The area sum is a sheet short on more than 1 job in 5
Adding up the part areas and dividing by the sheet area is the usual way to estimate sheets. We tested it on 1,000 jobs against real nests. Here is how often it under-orders, when it does, and the data to check it yourself.
What we found
| Jobs | Area sum too few sheets | Share |
|---|---|---|
| All 1,000 jobs | 224 | 22.4%, more than 1 in 5 |
| With a part over 600×450mm (783 jobs) | 194 | 24.8% |
| Smaller parts only (217 jobs) | 30 | 13.8% |
| Parts filling 80% or more of the last sheet (201 jobs) | 141 | 70% |
| Two or more sheets short | 15 | 1.5% |
Across all 1,000 jobs the area sum came to 2,905 sheets; the real nests needed 3,152. That is 247 sheets the area sum would not have ordered: about 1 sheet in 13.
The area sum never over-ordered. It can’t: it assumes no waste at all, so it is the smallest number that could possibly work, and the real nest is that or more.
One job from the test
Six parts of 655×726mm and two of 851×808mm, on 2440×1220mm board. Together they come to 1.42 sheets, so the area sum says 2. They need 3, and that is proved, not just the best layout found. Every part is at least 655mm both ways, so only one fits across the 1220mm board whichever way it is turned: they go in a single row, and even turned their narrow way their widths add up to about 5550mm, more than two boards’ 4880mm.
The other pattern is a job that adds up to just under a whole number of sheets. Of the jobs whose parts filled 80% or more of the last sheet, 70% needed one more sheet than the area sum said.
Why it happens
Parts don’t tile
Rectangles of different sizes leave strips no other part fits. The bigger the parts, the bigger the strips, which is why jobs with large parts miss more often.
Every cut takes a kerf
The blade or beam removes its width between parts. A few millimetres a cut decides whether four parts fit in a row or three.
Near a whole number, it decides
A job that adds up to 0.96 of a sheet has no room for waste at all; one that adds up to 0.6 has plenty. 141 of the 224 misses were jobs that filled 80% or more of the last sheet.
How we tested
- 1,000 generated jobs, 250 on each of four common sheet sizes: 2500×1250, 2440×1220, 3000×1500 and 2050×900mm.
- Each job has 2 to 8 part types. About 30% of part types are large (500 to 1200mm by 300 to 900mm, 1 to 6 off) and the rest small (60 to 600mm by 40 to 450mm, 1 to 30 off), the kind of mix a fabrication or joinery shop cuts.
- Area sum: total part area divided by sheet area, rounded up, the way it is usually done (no kerf).
- Real count: the fewest sheets CutNest’s nesting engine found, free placement, parts allowed to turn 90°, 3mm kerf. Every job that came out over the area sum was searched again ten times longer from three starting points; that found a tighter layout on 14 of them, which count as hits, not misses.
- Proof: on 808 of the 1,000 jobs, and on 32 of the misses, the count is proved the fewest any layout could use. On the rest it is the best layout found, so if anything the true number of misses is slightly lower than 224.
- These are generated jobs, not customers’ jobs: CutNest keeps cut lists on the user’s own computer and never sees them.
The data: every job, its parts, its area sum, its real count and whether the count is proved is in sheet-count-study.json (130KB). Paste any job into the sheet nesting calculator to check it. Questions to hello@cutnest.co.uk.
What to do instead
Nest the job before you order: on paper for a few parts, or with a cut list optimiser for anything more. If you must estimate by area, add a sheet whenever the parts fill 80% or more of the last sheet, and be wary on any job with large parts.
The free sheet nesting calculator and plywood & MDF calculator show the area sum and the real count side by side for your own parts.
Questions
Try it on your own job
Free, in your browser, no account. Your cut list stays on your computer.