Calculate how many smaller product boxes fit inside a master carton or shipping container across all 6 3D spatial rotations to maximize volume utilization.
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The Box Packing Calculator solves the three-dimensional orthogonal packing problem for shipping and manufacturing. It computes the maximum number of rectangular item boxes that fit inside a master carton, crate, or sea container by testing all 6 spatial orientations.
N = \max_{\pi} \left( \left\lfloor \frac{L}{o_1} \right\rfloor \times \left\lfloor \frac{W}{o_2} \right\rfloor \times \left\lfloor \frac{H}{o_3} \right\rfloor \right), \quad \text{Util} = \frac{N \cdot (l \times w \times h)}{L \times W \times H} \times 100\%Where π evaluates all 6 spatial permutations of product dimensions (l, w, h) against master container dimensions (L, W, H).
Scenario: Packing 6" × 4" × 3" retail packages into a 24" × 18" × 12" master carton
Master container volume: 24 × 18 × 12 = 5,184 cu in.
Item volume: 6 × 4 × 3 = 72 cu in.
Optimal alignment: 24/6 = 4 along length, 18/4 = 4 along width, 12/3 = 4 along height.
Total units packed: 4 × 4 × 4 = 64 boxes.
Packed volume: 64 × 72 = 4,608 cu in (88.9% space utilization).
Yes. It automatically evaluates all six rotational permutations of the item box (L×W×H, L×H×W, W×L×H, W×H×L, H×L×W, H×W×L) to determine the orientation yielding the maximum item count.
Unless the container dimensions are exact integer multiples of the item dimensions, there will be leftover void space along the edges that cannot accommodate another full item.
Yes. Enter the interior usable dimensions of the master box and the exterior dimensions of the item box including any bubble wrap or protective padding.
Yes! Enter standard pallet dimensions (e.g., 48" × 40" with your allowed maximum stack height) as the container dimensions.
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