A folded box is always smaller than the sum of its sides

The neutral axis, bend allowance, and why the flat pattern is never obvious.

Simply adding up the length of each face of a folded sheet metal box, measured from corner to corner on the outside, always overstates the flat piece of metal actually needed to make it, because the metal at each bend does not fold along a sharp mathematical line, it folds through a curved region where the outer surface stretches, the inner surface compresses, and only one specific layer somewhere between the two keeps its original length exactly unchanged.

Designing a sheet metal part is largely a matter of discovering what the press brake will refuse to do, and nowhere does that lesson arrive earlier or more directly than in working out, for the first time, exactly how long a flat piece of metal needs to be to fold up into a box of a stated finished size.

Why a bend consumes more material than it looks like it should

A sheet of metal bent through a right angle does not pivot around a knife-sharp crease the way a piece of folded paper appears to in a simplified sketch, it bends through a rounded region set by the tooling doing the bending, and across the thickness of that rounded region, the outer surface of the bend is stretched around a larger radius than the inner surface, which is compressed around a smaller one. Something has to give in between those two extremes, and it does, in the form of a layer running through the material's thickness that neither stretches nor compresses at all, simply following the bend at its own original, unchanged length the whole way through. Because the outer surface stretches, the flat length needed to produce it is less than a simple corner-to-corner measurement of the finished part would suggest, since some of what looks, on the finished part, like extra length folded into the corner was never extra length in the flat sheet to begin with, it was ordinary material that got stretched into occupying more room once the bend pulled it around the outside of the curve.

The bent-elbow comparison

Bending an arm at the elbow stretches the skin on the outside of the joint taut, visibly smoothing out any slack it had while the arm was straight, while the skin on the inside of the same joint does the opposite, bunching into loose folds as the two sides of the joint move closer together. Somewhere between those two surfaces, running roughly along the bone itself, sits a line that does neither, simply pivoting through the bend at essentially its own original length the whole time, neither stretched taut like the outer skin nor bunched loose like the inner skin. A folded sheet metal corner bends through exactly this same three-part pattern, an outer surface stretched, an inner surface compressed, and a single layer between them, called the neutral axis, that alone keeps the length it started with, and it is the position of that neutral axis inside the material's thickness, not the outer corner-to-corner measurement anyone would naturally reach for with a ruler, that actually decides how much flat material a given bend truly needs.

Why the flat pattern is never obvious from the finished shape alone

Working backward from a finished box to the flat piece of metal that folds up into it means working out, for every single bend, how much of the finished part's outer dimension was genuine flat length carried straight through from the sheet and how much was stretched into existence by the bend itself, a calculation that depends on the metal's thickness, the radius the tooling actually bends around, and how that specific material behaves under this specific kind of stretching. Two designers each measuring only the outer dimensions of an identical finished box, one assuming the flat pattern is simply the sum of those outer measurements and the other correctly subtracting the small amount consumed by each bend, will cut two visibly different flat blanks from the same drawing, and only one of the two will fold up into a box that actually matches the finished dimensions the drawing was describing.

The number that matters here

The flat pattern needed to fold a box is always somewhat shorter than the simple sum of each face's outer dimension, the missing length concentrated entirely within each individual bend rather than spread evenly across the whole part, and that missing length, though it depends on thickness and bend radius, commonly amounts to noticeably less than the material's own thickness for any single bend, a modest figure per bend that still adds up to a real, measurable difference across a part with several folds in it.

What this changes in practice

A flat pattern cut to the naive sum of a box's outer face dimensions comes out too long at every single bend, and a part folded from that oversized blank either binds against itself at each corner or simply refuses to close to the intended finished size at all, a mistake that shows up only once the folding actually happens rather than at any earlier stage where the flat pattern alone was being checked on a drawing. Getting the flat pattern right the first time means accounting for the neutral axis and the specific bend allowance it produces before a single sheet is cut, which is exactly the calculation the rest of this set builds directly on top of, starting with the limit on how tight a bend the same material can actually be folded through in the first place. Most sheet metal design software now calculates this automatically once a material and a bend radius are entered, and it is tempting to treat that as the end of the story, but the software's own figure is only as good as the bend radius and material properties actually entered into it, and a designer who does not understand why the correction exists in the first place has no way of noticing when one of those inputs is wrong.