Sheet nesting calculator (parts per sheet)
Find how many rectangular parts fit on a sheet of plywood, MDF or HDPE once the gap the bit cuts between parts and an edge margin are taken out, and how many sheets a run needs.
How to use this calculator
A router cuts a channel as wide as the bit between parts, and most makers keep a margin at the sheet edge for clamps, screws or out-of-square factory edges. So the usable area is smaller than the sheet, and every part needs one bit width of space beside it:
Parts across = floor((sheet width − 2 × margin + gap) ÷ (part width + gap))
Do the same for the length, then multiply. The calculator tries the part both ways round and keeps the better result.
Example: 12 × 18 in parts on a 4×8 sheet with a 1/4 in bit and a 1/2 in margin. Usable area is 47 × 95 in. Across: floor(47.25 ÷ 12.25) = 3. Along: floor(95.25 ÷ 18.25) = 5. That is 15 parts per sheet. Rotated, it is floor(47.25 ÷ 18.25) × floor(95.25 ÷ 12.25) = 2 × 7 = 14, so the first orientation wins.
Board feet are length × width × thickness in inches ÷ 144. A 4×8 sheet of 3/4 in material is 48 × 96 × 0.75 ÷ 144 = 24 board feet nominal. Sheet goods are normally sold by the sheet, but the figure is handy when comparing with solid lumber.
"4×8" plywood is 48 × 96 in, while metric sheets are commonly 1220 × 2440 mm, slightly larger. Baltic birch often comes in 5×5 ft (1525 mm) sheets. Real nesting software can mix orientations and nest odd shapes for a better yield. Got a cut list? Post it and let makers quote the whole run.
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Questions about this calculator
Why leave a gap between parts?
The router bit removes a strip of material as wide as its diameter. Parts can share a single cut line only if the toolpath is set up for common-line cutting, which is unusual in hobby router work.
Is 3/4 in plywood really 3/4 in?
Often not. Many sheets labeled 3/4 in measure a little thinner, and metric Baltic birch is 18 mm. Measure the actual sheet before cutting slots or dados.