Cut List Optimizer

Frequently Asked Questions

How does 1-D cut-list optimization work?

A first-fit-decreasing bin-packing algorithm sorts the required parts longest-first, then places each part on the first stock board with enough remaining length (accounting for kerf). It minimizes board count without exhaustive search.

Why does kerf matter in the calculation?

Every cut removes kerf-width material (typically 1/8 in for a table saw, 1/16 in for a thin-kerf blade). For N cuts on a board, usable length drops by N × kerf, so a 96 in board cut into 12 pieces loses about 1.5 in to a 1/8 in kerf.

How much waste should I expect?

Well-optimized cut lists with mixed part lengths typically yield 5–15% waste. Uniform short parts on long stock can hit under 5%; awkward mixes can climb past 25%, in which case buying a different stock length usually helps.

Should I add an end-trim allowance?

Yes - most rough lumber has a 1–2 in damaged end, and squaring a factory end on plywood costs another 1/4 to 1/2 in. Subtract that from each stock length before optimizing so the plan is realistic.

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How This Calculator Works

When you have a pile of identical-length stock (8 ft boards, lengths of trim, steel tube) and a cut list of parts to extract, the question is "how many boards do I buy, and how do I cut each one to waste the least?" This is the classic one-dimensional cutting-stock problem. This tool takes the stock length, the saw kerf (the material the blade turns to dust on every cut), and your list of part lengths with quantities, then packs them onto as few boards as possible using a proven greedy heuristic. It returns the number of boards needed, a cut layout for each one, the leftover offcut per board, total waste, and a yield efficiency so you can sanity-check the plan before buying lumber.

Formula / Method

The algorithm is First-Fit Decreasing (FFD) bin packing. All required pieces are expanded into a flat list and sorted longest-first. Each piece is placed on the first board that still has room for it plus a kerf allowance for every cut after the first on that board; if none fits, a fresh board is started. Kerf is charged once per saw pass (a board cut into k pieces consumes roughly k−1 kerfs of waste, plus any final trim). Yield efficiency = total part length ÷ (boards × stock length) × 100. FFD is not guaranteed optimal but is provably within about 22% of optimal in the worst case and usually within a board or two of perfect for real cut lists.

Worked Example

Stock = 96 in boards, kerf = ⅛ in (0.125), and a cut list of 24×4, 18×6, 30×2, 12×8 (lengths × quantities). Sorted longest-first the parts are two 30s, four 24s, six 18s, eight 12s. Board 1 takes 30 + 30 + 24 (+ two kerfs) ≈ 84.25 in used, 11.75 in offcut. The packer continues filling boards, fitting a 24 + 24 + 24 + 18 set onto another, and so on, until every piece is placed. Total part length here is (4×24) + (6×18) + (2×30) + (8×12) = 96 + 108 + 60 + 96 = 360 in. The tool reports the exact board count, what to cut from each, and the resulting efficiency - far better than eyeballing it and discovering you are one board short mid-project.

Common Mistakes

Ignoring kerf entirely - on a long list of short parts the lost ⅛ in per cut adds up to a whole missing piece.

Forgetting to leave a defect/trim allowance on rough lumber for snipe, splits, and end checks; add a couple of inches per board.

Buying for exactly the optimized count with no spare board - one mis-cut and the project stalls.

Mixing units (some parts in inches, stock in feet) - keep everything in one unit before entering.

Treating grain, figure, and color matching as free - the math packs by length only; you may need extra stock to match show faces.

Tips & FAQ

Is this layout optimal? First-Fit Decreasing is a strong heuristic, typically within one board of perfect for ordinary cut lists; for big production runs a true optimizer can occasionally shave one more board, but FFD is what most shops cut to. What kerf should I use? A thin-kerf blade is about 3⁄32 in (0.094), a full-kerf table-saw blade about ⅛ in (0.125), and a bandsaw far less; measure your own kerf on a test cut for accuracy. Should I cut the longest parts first in real life too? Yes - cutting longest pieces first preserves flexibility, because a short piece can come out of a long offcut but not the reverse. How do I plan for defects? Add the defect length as extra "parts" or inflate the stock allowance; rough lumber always loses material to crook, checks, and snipe. Sheet goods? This is a 1-D linear tool for boards and trim; cutting plywood is a 2-D problem (length and width) and needs a sheet-layout optimizer instead. Buy a spare: always purchase at least one board beyond the optimized count - the cost of one extra 8 footer is trivial against a stalled project. Use these numbers to estimate purchase quantity and a cutting order, then re-check against your actual stock and grain before the first cut.

Frequently Asked Questions

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