The problem in one sentence
Take a strip of 2 mm steel exactly 100 mm long and bend it 90° in the middle. Measure the two outside legs afterwards and they will add up to roughly 103.6 mm, not 100 mm. No material was added. The outside dimensions simply over-count the corner, because the sharp outside corner they imply does not exist — there is a radius there instead.
A flat pattern is the strip length you must start with so that, after bending, the part measures what the drawing says. Getting it right means accounting for exactly how much the corner over-counts.
Why the outside dimensions lie
When sheet metal bends, the outside surface stretches and the inside surface compresses. Somewhere between them is a layer that does neither — the neutral axis. That layer keeps its original length through the bend, which makes it the only honest measurement of how much flat material the bend consumes.
The neutral axis does not sit in the middle. Compression on the inside is more aggressive than stretch on the outside, so it migrates toward the inside face. How far it migrates is captured by the K-factor — a fraction of the material thickness, typically between 0.33 and 0.5.
Bend allowance: the honest length
The neutral axis sits at radius R + K × T from the bend centre, where R is the inside radius, T the thickness and K the K-factor. Sweep that radius through the bend angle and you get an arc length — the bend allowance:
That is the real amount of flat material inside the bend region. If your drawing dimensions each flange from the bend line to its outer edge, the flat length is simply flange + flange + BA.
Bend deduction: the practical version
Almost nobody dimensions to the bend line, because you cannot put a caliper on it. Real drawings give outside dimensions, measured to the imaginary sharp corner where the two outside faces would meet — the outside mould line.
The distance from that imaginary corner back to where the bend actually starts is the outside setback, and there is one at each end of the bend:
Bend allowance and bend deduction describe the same physical reality from two different measuring conventions. They always produce the same flat length. Mixing them up — subtracting a deduction from bend-line dimensions, say — is the single most common way a flat pattern comes out wrong.
Working the earlier example
2 mm mild steel, 90° bend, 2 mm inside radius, K-factor 0.4:
Which is where the 103.6 mm at the top of this page came from: bend a 100 mm strip once and the outside legs sum to 100 + 3.602 mm. Run it the other way — outside legs of 34 mm and 54 mm — and the blank is 34 + 54 − 3.602 = 84.398 mm.
Where hand calculation stops working
One bend is arithmetic. A four-sided enclosure is eight interacting numbers, and every hole position on a folded face has to be projected back onto the flat before it can be cut. Change one flange height and all of it moves.
There are three further complications worth knowing about:
- The radius is not what you asked for. In air bending the inside radius comes from the die opening, roughly the opening divided by 6.5 for mild steel. Specifying a radius the tooling cannot produce means your flat pattern is calculated for a bend that will never happen.
- Features near bends distort. A hole closer than about 2.5 times the material thickness to a bend line will pull oval when the part folds.
- Tight radii crack. An inside radius smaller than the material thickness risks fracturing on the outside of the bend, more so across the grain direction.
Coobic handles the projection automatically and warns about the last two while you draw. You give it a thickness, a K-factor and bend lines; it gives you the flat pattern, a live 3D fold, and a DXF with the bends on their own layers.