Examples
Examples
Try the starting example
- Usable roll width (cm)
- 100
- Gutter between rectangles and shelves (cm)
- 5
- Jobs: name, width cm, height cm, copies
- A,60,40,1 B,30,40,2
- Allow 90-degree rotation: yes or no
- no
- Required roll length (cm)
- 85
- Artwork rectangle area (cm²)
- 4800
- Unused roll area including gutters (cm²)
- 3700
- Placement coordinates and oriented sizes (cm)
- A#1: (0, 0; 60 × 40); B#1: (65, 0; 30 × 40); B#2: (0, 45; 30 × 40)
Try another scenario
- Usable roll width (cm)
- 60
- Gutter between rectangles and shelves (cm)
- 0
- Jobs: name, width cm, height cm, copies
- A,40,20,1 B,20,20,1
- Allow 90-degree rotation: yes or no
- no
- Required roll length (cm)
- 20
- Artwork rectangle area (cm²)
- 1200
- Unused roll area including gutters (cm²)
- 0
- Placement coordinates and oriented sizes (cm)
- A#1: (0, 0; 40 × 20); B#1: (40, 0; 20 × 20)
Calculation method
Calculation method
Required roll length (cm)
Choose each permitted orientation with minimum height that fits width, sort descending height, then first-fit into fixed-height shelves.
Artwork rectangle area (cm²)
Sum width × height of all requested rectangles.
Unused roll area including gutters (cm²)
Usable roll width × resulting roll length − artwork area.
Placement coordinates and oriented sizes (cm)
Top-left x,y and width×height for each placed copy; coordinates start at the roll origin.
Symbols and units
- a
- Usable roll width (cm)
- b
- Gutter between rectangles and shelves (cm)
- c
- Jobs: name, width cm, height cm, copies
- d
- Allow 90-degree rotation: yes or no
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- A feasible shelf heuristic for rectangles, not optimal nesting. Rotation choice is local minimum height, not a global search. No outside edge gutter, bleed, roll defects or print-direction constraint is added.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
OpenStax: arithmetic and geometry ↗
Background reading; this does not imply endorsement or independent review of SumFizz.