Box Perimeter

Twice the length plus the width. It would not deserve a page except that it is the input McKee's formula is most sensitive to after $ECT$, and that three separate conventions collide in it.

Why perimeter and not area. A corrugated box carries a top load through its four side panels standing on edge, so what resists the load is a length of loaded edge, not a footprint. $ECT$ is quoted as a force per unit of that edge — pounds-force per inch, kilonewtons per metre — and multiplying it by the perimeter gives, to first order, the load the box would carry if the panels did not buckle. Everything else in McKee's formula is the correction for the fact that they do. This is also why depth does not appear in $Z$: the panels are loaded on their bottom edges, and how tall they are affects whether they buckle rather than how much edge is bearing.

A bigger box is a stronger box, and this surprises people. On the same board, doubling the perimeter roughly multiplies compression strength by $2^{0.492}$, about 1.41. Strength goes up; strength per unit of floor area goes down, which is the number a pallet pattern actually cares about. Both facts are in the same exponent and they are not in conflict.

The perimeter is not the shape. Infinitely many rectangles share a perimeter, and McKee's formula cannot tell them apart because it only ever receives $Z$. The real boxes differ: a square footprint is the strongest arrangement of a given perimeter, because the four panels reach their buckling loads together, while in an elongated box the two wide panels buckle first and hand their share to the narrow ones, which then fail in turn. An elongated box therefore tests below what the formula predicts, and the discrepancy grows with the aspect ratio. If you are comparing a 16 x 12 against a 21 x 7 of the same perimeter, the formula says they are identical and they are not.

Three conventions worth keeping straight. Corrugated dimensions are quoted INSIDE, in the order length x width x depth, with length the longer footprint dimension — the one running along the manufacturer's joint. Inside is what matters because it is what the product has to fit into, and because the blank has to be larger by a caliper at every fold: a C-flute box loses about 4 mm of inside dimension for every wall it wraps. And this $Z$ is not the girth a carrier bills you by, which is normally the longest dimension plus twice each of the other two — a different quantity computed for a different purpose, and confusing the two is a good way to specify a box that is either overbuilt or mis-rated.