A cutting schedule, not a total-length shortcut

Fit different cuts into the stock.

Enter finished lengths and quantities, one stock length, saw kerf and trimming at each end. Every length must use the same unit: inches, millimetres or another consistent length unit.

Changing the unit label does not convert your numbers. Enter all measurements in one unit. This model counts kerf only between finished parts; include any final separation cut in your end-trim allowance. Up to six decimal places are supported.

Example cutting plan

What the diagram means

Colored blocks are finished pieces. Different part types cycle through three colors, so use the printed lengths to identify the exact cut. Thin dark sections show kerf between adjacent pieces; gray sections show the two entered end trims and the unassigned offcut. The diagrams are computational schematics, not photographs or records of completed work.

The fit equation

Sum of finished lengths + (piece count − 1) × kerf + 2 × end trim ≤ stock length

The model assumes usable end faces after the entered trimming. If the final piece must be separated from a remaining tail, reserve the necessary additional loss in the end-trim input; the calculation otherwise counts only cuts between finished pieces. Do not enter a kerf value that is already included in a finished part length.

Feasible plan versus proven minimum

The planner first packs longer pieces into the stock with the smallest remaining gap that can accept them. For up to 18 individual parts, a bounded branch-and-bound search can improve that arrangement. If the search completes, or the result reaches the volume lower bound, the minimum number of stock pieces is proven under the entered model. Otherwise the result is a feasible arrangement, not a proof that fewer source pieces are impossible.

Search is capped at 50,000 nodes, and the tool accepts up to 200 individual pieces across 30 part types. The lower bound is a mathematical limit, not a guarantee that pieces can actually be packed to meet it. Optimal means the minimum stock count here; it does not mean the least cutting time or the most useful remaining offcut distribution.

Keep fabrication requirements separate

This planner models one-dimensional, equal-length stock. It does not place sheet rectangles, combine alternative stock lengths, locate defects, account for grain matching, check tooling allowances or design structural joints. Verify each cut against the stock and your required tolerances before fabrication. Use the repeated-length cut calculator for a simpler uniform part schedule, or the cut-list guide for the purchasing workflow.

A check you can reproduce

With 100-unit stock, zero kerf and zero end trim, parts of 60, 40, 50 and 50 units fit into two stocks: 60 + 40 and 50 + 50. Their total finished length is 200, so fewer than two 100-unit stocks is impossible. Adding kerf changes the fit and must be calculated again; a perfect fit with zero loss should never be assumed after cutting allowances are introduced.