What the pan is measured from
Almost every argument about a flat pattern turns out to be an argument about which surface the dimensions were taken from. This page takes the inside base and the wall height from the inside face of the floor, because that is how a pan that has to hold something is usually specified: the tray has to swallow a part that is ten by eight, so the inside floor is ten by eight.
From there the arithmetic runs in three pieces per direction. The flat part of the floor is the inside base less the radius at each end, because the inside face starts curving a radius before it reaches the wall. The flat part of the wall is the height less one radius, for the same reason at the other end. And between them sits the bend allowance, the arc length along the neutral axis, which is where the metal that used to be a corner has gone.
| Piece | Length along the flat | Worked at 10 in base, 2 in wall, 0.125 t, 0.125 r, K 0.44 |
|---|---|---|
| Floor | base - 2 x radius | 10 - 0.25 = 9.7500 in |
| Wall, each | height - radius | 2 - 0.125 = 1.8750 in |
| Bend, each | (pi/2) x (radius + K x thickness) | 1.5708 x 0.1800 = 0.2827 in |
| Blank length | sum of all five | 14.0655 in |
The two routes have to agree
There is a second way to the same number and it is worth running as a check, because it starts from completely different measurements. Take the outside mould line dimensions: the base measured outside to outside is the inside base plus a thickness at each wall, and each wall measured from the underside of the floor is the height plus one thickness. Add those three legs and subtract one bend deduction for each bend.
For the worked example that is 10.25 plus two lots of 2.125, which is 14.5, less two deductions of 0.2173, which is 14.0655. The same figure to four decimal places. The calculator shows both, and if they ever disagree the arithmetic is broken, not the metal. The identity behind it is simple enough to write out: outside legs minus deductions equals tangent legs plus allowances, because a deduction is exactly two setbacks minus an allowance, and a setback is exactly the difference between an outside leg and a tangent leg.
Why the corner has to be cut away
Look at the flat blank at one corner. The square of material out there belongs to the long wall and to the short wall at the same time. When both walls fold up, that square has to be in two places at once, and since it cannot be, it either buckles into a lump between the walls or splits. So it comes out before forming, and the notch that removes it runs from the blank edge in as far as the bend zone.
Cutting exactly to the bend zone leaves the two walls just touching, which looks tidy on a drawing and behaves badly in practice. The corner of the notch sits right at the edge of the bend, in the region being worked hardest, and a sharp inside corner there is a ready-made crack starter. So the notch runs past the bend line by a relief distance, commonly one to one and a half material thicknesses, and the inside corner of the notch is either drilled round first or broken afterwards.
The drilled version is worth the extra step on anything that matters. Drill a hole centred so its edge lands where the relief depth wants it, then cut straight out to both edges tangent to the hole. The result has no sharp inside corner anywhere and the walls fold without the corner complaining.
Where the walls end up
Cutting the corner away means the finished pan has an open joint at each corner, the width of the relief plus whatever gap the notch left. That gap is normal on a bent pan, and it is why boxes that have to hold liquid get welded, soldered or sealed at the corners, and why boxes that only have to hold parts do not bother. If the corners have to close completely the part is not a plain pan any more; it needs tabs, a lapped corner or a different development.
Wall height also has a floor under it that has nothing to do with this arithmetic. A flange too short to bridge the die opening cannot be formed at all, and the die opening is set by the tooling in the machine. That constraint lives with the press brake tonnage calculator rather than here.
Related layouts
A single bend, or a chain of bends along one axis, is the bend allowance calculator and the multi-bend flat pattern calculator. Once the blanks are drawn, how many of them come off a sheet is the sheet nesting calculator, and gauge to thickness to weight is the gauge chart. The angle the walls actually land at when the ram lets go is the springback calculator.
Questions people ask
How do I calculate the blank size for a sheet metal box?
Work one direction at a time. The flat floor is the inside base less the bend radius at each end. Each wall contributes its height less one radius. Between every floor and wall sits a bend allowance, which for a ninety degree bend is pi over two times the quantity radius plus K-factor times thickness. Add them and that is the blank in that direction. Do the same across the other direction, then take a square notch out of each of the four corners so the walls do not collide when they come up.
How much corner relief does a pan need?
Enough that the notch clears the bend zone entirely and then some, with one to one and a half material thicknesses past the bend line being the range most shops settle on. The reason is not clearance for the walls, which are already clear, but the stress at the corner of the notch. If that corner sits inside the bend it is in the most heavily worked part of the part and it starts a tear. Drilling a round relief hole at the inside corner and cutting tangent out to the edges removes the sharp corner altogether.
Why is my finished pan taller or wider than the drawing?
Almost always a measurement basis mismatch. The commonest version is entering wall heights taken to the outside of the finished part into a calculation expecting inside heights, or the reverse, which throws every wall out by one material thickness. The second commonest is a K-factor borrowed from somewhere rather than measured, which shifts the bend allowance and therefore every flat length. The third is that the inside radius the tooling actually forms is not the radius on the drawing, which on an air bending press brake is normal, since the die opening sets the radius.
Can I use this for a pan with sloped sides?
No. Everything here assumes four walls folded at ninety degrees to a flat floor, which keeps each direction independent so the length and the width can be worked separately. Once the walls lean, the corners stop being square in the flat, the notches become angled and the development turns into a proper layout problem rather than an addition. A tapered four sided hopper is drawn as four separate trapezoidal sides with a triangulated development, not as one blank with corners removed.
What K-factor should I use for a box?
The one you measure. K-factor describes where the neutral axis settled for a specific combination of material, thickness, radius, tooling and forming method, and it is not published for your setup because nobody else has your setup. Bend a strip of the same material on the same machine with the same die, measure the flat you started with and the flanges you ended up with, and solve backwards for K. Values in the range of a third to a half are usual, tighter radii and harder material at the low end. Borrowing a number is a way to get close on the first article and no substitute for cutting a test piece when the material or the tooling changes.