A percentage needs its own geometric boundary
Two pallet plans can have the same footprint utilization and different volume percentages. That is not necessarily an inconsistency. Area utilization compares a layer’s carton footprints with an available rectangle. A cube ratio compares summed carton volume with a chosen three-dimensional envelope. The outer envelope may include the base, and a maximum-height reference can include unused headroom. These denominators must be identified before comparing the percentages.
This fictional comparison uses a 1200 by 800 mm base, 144 mm base height, and 1500 mm maximum total height. The carton footprint is 400 by 300 mm, horizontal rotation is allowed, and both case gap and edge clearance are 10 mm. The actual layout engine finds six cases per layer with best-found status. Compare vertical carton heights of 250 and 200 mm without changing those horizontal inputs. The inputs are hypothetical, not an approved packaging arrangement.
Keep the area basis visible
Six carton footprints cover 6 × 400 × 300 = 720,000 mm². After 10 mm clearance on each side, the usable rectangle is 1180 × 780 = 920,400 mm². The engine’s footprint utilization is therefore about 78.226858%. If someone instead uses the whole 1200 by 800 base as denominator, the coverage is 75%. Both calculations can be reproduced, but they describe different reference areas. Name the area rather than presenting two unexplained percentages.
The cube core’s stack envelope uses the full base length and width, even though the layout engine reports footprint utilization against its inset usable rectangle. Consequently, its geometric cube fill in this example is 75%, not 78.226858%. This is a useful reason to inspect definitions instead of assuming an area output and a volume output must be numerically identical. Gap space and inset margins remain inside the full stack envelope.
| Output or calculation | 250 mm cases | 200 mm cases |
|---|---|---|
| TI and HI | 6 and 5 | 6 and 6 |
| Carton count | 30 | 36 |
| Cargo stack envelope | 1.2 m³ | 1.152 m³ |
| External carton sum | 0.9 m³ | 0.864 m³ |
| Planned loaded envelope | 1.33824 m³ | 1.29024 m³ |
| Maximum-height reference | 1.44 m³ | 1.44 m³ |
| Geometric cube fill | 75% | 75% |
| Reference envelope fill | 62.5% | 60% |
Reproduce the horizontal and vertical results
Open the 250 mm case scenario and the 200 mm case scenario. Both retain the same six-case best-found footprint. Their whole-layer limits are five and six, because the available height above the base is 1356 mm. Planned total heights are 1394 and 1344 mm. The second plan has more cartons but a smaller carton-volume sum because each carton is shorter.
The cube display rounds geometric fill and footprint utilization to one decimal place: 75% and 78.2% here. The underlying ratios still have different denominators. Planned-envelope fill is 0.9 / 1.33824 ≈ 67.2525108% for the taller cases and 0.864 / 1.29024 ≈ 66.9642857% for the shorter cases. These ratios include the same base region but different cargo heights, so they need not match the 75% cargo-only fill.
Explain why more cases can mean less reference fill
The thirty-six-case plan contains six more cartons than the thirty-case plan, but carton count is not a volume measure when carton heights differ. The shorter carton cube is 0.024 m³ instead of 0.03 m³. Thirty-six times 0.024 is 0.864, while thirty times 0.03 is 0.9. At the shared 1.44 m³ reference denominator, those become 60% and 62.5%. Reporting “more cartons” as “more cube utilized” would lose this distinction.
Even when case dimensions stay unchanged, moving a maximum-height budget between complete-layer thresholds can alter reference fill without altering planned volume. The reference prism changes continuously with the budget, whereas a complete-layer stack changes in steps. A utilization comparison should therefore hold the reference definition constant or explicitly explain its change. Otherwise, an apparent improvement can arise solely from choosing a smaller denominator.
Reproduce and retain the input record
Inputs: base 1200 × 800 × 144 mm; case footprint 400 × 300; gap 10 mm; clearance 10 mm; rotation allowed; max total height 1500 mm. Compare case heights 250 and 200. Layout TI 6, best-found, usable area 920,400 mm². Preserve all ratio denominators: inset area, full cargo stack, planned envelope including base, and maximum-height reference.
Choose a metric for a concrete decision
For comparing horizontal layouts, use the stated area utilization alongside placements and count. For comparing unused space within the modeled cargo stack, use geometric cube fill. For reconciling an outer-dimensional record, retain planned envelope volume and identify the base contribution. For comparing with a fixed dimensional allowance, reference-envelope fill can be useful. None is a universal packing-quality score, and maximizing one does not establish an operationally acceptable load.
The best-found status also matters: this six-case result is a valid found layout, rather than a proof that no larger layout exists under the search model. The utilization percentages describe that result. They do not upgrade its search evidence to optimal status. Nor do they establish weight compliance, case compression suitability, restraint, or stability. Those decisions need their own inputs and checks, rather than an inference from a high geometric percentage.
For an audit worksheet, put the numerator and denominator in separate columns before the percentage. A row reading 720,000 divided by 920,400 mm² makes the area basis explicit; a row reading 0.9 divided by 1.2 m³ makes the cargo-volume basis explicit. A bare percentage copied from a screen loses that information. Keeping the fractions also allows another reviewer to reproduce the calculation without relying on the same display rounding.