on one sheet only because two shelves are turned so their length runs across the sheet width. Tick the grain box and the same list needs two sheets: with every part's length along the sheet, the two 72" sides leave a strip about 24" long, too short for any 34 1/2" shelf. On paint-grade plywood, turn the parts and save the sheet. On a visible walnut veneer, the turned shelves would show grain running front to back, which is the decision the tick box is for.

Common sheet sizes

Sizes are nominal; measure the sheets you buy, because a few millimetres of difference changes which parts fit side by side.

Where it stops being reliable

• It is a heuristic. Forty greedy strategies cover a lot of ground but do not prove anything unless the result meets the area bound. For a job of three or four expensive sheets it can be worth rearranging the largest parts by hand.
• It does not plan the cut order. The layout is guillotine-cuttable, but the sequence of rips and crosscuts is left to you. Rip long strips first on a table saw; a full sheet is easier to break down with a track or circular saw.
• It does not know about defects, face quality or matching. Choose which face and which region of the sheet each visible part comes from yourself.
• Rectangles only. Curved or angled parts should be entered as their bounding rectangle.