Rectangular Sheet Cutting & Order Budget Calculator
Lay out mixed rectangular parts and review stock quantities and costs.
Include rotation, kerf and edge margins, then save the layout and straight-cut schedule.
Default dimensions and prices are fictional. Plan rectangular parts of one material and thickness on one stock size. Dimensions are mm; prices are KRW.
Compare six straight guillotine layouts. Results do not guarantee global optimality or machine feasibility and are not curved laser nesting or CNC files.
Sheet layout and order budget
Heuristic layout · global optimality not guaranteed
Sheets to order
1 sheets
Area bound (not order quantity)
1 sheets
Budget from entered quotes
KRW 123,880
Product area yield
92.16%
The area bound ignores kerf and shape constraints. Use the verified layout count for order review. The selected count is 0 sheets above the bound.
- Stock purchase
- KRW 100,000
- Internal cutting charge
- KRW 3,880
- Confirmed extras
- KRW 20,000
- Cut length · count
- 3.88 m · 6
- Finished part count
- 4
- Usable width × height
- 980 × 980 mm
Source checked: 2026-10-13 · Recheck material, quotes and tolerances before ordering
Stock area accounting
| Item | mm² | m² |
|---|---|---|
| All stock | 1,000,000 | 1 |
| Finished parts | 921,600 | 0.9216 |
| Edge margins | 39,600 | 0.0396 |
| Kerf loss | 7,760 | 0.00776 |
| Separate remnants | 31,040 | 0.03104 |
| Non-product total (margins + kerf + remnants) | 78,400 | 0.0784 |
Six layout comparisons
Selection minimizes sheet count, then total budget, cut length and cut count. Changing quote rates or rotation constraints may change the choice.
| Layout strategy | Sheets | Total budget | Cut metres | Cuts |
|---|---|---|---|---|
| ★ Area · vertical first (selected) | 1 | KRW 123,880 | 3.88 | 6 |
| Area · horizontal first | 1 | KRW 123,880 | 3.88 | 6 |
| Longest side · vertical first | 1 | KRW 123,880 | 3.88 | 6 |
| Longest side · horizontal first | 1 | KRW 123,880 | 3.88 | 6 |
| Width · vertical first | 1 | KRW 123,880 | 3.88 | 6 |
| Width · horizontal first | 1 | KRW 123,880 | 3.88 | 6 |
Per-sheet layout and cut schedule
Origin is top-left: x points right and y points down. Part labels are row.instance; pale green marks remnants, grey borders mark margins, and red dashed lines mark kerf centres from the ordered cut table.
Finished part coordinates and dimensions
| Part ID | x mm | y mm | Width mm | Height mm | Rotation |
|---|---|---|---|---|---|
| #1.1 | 10 | 10 | 480 | 480 | 0° |
| #1.2 | 10 | 492 | 480 | 480 | 0° |
| #1.3 | 492 | 10 | 480 | 480 | 0° |
| #1.4 | 492 | 492 | 480 | 480 | 0° |
Straight-cut sequence (edge trimming excluded)
| Order | Axis | Start x, y (mm) | End x, y (mm) | Length mm |
|---|---|---|---|---|
| 1 | Vertical | 491, 10 | 491, 990 | 980 |
| 2 | Horizontal | 10, 491 | 490, 491 | 480 |
| 3 | Horizontal | 10, 973 | 490, 973 | 480 |
| 4 | Vertical | 973, 10 | 973, 990 | 980 |
| 5 | Horizontal | 492, 491 | 972, 491 | 480 |
| 6 | Horizontal | 492, 973 | 972, 973 | 480 |
View separate remnant coordinates and dimensions (3)
| Remnant | x mm | y mm | Width mm | Height mm |
|---|---|---|---|---|
| #1 | 974 | 10 | 16 | 980 |
| #2 | 492 | 974 | 480 | 16 |
| #3 | 10 | 974 | 480 | 16 |
TXT includes every sheet, part, cut, remnant and quote assumption. SVG and printing show the selected sheet. Confirm measurements, material, direction, machine, allowances, tolerances, trimming, tax and minimum charges with your supplier before ordering.
Why sheet area alone can understate an order
A collection of steel parts can have less area than one stock sheet and still fail to fit on it.
Widths and heights must work together, with enough space for kerf, edge margins and any material direction constraints.
Missing those conditions can lead to another stock purchase or a delayed order during fabrication.
This rectangular sheet cutting calculator places mixed rectangular sizes on identical stock sheets.
It provides part coordinates, a straight-cut sequence, sheet quantities and a budget based on your entered stock and cutting quotes.
Use it to prepare a supplier review with a clear scope for dimensions, losses and charges.
Suitable planning situations
Use it for small fabrication orders, rectangular supports or shelves, and repair parts sharing one material and thickness.
Review irregular shapes and different material groups with separate drawings and quotes.
Default prices are fictional, rather than market averages, and all amounts remain in KRW on both language versions.
Mixed-size layouts and purchasing worksheets
Track each part and orientation
Enter distinct widths, heights and quantities by row, and specify whether each row permits 90° rotation.
Labels use row.instance identifiers so repeated parts remain traceable.
Small parts may omit an on-diagram label, but their coordinates and dimensions remain in the table.
Keep stock and work costs aligned
Sum quoted sheet prices, per-metre or per-cut rates, and confirmed additional charges.
Compare six layouts by sheet count, budget and cut length.
The TXT worksheet covers every sheet; the selected SVG and printed schedule help explain that sheet to your supplier.
Identical stock sheets are assumed available in unlimited quantities.
The calculator does not fetch live steel prices, rank suppliers, combine different thicknesses or pack your existing offcuts.
Inputs, units and direction rules
- Stock and finished dimensions: enter lengths in mm with at most one decimal place.
Use drawing dimensions including supplier-confirmed finishing allowances, and verify stock size tolerances or actual measurements. - Margin on each side: one value applies separately to left, right, top and bottom.
Twice the margin is removed from each stock dimension.
Include edge-trimming kerfs in this allowance and distinguish per-edge allowance from total trim loss. - Kerf: the width removed by one internal straight cut.
The complete kerf must fit inside the current rectangle.
A positive leftover dimension smaller than the kerf makes that placement invalid; overhanging cuts are not modelled. - Grain and rotation: per-row rotation is available only without a direction constraint.
Any specified grain locks all parts to their entered stock-axis dimensions.
Thickness is a worksheet record only, and material suitability remains a drawing and supplier decision. - Quantity and prices: use up to 20 rows and 200 total parts, with a selectable lower calculation limit.
Prices and extra charges are whole KRW.
Use zero only for confirmed free items; unknown costs entered as zero understate the order budget.
Guillotine layout and budget formulas
Usable stock and the area bound
Usable width = stock width − 2 × margin per side
Usable height = stock height − 2 × margin per side
Area lower bound = ceil(Σ part width × height × quantity / usable sheet area)
Yield = total finished part area / total purchased stock area × 100
A part is placed at the top-left of a free rectangle, followed by at most two full-span straight cuts.
Vertical-first splitting divides the full current height, then separates the part in the resulting strip using a horizontal cut.
Horizontal-first splitting reverses the axes.
An exactly matching dimension needs no cut on that axis; remaining space stays as separate rectangular remnants.
Cost from the entered quote
Stock purchase = layout sheet count × price per sheet
Per-metre cutting charge = ceil(total internal cut length mm / 1,000 × rate per metre)
Per-cut cutting charge = internal straight-cut count × rate per cut
Total budget = stock purchase + cutting charge + confirmed extras
Descending area, longest side and width are each combined with two splitting directions, for six deterministic layouts.
Parts use a well-fitting existing free rectangle before another stock sheet is opened.
Selection minimizes sheet count, then total budget, cut length and cut count.
The tool verifies part quantities, cut-tree replay and area conservation, but this limited heuristic comparison does not establish a globally optimal layout.
Step-by-step use and export
- Confirm measured stock width and height, material thickness, margins and actual machine kerf.
Prepare stock-axis part dimensions if surface or rolling direction matters. - Add a row for each finished size, enter its quantity and set rotation permission.
Check that the total fits your chosen calculation limit. - Enter the stock price and select the supplier charging basis.
Put confirmed trimming, delivery, minimum charges and additional tax in extras, after checking what is already included. - Calculate and compare the order count, area bound, budget and six layouts.
Changing an input clears the previous result, so calculate again before using a revised schedule. - Select a sheet and inspect part coordinates, dimensions, ordered cuts and separate remnants.
TXT includes all sheets; SVG and printing show the currently selected sheet.
Request a final supplier quote using the same verified conditions.
Worked examples verified against the calculation
Four 480mm square parts
Assume 1,000×1,000mm stock, 3mm thickness, a 10mm margin on each side and a 2mm kerf.
Four 480×480mm parts have a combined area of 921,600mm², with a 980×980mm usable region.
Both the area bound and layout count are one sheet, with 6 internal cuts totalling 3,880mm.
At a fictional stock price of KRW 100,000, KRW 1,000 per metre and KRW 20,000 extras, the cutting charge is KRW 3,880 and total budget is KRW 123,880.
Yield is 92.16%; edge margins account for 39,600mm², kerf for 7,760mm² and separate remnants for 31,040mm².
These values were checked against the pure calculation function and do not represent market prices or recommended machine settings.
| Item | Result |
|---|---|
| Purchased stock | 1,000,000mm² |
| Finished parts | 921,600mm² |
| Edge margins | 39,600mm² |
| Kerf loss | 7,760mm² |
| Separate remnants | 31,040mm² |
| Internal cut length | 3,880mm |
| Budget from entered quotes | KRW 123,880 |
One sheet by area, two sheets by shape
With zero margins and zero kerf, two 600×600mm parts have 720,000mm² of finished area on 1,000×1,000mm stock.
The area bound is one sheet, but the two parts cannot sit side by side along either axis, so the layout needs two sheets.
An 80×100mm part fits 100×80mm stock only when 90° rotation is permitted; locking the material direction makes the part infeasible and withholds the total.
Reading sheet counts, yield and remnants
Separate the bound from a feasible order
The gap above the area bound may come from shape constraints, kerf or the heuristic choices.
Do not label it confirmed waste or multiply it by stock price as a guaranteed saving.
If your supplier offers another stock size, recalculate using that size and its actual quote.
Non-product area has different components
Non-product area combines edge margins, kerf loss and separate remnants.
It is neither confirmed disposal area nor recoverable scrap cash.
Inspect remnant coordinates and dimensions instead of treating their combined area as a single large sheet.
Cut coordinates describe the kerf centre, with a top-left origin.
The centre may require two decimal places when the entered kerf has an odd tenth of a millimetre; input dimensions still allow only one decimal place.
Use the numeric worksheet, rather than visual scale alone, to compare the result with drawings.
Three practical quote-review situations
Ordering mixed parts together
Supports, covers and reinforcing plates can be reviewed together when material and thickness match.
Keep separate rows if identical dimensions have different rotation or surface requirements.
Record the worksheet identifier alongside the drawing identifier so the supplier can reconcile quantities.
Reviewing a rotation restriction
Do not remove a grain restriction solely to reduce the sheet count.
Change it only after a designer or supplier confirms that rotation is acceptable.
This tool models a simple axis lock and does not determine more complex material direction requirements.
Comparing supplier quotes
Equal sheet counts can still produce different budgets when charging bases, minimum fees and tolerances differ.
Confirm per-metre versus per-straight-cut charging and whether edge trimming is included.
Record the quote scope to avoid adding the same charge again in extras.
Process assumptions and model limits
The guillotine model only divides a current rectangle from one side to the opposite side using a straight cut.
Curved or irregular laser nesting, common-line cutting and automated CNC toolpaths have different requirements.
Overhanging kerf exceptions are not applied, so actual machine practice may differ.
- Defects, holes, heat deformation, clamps, machine access, cut-order stress and finished tolerances are excluded.
Verify them against supplier instructions and drawings. - Existing offcuts, finite inventory, mixed thicknesses, quantity discounts and scrap proceeds are not calculated automatically.
Compare alternative stock quotes by recalculating each set of conditions. - Thickness and dimensions do not establish structural strength, suitability or safe machine operation.
Treat the schedule as planning input pending professional fabrication review.
Checks before placing an order
- Align material, surface, thickness and units, then confirm measured stock and size tolerances.
Get new kerf assumptions and rates when thickness changes. - Check that the supplier allowance is per edge rather than a combined trim loss.
Edge-trimming work is excluded from the modelled internal cutting charge. - Align cut charging basis, minimum fees, delivery and tax inclusion.
Do not add trimming again when it is already included in the stock quote. - Reconcile all-sheet quantities in TXT with the drawings, and identify the sheet shown by each SVG.
After changing dimensions or quantities, send an updated worksheet for supplier confirmation.
Frequently asked questions
Can I order only the area lower bound?
The bound rounds up total finished area divided by usable sheet area.
It ignores kerf, rectangle shapes and rotation restrictions, so a feasible layout may need more sheets.
Use the verified layout count when requesting a supplier quote.
Is this the globally optimal layout?
The tool compares six sorting and straight-splitting combinations and selects the best by its stated priorities.
It does not exhaustively search every rectangular layout or cut sequence, so global optimality is not guaranteed.
Reaching the area bound does not establish the lowest cutting cost or practical machine feasibility.
What happens to rotation when grain is specified?
With no direction constraint, each row may allow 0° or 90° rotation.
Selecting stock-width or stock-height grain locks every part to its entered width and height, regardless of the rotation checkbox.
Split orders with differing grain requirements according to supplier drawings.
Does zero kerf mean zero cutting charges?
A zero-width kerf still requires a straight cut when a surplus dimension must be separated.
A positive per-metre or per-cut rate therefore produces a charge.
Only an axis that exactly matches the current usable rectangle needs no separating cut; edge trimming remains separate.
Does thickness change packing or calculate weight?
Thickness records the specification of one consistent material and thickness group.
The calculator does not infer weight, strength, heat effects or prices from thickness.
Update confirmed kerf, machine assumptions and quote rates when thickness changes.
Can all remnant area be reused in the next order?
Remnant area is the sum of separate rectangles left after cutting.
A narrow strip and one large sheet may have equal areas but different uses.
Check their coordinates, dimensions, condition and clamping allowances; no remnant value is deducted from the budget.
Why might the actual quote exceed the calculated budget?
The model sums entered stock prices, straight cuts inside the usable area and confirmed extras.
Edge trimming, minimum charges, thickness-dependent work, tolerances, delivery and additional tax may be separate.
Align quote scope and charging basis, then record extras without duplication.
What if parts do not fit or exceed the calculation limit?
Totals above your chosen limit or 200 parts fail input validation.
If any part cannot fit after margin, kerf and direction constraints, the complete order total is withheld.
Check measurements and stock specifications, and split material groups without assuming automatic remnant sharing between orders.
Source and next steps
Source checked on 2026-10-13.
Google OR-Tools two-dimensional non-overlap constraint definition was consulted for rectangle boundary modelling.
This implementation uses its own pure TypeScript packing and verification; it does not run OR-Tools.
Recheck stock and cutting rates, material direction, margins and tolerances using supplier specifications and quotes at every order.
Enter your required parts and save the complete TXT worksheet for a supplier quote under the same conditions.
Decide the order quantity and preparation budget after the sheet count and quote scope are confirmed.
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