Decide when rounding changes the physical question
A spreadsheet may display pallet dimensions as whole millimetres even when the source is inches. Rounding looks harmless until a row fits exactly at a decimal boundary. The packing model uses the numeric dimensions entered, not the hidden source value or a measurement tolerance. Preserve exact unit conversions through the fit check, then choose reporting precision separately.
NIST's exact international-foot definition gives 0.3048 metre per foot. One inch is one twelfth of that foot, giving 25.4 mm. Thus 48 by 40 inches becomes 1219.2 by 1016 mm, and a 24 by 20 inch case footprint becomes 609.6 by 508 mm. These are unit relationships, not assertions that an actual measured pallet or case has those exact dimensions.
Compare conversion precision with an actual smaller boundary
In fictional comparison A, the available base is exactly 1219.2 by 1016 mm and cases are exactly 609.6 by 508. Two case lengths sum to 1219.2 and two widths sum to 1016, so four fit. The mixed engine returns four and proves the count by area equality. This tight result has no spare span along either grid axis.
Comparison B assumes the available length is instead measured or specified as 1219 mm, while cases retain 609.6 mm length. Two case lengths need 1219.2, exceeding that base by 0.2 mm. The best uniform grid contains two; a mixed arrangement finds three, with an area bound of three and optimal status. The changed count follows from a genuinely smaller declared rectangle, not from a mysterious unit-conversion error.
| Comparison | Base length / width | Case length / width | Uniform TI | Mixed TI |
|---|---|---|---|---|
| A: exact nominal conversion | 1219.2 / 1016 mm | 609.6 / 508 mm | 4 | 4 |
| B: smaller declared base | 1219 / 1016 mm | 609.6 / 508 mm | 2 | 3 |
| C: case rounded down | 1219 / 1016 mm | 609 / 508 mm | 4 | 4 |
C returns four because the model is now packing a smaller case: two 609 mm lengths need only 1218 mm. It is a correct calculation for those altered inputs, but it does not place the 609.6 mm cases from B. A colleague reviewing only the returned count could miss that the source case was rounded down. Preserve the input record to detect that substitution.
Reproduce all three records
Open A with exact conversions, B with the smaller base, and C with the altered case. The height inputs select one layer solely to make the comparison easy to inspect.
Switch to Uniform in each run and confirm four, two, and four. Then return to Mixed and confirm four, three, and four. That extra comparison distinguishes the effect of numerical dimensions from the effect of permitting mixed orientations. Do not compare a mixed result on one tab with a uniform result on another and attribute the whole difference to rounding.
Keep display rounding out of coordinate validation
A displayed coordinate rounded to a whole millimetre may make two rectangles appear to touch or overlap even when the underlying coordinates contain decimals. Save the coordinate export or full numeric values when validating a tight result. Round only the presentation required by the receiving record; do not feed rounded coordinates back into a proof as though they were the original placement.
The engine uses a small numerical comparison tolerance for floating-point arithmetic. That tolerance is not a physical clearance or manufacturing allowance. It does not justify treating a measured 0.2 mm shortfall as available space. Operational fit needs an appropriate measurement basis and confirmed allowances, which must enter the geometry explicitly rather than being inferred from software tolerances.
Track the direction of every rounding choice
Rounding a case down makes fit easier in the model, while rounding an available span down makes fit harder. Rounding both to whole millimetres can hide which effect dominates. A tidy-looking row of integers is therefore not automatically conservative or faithful. Retain the decimal source values and label any intentional alternative scenario. If the receiving system stores only integers, keep a separate source record so its display limitation does not become a physical assumption.
Separate nominal conversion from measured dimensions
An exact conversion changes units without changing the quantity. It does not improve the accuracy of a nominal size or a tape measurement. A pallet sold under a nominal footprint can still need actual measurement for a tight packing task. A filled carton can differ from its drawing because outside projections or bulges matter to the envelope. Record the source of each dimension before deciding which decimals are meaningful.
When uncertainty affects a boundary, compare explicitly stated scenarios rather than rounding opportunistically until the count improves. Do not invent a universal margin or safety factor. The responsible operation should supply the usable base and packed-case envelopes needed for the decision. A sensitivity table is helpful because it shows exactly which assumed dimension changes the count.
Precision and fit record
Source units for A: base 48 by 40 inches, case 24 by 20 inches. Conversion: 25.4 mm per inch. Converted inputs: base 1219.2 by 1016, case 609.6 by 508. Zero gap and clearance. Mixed result 4 optimal. B changes base length to 1219 while retaining the same case, giving 3 optimal. C changes case length to 609 and no longer represents the original case. Retain source, converted values, and measured-value revisions separately.
The methodology explains numeric fit checks. A reliable handoff preserves the physical dimensions and lets formatting follow the calculation, rather than letting display rounding choose the packing answer.