Why volumetric math overstates what fits
Ask most people how many cartons fit in a container and they will reach for the same calculation: container volume divided by carton volume. It is fast, it is intuitive, and it produces a number that is reliably too high.
The gap between volume and geometry
Volume is a scalar. Packing is not. A 40-foot container has a fixed internal width, height and depth, and a carton can only be placed at whole multiples of its own dimensions along each axis. The moment a carton does not divide evenly into a container dimension, the remainder becomes unusable space — and that remainder exists on all three axes at once.
Consider a container 240 cm wide and a carton 50 cm wide. Four cartons span 200 cm. The remaining 40 cm is not enough for a fifth. That 40 cm strip runs the entire height and depth of the container, and volumetric math has already counted it as usable.
The error compounds
That would be manageable if it happened once. It happens three times, once per axis, and the effects multiply rather than add. A few percent of waste on each dimension can compound into a double-digit shortfall against the volumetric estimate.
This is why a load that "definitely fits" on paper arrives at the dock and does not. The arithmetic was never modelling the problem.
Orientation is a decision, not a detail
A carton can usually be placed in more than one orientation, and so can the container be loaded along different axes. Those choices interact: the orientation that fits the most cartons along the width may waste more along the depth. There is no shortcut that identifies the best combination — it has to be tried.
PackerAI works through the container orientations and reports the arrangement that actually produced the highest count, along with where every carton sits. The number comes with its working attached, which means a surprising result can be inspected rather than argued about.
What to do instead
Treat volumetric math as an upper bound and nothing more. It tells you what is impossible, not what is achievable. Before you quote a load, book a container, or order a pallet of boxes, check the geometry — because that is the constraint that will actually decide the outcome.