Examples
Examples
Try the starting example
- Usable shelf width (cm)
- 60
- Usable shelf depth (cm)
- 40
- Usable shelf height (cm)
- 20
- Gap between containers and above each (cm)
- 2
- Containers: name, width, depth, height cm, copies
- Box,28,18,10,4
- Containers placed
- 4
- Placement coordinates and sizes (cm)
- Box#1: (0, 0; 28, 18); Box#2: (30, 0; 28, 18); Box#3: (0, 20; 28, 18); Box#4: (30, 20; 28, 18)
- Containers left unplaced
- None
- Unused shelf footprint (cm²)
- 384
Try another scenario
- Usable shelf width (cm)
- 60
- Usable shelf depth (cm)
- 40
- Usable shelf height (cm)
- 20
- Gap between containers and above each (cm)
- 2
- Containers: name, width, depth, height cm, copies
- Box,30,20,19,2
- Containers placed
- 0
- Placement coordinates and sizes (cm)
- None
- Containers left unplaced
- Box#1, Box#2
- Unused shelf footprint (cm²)
- 2400
Calculation method
Calculation method
Containers placed
Sort largest footprint first; first-fit into nonoverlapping free rectangles. No rotation or stacking.
Placement coordinates and sizes (cm)
Give x,y measured from shelf front-left and the original container footprint.
Containers left unplaced
List copies that cannot fit the chosen rectangular-split heuristic or required top gap.
Unused shelf footprint (cm²)
Shelf width × depth − total placed container footprint; includes inter-container gaps.
Symbols and units
- a
- Usable shelf width (cm)
- b
- Usable shelf depth (cm)
- c
- Usable shelf height (cm)
- d
- Gap between containers and above each (cm)
- e
- Containers: name, width, depth, height cm, copies
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 single measured shelf and one layer of unrotated containers. The entered gap applies between containers and above them; no outer-edge gap is added. It does not validate food storage, ventilation or shelf load limits, and the heuristic is not globally optimal.
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.