Cut List Calculator: How Many Boards to Buy, With Saw Kerf

Why total length divided by board length under-counts

Adding up the cuts and dividing by the board length answers a different question: how much wood you need. It ignores the fact that each cut comes from one board. Three 50 in pieces total 150 in, which looks like two 8 ft boards (192 in). Two 50 in pieces total 100 in, which is more than one board holds, so each board yields a single 50 in piece and the job needs 3 boards. Roughly 48% of the wood you buy is left over.

A good cut list also asks which pieces go together on a board. That is a packing problem, and the calculator solves it for you.

How much saw kerf matters

Every cut removes a strip of wood as wide as the blade. A full-kerf blade is often around 1/8 in wide and a thin-kerf blade is narrower. Check your own blade, because the exact width depends on the saw and the blade. On a board with several cuts the kerfs add up, and sometimes one kerf decides whether the last piece fits.

A list that fills boards exactly with no allowance, like 48 + 48 or four 24 in pieces, only works when the kerf is zero. In the shop the blade has a width, so a perfect fit is not something to count on. The workbench list needs the same number of boards at every kerf shown, because none of its boards is full enough for one kerf to matter. The kerf only changes the count when a board is nearly full.

Worked example: a 2×4 workbench frame

A workbench frame needs four legs at 34 1/2 in, four long rails at 57 in, six short rails at 21 1/2 in and three stretchers at 40 in, all cut from 8 ft 2×4s with a 1/8 in kerf. That is 17 pieces and 51′ 3″ of cuts. The calculator reports 7 boards and 8.5% left over, and the search proves that 7 is the minimum. The arrangement it found:

Dividing total length by board length gives 7 boards here as well. This list happens to pack well; the two earlier examples show where that shortcut fails.

Does board length change the answer?

Yes, and not in a simple direction. A longer board does not always waste less: what matters is which cut lengths add up to fill a board. The same workbench list on different board lengths:

For this list the 8 ft and 14 ft boards waste the least (8.5%), while the 16 ft boards waste the most because the pieces leave awkward gaps. Price per foot and availability vary, so the cheapest plan is not always the one with the fewest boards or the least waste. Try a few lengths, then compare the result with what your supplier stocks.

When a smarter arrangement saves a board

The simple method places the longest cut first on the first board with room. It is quick and usually good, and a published result shows that it never uses more than 11/9 of the best possible number of boards, plus a small constant (Dósa, 2007). Sometimes a different arrangement saves a board. A list of ten 92 5/8 in studs, six 41 in pieces and four 25 1/2 in pieces is one example: longest-first uses 15 boards and the calculator's search finds 14.

The calculator runs this search for you. When it finishes it can say that the count is the proven minimum. For a very long list with many different lengths it may stop before it can prove that, and then it tells you so and gives the best layout it found. A list of 12 × 36 in, 8 × 42 in and 6 × 30 in pieces needs 12 boards even though the lengths alone suggest 10; here the search proves the answer.

How to enter a cut list

Put one cut per line as length, then x, then quantity: 34 1/2 x 4 is four pieces 34 1/2 in long. Lengths are in inches unless you write feet, as in 5' 2 1/2" x 2. A line with no quantity is one piece. Enter the finished length of each piece. If a piece needs a mitred end or a trimmed edge, add the allowance first, because the tool cuts exactly the length you give it.

The board length is the length you plan to buy. If you trim a clean end off each board before measuring, subtract that from the board length. Leave the kerf at 1/8 in unless you know your blade. Material is lost between neighbouring pieces whichever side of the line you cut, so enter 0 only to see the best case with nothing lost to the blade.

What the layout does not model

The calculator packs lengths along a board. It does not account for knots, crook or checks, grain direction, tapered cuts or the width of rip cuts. For sheet goods such as plywood, where you cut in two directions, you need a two-dimensional layout; this tool handles lengths only. Buy a spare board or two if the lumber is rough or you must cut around defects, and set aside the best boards for the visible pieces.

Cutting order that avoids errors

• Label each piece with a letter or number from the layout before you cut, so a board never gets cut twice for the same piece.
• Mark every cut on a board from the same end, rather than chaining one mark from the last. Chained marks add up small errors.
• Use a stop block for pieces that repeat, so four legs come out the same length.
• Mark the waste side of each line with an X so the kerf comes off the side you meant to lose.
• Cut the long pieces from a board first and check the leftover against the next piece before you commit to it.

If a measurement needs fraction math, the feet and inches calculator adds and subtracts lengths without converting to decimals.

Sources

The worst-case bound for the longest-first method is from György Dósa, "The tight bound of First Fit Decreasing bin-packing algorithm is FFD(I) ≤ 11/9 OPT(I) + 6/9," in Combinatorics, Algorithms, Probabilistic and Experimental Methodologies (ESCAPE 2007), Lecture Notes in Computer Science 4614, Springer (doi:10.1007/978-3-540-74450-4_1). Construction Pro for iPhone and iPad includes a Cut Optimizer tool for the same job in the field.

Frequently asked questions