Woodworking calculator
Cut List Optimizer (Linear Cutting)
When a project calls for a long list of parts cut from standard stock lengths, fitting them efficiently saves both money and waste. This optimizer takes the lengths and quantities you need, along with the stock length you buy and your saw kerf, then packs the parts into as few boards as possible. It returns a board-by-board cutting layout and the total number of stock pieces to purchase, so you walk into the shop with a plan instead of guessing.
How it works
Laying out parts on stock is a one-dimensional cutting-stock problem, a close cousin of bin packing. You have boards of a fixed length, the bins, and you need to fit pieces of various lengths into them while using the fewest boards. Each cut also removes a sliver of wood equal to the saw kerf, so the tool subtracts the kerf for every cut, which adds up across a long list and can be the difference between fitting one more part on a board or not.
The optimizer uses a first-fit-decreasing strategy. It sorts the required pieces from longest to shortest, then places each one on the first board where it still fits, opening a new board only when no existing board has room. Sorting longest-first packs the awkward big pieces early and lets the small pieces fill the gaps, which in practice gets very close to the best possible result.
It is worth knowing that first-fit-decreasing is a heuristic, not a guaranteed optimum. The exact cutting-stock problem is computationally hard, so for very large lists the true minimum may use one fewer board than the tool finds. For ordinary furniture and trim projects the difference is rare, and the layout it produces is reliable, fast, and easy to follow at the saw.
Worked example
Cutting 40, 40, 30 and 20 inch pieces from 96 inch stock packs into 2 boards (32% waste): one board holds the two 40s, the other the 30 and 20.
Frequently asked questions
What is saw kerf and why does it matter?
Kerf is the width of material a blade removes on each cut. Across a long parts list those slivers add up, so the optimizer subtracts the kerf for every cut to avoid laying out boards that will not really fit.
How does the optimizer decide the layout?
It sorts your pieces from longest to shortest, then places each piece on the first board with room, opening a new board only when none fits. This first-fit-decreasing method packs big pieces early and fills gaps.
Is the result the absolute minimum number of boards?
Usually but not always. Linear cutting is a hard cutting-stock problem, so the first-fit-decreasing heuristic gets very close to optimal and occasionally uses one extra board on very large, awkward lists.
Can I mix different stock lengths?
The core layout assumes one stock length at a time. Run the tool once per stock length you plan to buy, or pick the length that yields the fewest boards and least offcut for your particular parts list.
Does it account for grain or defects?
No, it optimizes purely on length and kerf. You still need to inspect each board and skip knots, checks, or wane, so buy a little extra stock to allow for cutting around natural defects in the wood.
Related calculators
Sources
These calculators are for planning and estimation. Engineering results (shelf sag, wood movement) use published average material properties; real boards vary by grade, grain, moisture and defects. Verify load-bearing designs with a professional.