Carton Orthogonal Case-Pack Calculator
Which uniform orthogonal product rotation fits the most rigid rectangular units in one carton?
Method, formula and assumptions
Evaluate all six orthogonal dimension permutations. Each uniform layout count multiplies three floored axis fits. Select the largest count and round quantity/count up to cartons.
Input definitions and supported units
- Carton inside length (cm): Measured or assumed numerical value, from 0.1 to 1000; must be positive.
- Carton inside width (cm): Measured or assumed numerical value, from 0.1 to 1000; must be positive.
- Carton inside height (cm): Measured or assumed numerical value, from 0.1 to 1000; must be positive.
- Product dimension A (cm): Measured or assumed numerical value, from 0.1 to 1000; must be positive.
- Product dimension B (cm): Measured or assumed numerical value, from 0.1 to 1000; must be positive.
- Product dimension C (cm): Measured or assumed numerical value, from 0.1 to 1000; must be positive.
- Units to pack: Whole-number count, from 0 to 1000000000; zero is supported where the stated method permits it.
Worked example with answer
A 30 x 20 x 15 cm inner carton with 10 x 5 x 3 cm units holds 60 in its best uniform layout, using 100% geometric volume. Packing 1,000 units needs 17 cartons with 20 unused unit slots.
How to use the results
The model chooses one rotation per carton, not mixed nesting. It gives a unit case pack and carton count, unlike upright pallet-layer planning.
Results retain full precision internally and display up to four decimal places. Very small nonzero results use scientific notation rather than appearing as zero. Check the labels before comparing values across units.
Limitations and references
All rotations must be permitted by the product. Cushioning, tolerances, crush resistance, orientation restrictions and shipping mass are excluded.
The method is a self-contained arithmetic, geometric or explicitly stated mathematical model. There are no imported tariffs, empirical presets or equipment specifications; measured values and allowances must come from your own process.
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Creator & reviewers
Creator persona
- Riley ChenTime planning & productivity
Reviewer personas
- Avery BennettPersonal finance & everyday budgeting
- Devon ShawFormula & assumptions review