Cutting-plan arithmetic
Keep the pieces.
Account for the lost length.
A list of finished lengths is not the same as a stock order. This guide explains the length model used to suggest a board quantity and grouping.
1. Start with interchangeable stock
Enter the length of one stock board or strip in millimetres. All stock in a plan uses this same length and is treated as interchangeable. The tool does not compare widths, thicknesses, materials, grain or visible defects.
Enter each finished length with the quantity you need. A 70 cm finished piece is 700 mm. Give the rows useful names so the diagram and download show what each piece represents. Calculate different stock systems separately.
2. Reserve a combined end allowance
The optional end allowance is a total amount subtracted once from each board. It combines any lengths you reserve at both ends, including losses from end-trim cuts. It is not applied independently to each end and it is not multiplied by the number of pieces.
For a 2,400 mm stock length with a 20 mm total end allowance, the usable span is 2,380 mm. The diagram places half the allowance at each end to make the accounting visible. That display does not prescribe where the real trimming happens.
3. Understand the kerf convention
Kerf is the length allowance for material removed by a separating cut in this model. A full kerf is reserved between adjacent pieces. When some length remains after the final piece, a final cut is assumed to separate that piece from the remainder.
If the end strip is narrower than the entered kerf, the entire narrow strip is counted as cutting loss. When the finished pieces and between-piece kerfs exactly fill the usable stock, no extra cut or kerf is added after the last piece. A single piece exactly equal to the usable stock therefore has zero piece-separating cuts in this arithmetic model.
The displayed cut count concerns separating the requested pieces. It excludes cuts associated with the combined end allowance. This is length accounting, not equipment instructions or a machine cutting schedule.
For each board:
finished piece lengths + kerf loss + combined end allowance + remaining offcut = stock length
4. Read the suggested grouping
The planner expands each quantity into individual pieces and sorts them from longest to shortest. It tries the first existing board, then the next, placing the piece into the earliest board that has space under the kerf model. If no board fits, it adds another board.
This makes a fast, repeatable suggestion. It does not prove that another arrangement cannot use fewer boards. For example, with a 10-unit stock length and no allowances, lengths 6, 5, 3, 2, 2 and 2 produce three boards in first-fit decreasing: 6+3, 5+2+2, and 2. Yet they can fit into two boards as 6+2+2 and 5+3+2. Both layouts satisfy that simple model.
What the arithmetic lower bound means
The lower bound starts from total piece length and between-piece kerf capacity. It asks how few boards could possibly hold that demand if the lengths packed together perfectly. Combinations can prevent that ideal packing.
A suggestion equal to the lower bound reaches the minimum board count under this specific length model. A larger suggestion should invite a closer look at possible arrangements; the difference alone does not prove another layout exists.
5. Separate offcuts from cutting loss
Kerf loss and the reserved end allowance are shown separately from offcuts. The offcut number is remaining length after those deductions. It does not promise that the material has the size, quality or shape needed for another job.
The bars may not show very small segments clearly on a narrow screen. Use the written quantities below each board for exact accounting. The order of labels in a board is a suggested grouping, not a set of operating steps.
6. Use your own quoted prices
Enter the final price of one stock board and a total delivery amount in Australian dollars. The optional budget multiplies the suggested board count by the board price and adds delivery once. It excludes fixings, finishes, tools, labour and other project costs.
Before ordering
- Confirm the stock length and the unit for every requested finished piece.
- Check that your kerf and end allowances match the arithmetic convention explained here.
- Review the grouping against the actual stock and any quality, grain, width or fitting requirements.
- Compare other arrangements if reducing the suggested board count matters.
- Keep the downloaded assumptions with your shopping quantities.
Cutplan provides shopping arithmetic. It does not provide structural, engineering, installation or safety advice.