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Bar and tube cut list optimizer

Paste the parts with length and quantity, enter the stock length (or several, to compare) and kerf and get the saw plan: how many bars to buy, how to cut each one, what is left over and how much of your stock drops gets used.

Pre-sizing and estimating tool: results do not replace design, calculations or reports signed by a licensed professional, nor verification against the applicable codes and standards.

Pre-sizing
Stock lengths

Fill in more than one length (e.g. 20 ft and 24 ft) to compare a plan for each and a mixed plan. With no price per bar, weight per foot × length × price per lb is used.

Cutting
Parts
See what was read

Separate with semicolons or paste from a spreadsheet. The ID is optional.

Drops in stock (optional)
See what was read

Same unit as the part list. Drops are used before any new bar.

Weight and cost
—Bars needed
—

Cutting patterns

Each horizontal bar is one pattern; the label says how many bars are cut that way. Blue and green: parts; gray: kerf and end trim; orange: usable drop; red: scrap.

Tap the chart to see the values.

Cut plan

Take it to the saw: each row says how many bars to cut and the piece sequence. Lengths in the list unit.

Next step

Take this page’s results to another calculator with the fields already filled in.

The calculation report gathers this page's inputs, results, equations, assumptions and references, with fields for project, engineer and revision. The full report also includes the charts and interpretations, in color. In the print dialog, choose Save as PDF.

Method, assumptions and references

Equations used

Usable length = stock − end trim; each part uses length + kerf; capacity = usable + kerf (the last cut is not needed when a part ends at the bar end)
Lower bound = ⌈Σ (length + kerf) ÷ capacity⌉; if bars = lower bound, the plan is optimal
Drop = usable − Σ parts − n · kerf; usable if drop ≥ minimum drop; yield = Σ parts ÷ (bars × stock length)
Bar price = price entered or weight per foot × length × price per lb; mixed plan: for each bar opened, picks the length with the lowest price ÷ part length fitted (0/1 knapsack); recommended = lowest cost of new bars (with no price: least length bought)
Weight = bars × length × weight per length; cost = weight × price − (trims + scrap) × weight per length × scrap price

Assumptions and limits

  • First Fit Decreasing and Best Fit Decreasing heuristics, with order variations and a step that tries to empty the least used bar. The result is a good plan, not necessarily the optimum, unless it equals the lower bound.
  • With one stock length and no stock drops, the calculator also checks every pattern combination when there are few distinct part lengths (proven optimal). With several lengths (up to 4) it compares a plan with each one and a mixed plan (length chosen per bar, bars switched to the cheapest length that still works and the least used bars refilled); with stock drops, the longest drop is filled first. These cases are heuristic.
  • All bars have the same section. Square cuts; miter cuts need the angle projection added to the length. Stock drops are taken as straight with no end trim. Bar defects are not considered.

Standards and technical documents

  • Gilmore, P. C.; Gomory, R. E. A linear programming approach to the cutting-stock problem. Operations Research 9(6), 1961
  • Johnson, D. S. et al. Worst-case performance bounds for simple one-dimensional packing algorithms. SIAM Journal on Computing 3(4), 1974
  • Wäscher, G.; Haußner, H.; Schumann, H. An improved typology of cutting and packing problems. European Journal of Operational Research 183, 2007
  • Martello, S.; Toth, P. Knapsack Problems: Algorithms and Computer Implementations. Wiley, 1990 (bin packing lower bounds)

U.S. regulations

  • OSHA 29 CFR 1910.212 and 1910.213: machine guarding and woodworking machinery (saws)
  • OSHA 29 CFR 1910.132 and 1910.95: personal protective equipment and occupational noise exposure
  • OSHA 29 CFR 1910.243: guarding of portable powered tools (abrasive wheels)

Frequently asked questions

What is a bar cut list optimizer?

It tells you how many stock lengths to buy and how to cut each one to get all the parts with the least waste. Fabricators, welders and woodworkers use it for tubes, angles, flat bar and lumber that come in 20 or 24 ft lengths. The calculator groups bars cut the same way into patterns ready for the saw.

How do I read the example result?

The 58 parts fit in 10 bars of 20 ft, in 4 cutting patterns, at 98.8% yield. Total waste is 2.33 ft (1.2% of stock bought), mostly short drops and end trims. At 3.05 lb/ft and $1.20/lb, the 10 bars weigh 610 lb and cost $732.02.

When is the plan optimal?

With one stock length and no stock drops, when the bar count equals the lower bound (sum of parts with kerf ÷ usable bar length): no plan can use fewer bars. When the list has few distinct lengths the calculator also checks every pattern combination and shows "Proven optimal". With several lengths or stock drops the plan is a good heuristic result, not necessarily the optimum.

Should I buy longer stock?

Fill in the 2nd length and, if the price per pound differs, the price of each bar: the calculator builds a plan with each length alone and a mixed plan and recommends the lowest cost. In the example, adding 24 ft stock at the same price per pound does not pay: 10 bars of 20 ft cost $732.02, against $790.58 with 24 ft bars only and $746.66 for the best mix. Long bars also need suitable trucking and rack space.

What is a usable drop, and how do I use the ones in stock?

It is the leftover worth keeping for another job; anything shorter than the minimum entered (2 ft in the example) goes to scrap. On the next job, list those drops under "Drops in stock" (length; quantity): they are used before any new bar, and the result shows how many were used. In the example, listing two 120 in drops cuts the purchase from 10 to 9 bars of 20 ft.

Can I use my existing spreadsheet?

Yes: copy the ID, length and quantity columns and use "Paste from Excel", or load the .xlsx or .csv file. Pick the unit of the list lengths (in, ft, mm, cm or m). The ID is optional and shows next to each length in the plan.

What are the limits?

Cuts are square and each plan covers one shape; for miter cuts add the angle projection to the part length. With several lengths or stock drops the result is heuristic. Bar defects, saw cut order and handling of long bars are not considered. For lists with several sizes, run one plan per shape.