Packing indexTool 02 / Space

Packing Cube Matrix

Count identical cubes along three bag dimensions.

Your scenario

Sample values explain the method; they are not recommendations. Replace them, then calculate.

What this tool helps you organize

Count identical cubes along three bag dimensions. It is one defined worksheet, not a complete assessment of your circumstances.

Fixed orientation only; soft-sided shapes, handles and packing pressure are excluded.

Method and calculation rules

Count = floor(bag L/cube L) × floor(bag W/cube W) × floor(bag H/cube H). Volumes convert cm³ to liters.

Display values are rounded for readability. The calculation uses the entered numbers before display rounding. Whole-unit outputs use the rounding rule stated in the method.

Know your inputs

  • Bag internal length (cm) — Accepted range: 0.01 to 1000000.
  • Bag internal width (cm) — Accepted range: 0.01 to 1000000.
  • Bag internal height (cm) — Accepted range: 0.01 to 1000000.
  • Cube length (cm) — Accepted range: 0.01 to 1000000.
  • Cube width (cm) — Accepted range: 0.01 to 1000000.
  • Cube height (cm) — Accepted range: 0.01 to 1000000.

A worked example

Illustrative inputs: Bag internal length (cm): 55; Bag internal width (cm): 35; Bag internal height (cm): 23; Cube length (cm): 25; Cube width (cm): 16; Cube height (cm): 10.

Cubes in fixed orientation: 8

Cube volume: 4 L

Bag bounding volume: 44.28 L

These sample figures illustrate the formula, not a recommended target or a prediction.

How to use the working copy

Define a single scenario, check the units and replace each sample value that does not match it. Calculate and read all three result components, not just the most favorable number.

Change one assumption to compare scenarios. An edited field makes the previous answer stale; recalculate before downloading or printing. Reset sample clears the open result and restores the example entries.

What the answer cannot establish

Fixed orientation only; soft-sided shapes, handles and packing pressure are excluded.

The tool does not verify the accuracy, completeness or current validity of your inputs. Use authoritative current information and qualified judgement when the decision requires them.

Questions about this worksheet

Are the starting values a suggested target?

No. They show how the arithmetic behaves. Use your own checked values and do not infer a recommendation.

Why is my previous result marked stale?

Changing an input means the displayed answer no longer describes the current fields. Recalculate to refresh it.

Can I share an export?

Review the entries and limitations first. A downloaded file is a working copy, not an independently verified report.

Your entries and privacy

The bundled calculation runs in this open browser page. Inputs are not automatically saved as a server-side calculation history. Browser refresh or navigation may clear them.

Contact messages and technical website records are separate from calculator arithmetic. Read the Privacy Policy for the distinction; do not enter confidential records or credentials.