About LCuts and its methods

How the tools work

Every tool is JavaScript that runs in your browser. There is no account, no server-side processing, and nothing you enter is transmitted or stored. The default example on each page is calculated when the site is built, by the same code that runs as you type, so the page shows a real result even with JavaScript switched off.

Lengths can be typed the way they are read off a tape: 36, 36.5, 36 1/2, 36-1/2, 8' or 8' 6". The two optimizers are unit-agnostic: with the decimal display, millimetres work as long as every number is in millimetres.

The two optimizers are heuristics

Cutting pieces from boards is the bin-packing problem, and cutting rectangles from sheets is its two-dimensional version. Both are NP-hard: no known method finds the guaranteed best answer quickly for every input. So both optimizers use well-established heuristics, run several variants, keep the best, and print a lower bound. When the answer equals the bound it is provably optimal; when it does not, a better plan may exist.

• Cut list optimizer: first-fit decreasing and best-fit decreasing, fewer boards wins, ties go to the plan with the longest offcut. Kerf is charged between neighbouring pieces. Lower bound: ceil(Σ(piece + kerf) / (usable + kerf)). First-fit decreasing is proven never to use more than 11/9 of the optimal board count plus less than one board. Assumes one stock length and defect-free boards.
• Sheet cut optimizer: a guillotine free-rectangle packer, run with five sort orders, two fit rules, two split rules and two rotation policies (forty combinations when rotation is allowed). Guillotine splitting means every layout can be cut with through-cuts. Kerf is handled by enlarging each part and the sheet by one kerf. The grain option forbids rotation. Lower bound: total part area divided by usable sheet area, which ignores shape and so is often not reachable. Does not plan cut order, defects or face selection.

The calculators are arithmetic

• Board feet: one board foot is 144 cubic inches, thickness(in) × width(in) × length(ft) / 12. Exact. Hardwood thickness in quarters (8/4 = 2"). Surfaced-thickness figures in the reference table are the commonly quoted standards and vary by mill. The waste allowance is your choice; no figure is universally right.
• Lumber cost: conversions between price per board foot, per linear foot and per piece follow from the board-foot definition. The job total rounds up to whole boards and assumes parts can come from any board. Default prices are examples, not quotes. It compares prices; it does not recommend what to buy.
• Stud calculator: layout studs ceil(length / spacing) + 1, plus two kings and two jacks per opening minus the layout studs inside it, plus the chosen extras for corners and intersections. Plates are three times the wall length; header stock is two plies of opening width plus 3". A materials estimate, not a structural design: header sizes, jack counts for wide openings, and everything else structural come from your plans and the building code.
• Drywall: two methods shown side by side, because they disagree. By area: net surface plus waste, divided by sheet area. By layout: horizontal 4 ft courses per wall and ceiling, openings not deducted. Tape is measured from the layout. Screws use the rule of thumb of about one per square foot. No joint-compound estimate, because coverage varies too much by product. Rectangular rooms only.
• Fabric yardage: rectangular pieces laid in rows across the usable width (and, when there is no repeat, a guillotine strip packer), shortest layout kept. Repeats round each row up to whole repeats; one-way fabrics forbid turning pieces. Shrinkage scales the length; the result is rounded up to 1/8 yard and 10 cm. Curved garment pieces nest better than their bounding rectangles, so treat garment results as an upper estimate.
• Quilt backing, binding and batting: backing is the top plus overage on every side, pieced from whole widths with a seam allowance at each join, both directions compared. Binding is the perimeter plus an allowance, with each diagonal join counted as using one strip width. Packaged batting sizes are typical and vary by brand.

The project plans are rules, not drawings

Each project plan is written as a set of rules taken from standard practice for that kind of build, not copied from any published plan: the shelves of the bookshelf fit between its sides, so each is the outside width minus two board thicknesses; the workbench's cross rails are spaced so the top is supported at least every 24"; the sawhorse leg is its rise divided by the cosine of the splay angle. Your dimensions go through those rules to produce the parts, the drawing, the hardware counts and the steps. Every plan's rules are unit-tested against hand-checked numbers at its default size and at a changed size.

• Actual lumber sizes. Parts are drawn and listed at actual (dry, surfaced) sizes from the American Softwood Lumber Standard (PS 20): a 2x4 is 1 1/2" × 3 1/2", a 1x12 is 3/4" × 11 1/4", a 4x4 is 3 1/2" square. The shopping list names the nominal size. Sheet goods are taken as 4 × 8 ft.
• Shopping list. Board parts are grouped by cross-section and run through the cut list optimizer with your board length (a longer standard length is used when a part needs it); sheet parts go through the sheet cut optimizer with rotation allowed. Both use a 1/8" kerf unless you change it. Board feet bought are counted on nominal size, the way a lumberyard tallies them.
• Warnings are rules of thumb. Shelf sag (about 32" for 3/4" pine or plywood), bed width (about 4 ft to reach the middle), workbench height (32-40") and floating-shelf studs (at least two) are common guidance, not engineering. None of the plans has a load rating.

Units

The building and sewing calculators use US customary units (inches, feet, yards), with metric equivalents where they are commonly needed, such as fabric by the metre. A yard is exactly 36 inches and 0.9144 metres; an inch is exactly 25.4 mm.

Safety and advice

These tools estimate quantities. They do not check designs against building codes, do not size structural members, and are not professional advice. For anything structural, fire-rated or inspected, follow your plans and ask your local building department.

Corrections

If a number here is wrong, the method is stated on each page precisely so that it can be checked. Errors that are found are fixed, and the fix applies to every page that uses the same code.