About this calculator
Count identical rectangular products in a carton using repeated grids. Inside carton dimensions, clearance at each wall, gaps between neighbors and permitted product orientation define the usable arrangement.
Inputs
How to use this calculator
Carton scenario
- Internal carton length (in)Use usable inside dimensions, not outside shipping measurements.
- Internal carton width (in)Account for inserts or obstructions separately.
- Internal carton height (in)Use measured usable height.
Shared inputs
- Product or bundle length (in)Rectangular outer dimensions including immediate packaging.
- Product or bundle width (in)One identical product for grid counting; one fixed bundle for box selection.
- Product or bundle height (in)Original upright height.
- Clearance at each wall (in)Applied at both ends of each axis. Enter usable clearances for your packaging design.
- Gap between adjacent products (in)Applied only between neighbors, not after the last product.
- Allowed product orientationsChoose side laying only when the product and packaging allow it.
Enter the shipment or scenario values, then select Calculate result.
Method
Formula and variables
Usable side = max(0, internal carton side − 2 × wall clearance). Count per axis = floor((usable side + product gap) ÷ (oriented product side + gap)). Multiply the three counts. Compare the allowed uniform orientations and report the largest grid.
- Internal carton length (in)
- Use usable inside dimensions, not outside shipping measurements.
- Internal carton width (in)
- Account for inserts or obstructions separately.
- Internal carton height (in)
- Use measured usable height.
- Product or bundle length (in)
- Rectangular outer dimensions including immediate packaging.
- Product or bundle width (in)
- One identical product for grid counting; one fixed bundle for box selection.
- Product or bundle height (in)
- Original upright height.
- Clearance at each wall (in)
- Applied at both ends of each axis. Enter usable clearances for your packaging design.
- Gap between adjacent products (in)
- Applied only between neighbors, not after the last product.
- Allowed product orientations
- Choose side laying only when the product and packaging allow it.
Interpret the result
The count is the best allowed uniform orientation among entered carton scenarios. It is not a mixed-orientation packing optimum or a protection assessment.
Outputs: Maximum uniform-grid product count and orientation
Rectangular identical products in one uniform orientation. No mixed orientations, deformable packing, nesting, compression, weight limit or packaging protection is solved. A zero fit is valid. The result is a grid estimate, not a proven 3D optimum. Carton scenarios are alternatives.
Worked example
Check the arithmetic
This example uses the starting values shown above. The arithmetic below is calculated independently of the interactive result.
Work through the calculation
- Default upright grid: floor(12 ÷ 4) × floor(10 ÷ 3) × floor(8 ÷ 2) = 3 × 3 × 4 = 36 products.
- The other upright footprint orientation fits floor(12 ÷ 3) × floor(10 ÷ 4) × 4 = 32. The allowed maximum is 36.
Compare the displayed result
Expected displayed result: 36 products
FAQs
Why is clearance subtracted twice from each carton side?
There is a wall at each end of an axis. Gaps apply only between neighboring products; wall clearance reserves space at both outer ends.
Example inputs and options
Starting values are examples unless a field identifies a dated rule. Unit selectors convert only fields marked for conversion. Rates and model options keep the units and basis shown in their labels.
- Internal carton length (in)
- Example: 12
- Internal carton width (in)
- Example: 10
- Internal carton height (in)
- Example: 8
- Product or bundle length (in)
- Example: 4
- Product or bundle width (in)
- Example: 3
- Product or bundle height (in)
- Example: 2
- Clearance at each wall (in)
- Example: 0
- Gap between adjacent products (in)
- Example: 0
- Allowed product orientations
- Example: Upright: compare two footprint orientationsOptions: Upright: compare two footprint orientations; Compare all six orientations, including side laying