Metal · Cutting
Linear cutting optimizer
Paste the lengths you need, set the bar length and the blade's kerf, and it works out how to cut them from the fewest bars — which bar gets which pieces, which offcuts are long enough to keep, and a cut list to print. The example below, 54 pieces for a steel frame from 6 m bars, needs 10 bars: the theoretical minimum. Cutting one length at a time would take 13.
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How the plan is worked out
Each bar loses the trim at both ends; what is left is the usable length. Every cut turns one kerf of material into dust, so a bar holding n pieces needs room for the pieces and the kerfs between them.
Two complete plans are built and the better one is kept. The first fills bar after bar with the combination of pieces that leaves the least behind, found by an exact search over what is still to cut. The second is best-fit decreasing: longest pieces first, each into the bar it fills best. On very long lists the first one is used to repack the bars the second left emptiest. Better means less new material bought, then fewer bars, then the longest offcut to keep.
It is a heuristic, not a proof of the optimum — which is why the lower bound sits next to the answer. Checked against an exhaustive search on 784 small jobs, it found the true minimum in 783.
Worked example you can check
The example list: 54 pieces, 6000 mm bars, 3 mm kerf, 10 mm trim at each end, offcuts from 500 mm kept.
| Bars | Cuts, mm | Offcut, mm |
|---|---|---|
| 1 | 850 + 600 + 600 + 600 + 600 + 450 + 450 + 450 + 450 + 450 + 450 | 0 |
| 1 | 1200 + 850 + 600 + 600 + 450 + 450 + 450 + 450 + 450 + 450 | 0 |
| 1 | 850 + 850 + 850 + 850 + 850 + 850 + 850 | 9 |
| 1 | 1650 + 1650 + 850 + 850 + 450 + 450 | 62 |
| 1 | 1650 + 1650 + 1650 + 850 | 168 |
| 1 | 1650 + 1650 + 1200 + 1200 | 268 |
| 1 | 1650 + 1200 + 1200 + 1200 | 718 · kept |
| 1 | 1200 + 1200 + 1200 + 1200 | 1168 · kept |
| 2 | 2400 + 2400 | 1174 · kept |
10 bars, which is the lower bound, so no plan can use fewer. Waste 1.4 %, and 4 offcuts totalling 4234 mm go back on the rack. Cut one length at a time and the same list takes 13 bars.
What this page does not do
- Straight cuts only. For a mitred profile, add what the mitre takes to the piece length.
- One profile at a time. Different sections, alloys or colours are different jobs.
- No machine limits. It does not know the shortest piece your saw can clamp, or a pusher's reach.
- The kerf is what you type. Measure your blade; a worn or offset blade cuts wider.