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Geometry & Practical Projects

Packing Box Volume Calculator

Find how many identical items fit in a box in a grid, the best orientation, box volume and space used.

Your inputs

Results

Items that fit (same orientation, grid packing)

24

Box volume
96 L
Space used
100%
Best item orientation (L × W × H)
20 × 20 × 10 cm
Volume-only upper bound
24

✓Exact calculation — rounded only for display

What this calculator does

For shipping and storage, find how many identical items fit in a carton by testing every orientation of the item, and see how much of the box is wasted space.

Formula and method

For each of the 6 orientations: count = ⌊L/l⌋ × ⌊W/w⌋ × ⌊H/h⌋; the best orientation is reported.

Worked example

Calculated by this tool with its default inputs:

Inputs

  • Box inside length (cm): 60
  • Box inside width (cm): 40
  • Box inside height (cm): 40
  • Item length (cm): 20
  • Item width (cm): 20
  • Item height (cm): 10

Results

  • Items that fit (same orientation, grid packing): 24
  • Box volume: 96 L
  • Space used: 100%
  • Best item orientation (L × W × H): 20 × 20 × 10 cm
  • Volume-only upper bound: 24

How to read the results

The volume-only upper bound shows how much space is lost to awkward sizes.

Assumptions and limitations

  • Only same-orientation grid packing is considered; mixed orientations can sometimes fit more.

Quantities and costs are planning estimates. Add sensible allowances, and check with suppliers, carriers or professionals before buying, shipping or building.

Questions

Why fewer than volume suggests?

Items cannot be cut to fill leftover gaps.

Methodology and verification

Result type
Exact mathematical calculation (rounded only for display)
Formula version
1.0
Automated verification
3 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
Editorial review
Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.

Privacy

Everything you enter is calculated in this browser and is not sent to Numerith or anyone else. Inputs are added to a share link only if you choose to include them. Privacy policy