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Sheet cutting layout calculator, nesting that matches the machine that will actually cut it

Enter the sheet size, the parts and the spacing your cutting method needs, choose guillotine or free nesting to match the actual machine on the shop floor, and the tool lays the parts out, reports material utilisation and waste, and checks the result against a geometric lower bound that no algorithm can beat.

Open the cutting layout calculator A free account opens this tool. The interface is in English and nothing you enter leaves your browser.

How it works

Three steps. The machine decides the algorithm, not the other way round.

  1. Enter the sheet size, spacing and grain direction

    Spacing depends on your cutting method and material, waterjet on metal typically wants around 3.8 millimetres, soft or laminated sheet more, and grain direction, if the material has one, restricts which rotations are allowed later.

  2. Add the parts and choose guillotine or free nesting

    Pick guillotine if the actual machine is a panel saw or shear that can only cut straight across, and free nesting if it is a laser, waterjet or CNC router that can follow any contour. The two produce genuinely different layouts, not just different numbers.

  3. Read the layout, the material utilisation and the lower bound check

    The result shows how many sheets are needed, how much material is wasted, and confirms the sheet count against the geometric lower bound, so an impossible result is caught before it reaches an order.

The cutting stock problem is NP-hard, so this uses a heuristic on purpose

Formalised by Gilmore and Gomory in 1961 to 1963, classified NP-hard in Garey and Johnson's 1979 textbook, Computers and Intractability.

First Fit DecreasingGuillotine cuttingMaximal rectangles nestingGeometric lower boundGrain and rolling direction

Built to respect the machine and admit what an algorithm cannot promise

A layout that looks efficient on screen but cannot actually be cut is worse than a slightly less efficient one that can.

  • Guillotine and free nesting are not interchangeable

    A panel saw or a metal guillotine shear can only cut edge to edge across the whole piece, it physically cannot turn mid-cut, so a layout built for free nesting simply cannot be produced on it. A laser, waterjet or CNC router can follow any closed contour instead, and the free-nesting method behind that option is the maximal rectangles algorithm, published by Jukka Jylanki in 2010. The tool asks which machine you have and builds the layout for that machine, not for the highest theoretical yield.

  • Grain and rolling direction are treated as a real constraint, not a preference

    Wood splits far more easily along the grain than across it, rolled metal sheet carries different tensile strength and bend behaviour with and against the rolling direction, and composite fibres carry almost all of a part's load along their own orientation. When a grain axis is set, ninety degree rotation is refused for every part on that layout, even if free rotation was requested, because rotating across the grain changes the load direction relative to the material's structure.

  • A geometric lower bound that catches an impossible result

    No algorithm can fit parts with a given total area into fewer sheets than that area divided by the usable area of one sheet, rounded up. It is a simple check, entirely independent of whether the layout used guillotine or free nesting, and if a result ever claims fewer sheets than this bound, the parts are overlapping somewhere in the calculation, not genuinely optimised.

  • Spacing shown as its own number, separate from kerf

    Kerf is the material the tool itself removes, typically 0.1 to 0.3 millimetres for a fiber laser on metal. Spacing between parts is a different, additional allowance, around 3.8 millimetres for waterjet on metal and up to 6.4 to 12.7 millimetres for soft or laminated sheet that flexes under its own weight. A single 10 millimetre spacing added between parts on a 1000 millimetre sheet can drop a row from five parts to four, a fact the tool shows rather than lets you discover on the shop floor.

Frequently asked questions

Why does the tool ask which machine I am using before it nests the parts?

Because a guillotine machine, a panel saw or a metal shear, can only make straight cuts from one edge of the material to the other, it cannot turn mid-cut. A layout built for free nesting, which assumes the machine can follow any closed shape, may simply not be producible on a guillotine machine, the part gets stuck in the material or has to be abandoned. Telling the tool your machine type avoids designing a layout you cannot actually cut.

What is the difference between kerf and the spacing between parts?

Kerf is the width of material the cutting tool itself removes, for a fiber laser on metal that is typically 0.1 to 0.3 millimetres depending on thickness, metal type and gas. Spacing is a separate, additional allowance between two neighbouring parts in the drawing, needed because the tool has physical width and leaves a thermal or mechanical effect on the material around the cut, and it is usually larger than the kerf itself, especially for waterjet or for soft, laminated materials that can flex.

Why can't I rotate a part ninety degrees even though I asked for free rotation?

Because a grain or rolling direction has been set for the layout. Wood splits much more easily along the grain than across it, and rolled metal sheet has different mechanical properties with and against the rolling direction. Rotating a part ninety degrees on the sheet does not just change how it looks, it changes which direction the part's load runs relative to the material's internal structure, so the tool refuses that rotation once a grain axis is in play.

How do I know if a nesting result is actually possible, not just optimistic?

Check it against the geometric lower bound, the total area of all parts divided by the usable area of one sheet, rounded up. No algorithm, however good, can beat that number, it is pure area arithmetic and does not depend on whether guillotine or free nesting was used. If a result ever claims fewer sheets than the lower bound allows, the parts are overlapping somewhere in the layout, not genuinely fitting.

Should I order exactly the amount of material the calculator says I need?

No. The calculator uses a heuristic on an idealised sheet with no defects, real material has scratches, rust spots or uneven sections exactly where the best-planned part was meant to go, and production always needs margin for measurement error and test cuts. Ten to fifteen per cent more material than calculated is a reasonable buffer, rising to around twenty per cent for high-cost parts or tight tolerances, where a rejected part costs far more than the spare material would have.

Is the cutting stock problem solved exactly, or is this an approximation?

An approximation, deliberately. The underlying problem, arranging parts onto sheets to minimise waste, is proven NP-hard, meaning the time needed to search every possible arrangement grows explosively with the number of parts, so no practical software searches for the guaranteed best layout. The tool uses First Fit Decreasing, sorting parts by size before placing them, a heuristic that reliably gives a good result quickly without claiming to be unbeatable.

Other tools

Part of the EduFacturing tool set for sheet metal and cutting.

Sheet Metal Unfold Tool — ProUnfold a bent sheet metal part before it goes anywhere near a nesting layout.Laser Cutting Quote Calculator — ProTurn a nested layout into a laser cutting quote with the assumptions shown.CNC Milling Quote Calculator — ProA quote calculator for parts that get machined instead of cut from sheet.Laser Cutting DefectsDiagnose a defect on a part that came off a laser-cut sheet.