Linear Cut List Optimizer

A linear cut list optimizer for boards, tubes and bars

Not everything is cut from a sheet. Studs, 2x4s, pipe, conduit, angle iron, trim and tubing all come in fixed lengths, and you cut pieces off the end. This linear cut list optimizer is for that job. Enter the stock length you buy, the saw kerf and the lengths you need with their quantities, and it works out how many lengths to buy and how to cut each one with the least left over.

It is the one-dimensional version of the sheet tool: only length matters, because width and thickness stay the same. That makes it a good fit for framing lumber, fence rails, deck boards, closet shelving, metal tube frames and similar projects. It runs in your browser, with no account, on a phone or a computer.

How to use the linear cut list optimizer

1. Enter the stock length. This is the length you buy, for example the length of a stud or a stick of tubing. You do not have to say how many pieces of stock you have; the tool tells you how many to buy.
2. Enter the kerf. The blade removes a small strip at each cut, and the tool subtracts it between pieces.
3. List the lengths you need. One row per length, with the quantity. In inches you can type fractions such as 41 5/8.
4. Press Calculate. You get the number of pieces of stock, the share of material used, a bar for each piece of stock showing where the cuts fall, and a numbered cut order.

The same units switch as the sheet tool applies: inches or millimeters.

How the cuts are planned along a length

This is a bin packing problem in one dimension. Each piece of stock is a bin, and each required length is an item that must fit inside with kerf between neighbors. The tool uses two well-known greedy approaches: sort the lengths from longest to shortest, then either put each one in the first stock piece with room, or in the stock piece where it leaves the smallest gap. It runs more than one variant and keeps the layout that needs the fewest pieces of stock.

Starting with the longest pieces matters. A long piece is the hardest to place, and short pieces can fill the gaps afterward. If you plan the short ones first, you can end up with several stock pieces each holding a gap that is too short for the long piece you still need.

Why the kerf counts here too

Imagine a stock piece cut into four parts. That takes three cuts, so three kerfs are lost between the parts. The layout accounts for this, so the last piece is the right length instead of a few millimeters short.

Cut order and stop-block setups

Each stock piece in the result has a numbered cut list that says where to cut from one end, such as 1. Cut at 36" from the left end, and then moves along the piece. In the shop, a repeated length is easiest with a stop block on a miter saw or crosscut station: set the stop once and cut every piece of that length before changing it. When the same length appears on several stock pieces, you can group them in your own workflow so the stop only moves when the length changes.

The bar chart shows each stock piece as a horizontal strip, with the parts in order and the waste at the end drawn in gray hatching. Labels show the length of each part so you can mark pieces as you cut them.

Lumber, tubing and offcuts

For dimensional lumber, the cross-section size does not matter to this tool, because only the length is planned. The factory ends of a board or tube are not always square or clean. If you plan to trim a rough end before you start, subtract that trim from the stock length you enter.

The waste at the end of each stock piece is the offcut. A short offcut can be kept for blocking, cleats or test pieces. The tool shows how much is left on each piece so you can decide.

Limits of the linear planner

• The result is not guaranteed to be the minimum. Greedy methods are good and fast, but they cannot promise the fewest possible stock pieces in every case.
• Solid wood needs your eyes. Knots, splits, bow and twist in lumber may make a section unusable. The tool assumes every inch of the stock is good, so you may need to cut around defects and re-plan.
• One stock length at a time. If you have two stock lengths, calculate each separately.
• Angled cuts are not modeled. Miters and bevels use more length than a square cut. Add the extra to your part length.
• Check the numbers. Compare the lengths and counts in the result with your own list before you cut.

Linear optimizer versus doing it by eye

By eye, you tend to work through your list from top to bottom and put each piece on whatever stock is lying around. That works for a few pieces. For a dozen different lengths it usually leaves more offcuts than needed. The optimizer is quick to try, so you can test whether changing one length slightly means one fewer board. Compared with sheet-based tools, this page handles only lengths, which keeps it simple. If your project also needs sheet goods, use the main sheet tool for those parts and this one for the lumber.

What is free here

Calculations, the cutting bars, the cut order, printing and copying as text are free, with no daily limit. You can save three projects in your browser. A Pro plan at $9 per month is shown under the results to find out whether anyone wants it; it is not available yet and nothing is charged.

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