Use two independent equations for a complete-layer stack
A complete-layer result should satisfy case count equals TI times HI and total loaded height equals pallet base height plus HI times vertical case height. Verify both equations using the same case orientation and dimensional boundary as the original calculation. A report can have a correct quantity but a mislabeled cargo height, or a correct height and a quantity that actually includes a partial layer. One matching number does not resolve the other.
These equations describe identical complete layers on a stated base. They do not reconstruct an arbitrary irregular or partial stack from quantity alone. When the record describes complete layers, use integer TI and HI. When it describes a partial top layer, retain its arrangement and measured highest point separately. Do not divide a remainder across the layer and treat the resulting average as an outside height.
Rebuild a forty-eight-case scenario
Assume eight cases per complete layer, each case standing 240 mm tall, on a 144 mm base. A supplied total loaded-height condition of 1600 mm gives floor((1600 − 144) / 240) = 6 complete layers. The case count is 8 times 6 = 48, and the occupied total height is 144 + 6 times 240 = 1584 mm. The remaining dimensional headroom is 16 mm.
The 1600 mm condition includes the base in this scenario. It is not a cargo-only height and should not have another base height added to it before calculating the layers. Likewise, 1440 mm is the case stack’s cargo height, not the total height of the loaded unit. Preserve the label attached to each height rather than treating all three numbers as interchangeable references to the same object.
| Reported statement | Reconstruction | Diagnostic conclusion |
|---|---|---|
| TI 8, HI 6, total 48 | 8 × 6 = 48 | Consistent complete-layer quantity |
| Total loaded height 1584 mm | 144 + 6 × 240 = 1584 | Consistent base-plus-cargo height |
| Cargo height 1440 mm | 6 × 240 = 1440 | Valid cargo-only value |
| Total loaded height 1440 mm | Base missing from the label | Correct to 1584 for this stack |
| Forty-nine cases described as six full layers | 49 is not 8 × 6 | Investigate a partial case group or quantity error |
| Fifty-six cases at TI 8 | HI would be 7; height 1824 mm | Exceeds the stated 1600 mm total condition |
Reverse the result without hiding an inconsistent fraction
If the recorded total is forty-eight and TI is eight, the implied HI is 48 / 8 = 6. If the recorded loaded height is 1584, the implied HI is (1584 − 144) / 240 = 6. Those independent reconstructions agree. If someone records the limiting value 1600 as occupied height, the height reconstruction gives 6.066666 recurring, which is not a complete-layer count. That indicates a label or scope problem, not permission for a fraction of a case layer.
If total quantity is forty-nine, dividing by eight gives 6.125. The report must explain a partial layer or correct the quantity; it cannot describe the result as six identical full layers. A single extra case could make the highest point 1824 mm when placed on top of the six layers, but another accepted placement could have a different envelope. Quantity does not determine that extra case’s position or whether the arrangement is suitable.
Check the source limit as well as the occupied height
A loaded height below the entered condition supports the arithmetic comparison only when the condition describes the same base-to-top measurement boundary. If the source document gives cargo height alone, convert its meaning explicitly before entering a total-height field. Keep the original wording with the derived input so another reviewer can see whether the base was included once. Do not silently reinterpret an ambiguous height label.
Case height also needs the correct vertical direction. A horizontal footprint rotation keeps the 240 mm height unchanged in this example. Placing a carton on another face is a different physical arrangement requiring its own instructions and height input. If an observed cap or sheet changes the finished outside height, record it separately or use the direct measured total. Avoid adding its thickness twice when the measurement already includes it.
Make a quantity-and-height verification record
Write TI, HI, total case count, vertical case height, empty base height, occupied total height and the source height condition with its measurement boundary. For the example retain 8, 6, 48, 240, 144, 1584 and a 1600 mm total limit. Record both reverse calculations. Explain any partial group, accessory height or inconsistent fraction before closing the check.
Reproduce the complete-layer calculation directly
Open the forty-eight-case complete-layer example. Verify that the uniform layer is eight, HI is six and occupied loaded height is 1584 mm. The input limit remains 1600 mm. Use the TI-HI calculator when additional documented gross or rated-payload conditions must be included.
If a mass condition reduces HI, use the reduced complete-layer value in both equations. Do not retain the height-only quantity while copying the weight-constrained height. In a planned-HI validation mode, a failed condition can leave the proposed count visible for review; identify it as the proposed stack rather than a newly calculated permissible maximum. Read mode and check status before sharing the numerical result.
Distinguish arithmetic agreement from physical verification
Agreement between quantity and height equations confirms that the stated complete-layer record is internally consistent. It does not establish that the actual pallet has those layers or that all cases have the recorded vertical dimension. Compare the record with the finished unit when the task requires an observed envelope. A packing worksheet also does not establish carton stacking strength, pallet application rating or transport approval. Retain those separate requirements with their actual evidence.
Reference scope
EPAL 1 product information supports the 144 mm reference base height used here. The 240 mm case height and 1600 mm total condition are explicit scenario assumptions.