LifeTally
Box grid packing calculator
How many identical boxes fit in each uniform rectangular grid?
Compare six shared orientations using usable container dimensions and outer item dimensions.
Your dimensions in centimetres
Use measured usable inner container dimensions and outer item dimensions including packaging. All six values use centimetres; fractions are allowed. A zero container dimension gives a zero-capacity limiting case.
Compare orientations
| Item edges along L × W × H | Along L | Along W | Along H | Total |
|---|---|---|---|---|
| A–B–C 25 × 18 × 12 cm | 2 | 2 | 2 | 8 |
| A–C–B 25 × 12 × 18 cm | 2 | 3 | 1 | 6 |
| B–A–C 18 × 25 × 12 cm | 3 | 1 | 2 | 6 |
| B–C–A 18 × 12 × 25 cm | 3 | 3 | 1 | 9 |
| C–A–B 12 × 25 × 18 cm | 5 | 1 | 1 | 5 |
| C–B–A 12 × 18 × 25 cm | 5 | 2 | 1 | 10 |
How the estimate works
For each orientation, divide each usable container dimension by the item edge along that axis and round down to a whole count. Multiply the three counts. Repeat for all six permutations of A, B and C. Unused strips of space are not combined.
nL = ⌊L ÷ x⌋; nW = ⌊W ÷ y⌋; nH = ⌊H ÷ z⌋
N = nL × nW × nHOnly regular axis-aligned grids with one shared orientation are compared. This is not an optimiser for mixed orientations or diagonal placement. No gaps, irregular shapes, weight, stacking strength or loading path are modeled; physical fit is not guaranteed. If rotation is restricted, use only permitted rows; the highest count may not apply.
OpenStax: rectangular solids and counting layers ↗Check the filled example
Chosen example: container 60 × 40 × 30 cm; item 25 × 18 × 12 cm. A–B–C gives 2 × 2 × 2 = 8. C–B–A gives 5 × 2 × 1 = 10, the highest of these six grids. These are example dimensions, not a shipping standard.
Accepted input values
Accepted numeric inputs are shown below. Whole counts use their decimal representations and are displayed in full, including very large counts. This does not remove input precision limits.
- Usable container length L, cm
- 60
- Usable container width W, cm
- 40
- Usable container height H, cm
- 30
- Outer item edge A, cm
- 25
- Outer item edge B, cm
- 18
- Outer item edge C, cm
- 12