Bend Deduction

The bend allowance answers "how much material is in the bend". The bend deduction answers a different question — "what do I cut the blank to" — and it is the second one that a flat pattern actually needs. Getting these two confused is the commonest flat-pattern error there is, and it is worth being slow and clear about why they differ.

Parts are dimensioned to the outside. A drawing of a bent bracket gives you flange lengths measured to where the outside faces would meet if the corner were perfectly sharp — the theoretical apex. But real material does not go round a sharp corner; it goes round a radius, and the arc it travels is shorter than the two straight lines to the apex. The difference at each end is the outside setback, $OSSB = (R + t)\tan(\theta/2)$, the distance from the apex back to the tangent point where the bend actually begins.

So: take the two outside flange dimensions from the print, add them, and you have the length of a part with an imaginary sharp corner. Subtract the two setbacks and you have the two straight legs of the real part. Add the bend allowance and you have the developed length of the blank. Collect the correction into one number and you get $BD = 2(R+t)\tan(\theta/2) - BA$, and the layout rule is as simple as it gets: flat length = flange + flange − BD.

The two numbers are not interchangeable and they are not even close. On a 90° bend in 2 mm sheet over a 3 mm inside radius the allowance is 6.03 mm and the deduction is 3.97 mm — use the wrong one and every bend in the part is out by 2 mm, with every hole position downstream of it out by the same. On an acute bend the gap widens dramatically: at 135° of bend in 1.5 mm sheet the allowance is 4.95 mm and the deduction is 9.54 mm, nearly double. A shop that has been using the wrong quantity gets away with it on square corners for years, then produces one acute part and cannot understand what changed. Nothing changed. The error was always there; the square corner was just forgiving.

The deduction can be negative, and that is not an error. On a gentle bend with a large radius relative to the thickness, the neutral arc is longer than the two setbacks it replaces, so the blank comes out longer than the summed outside flanges. Subtracting a negative adds; keep the sign and the arithmetic looks after itself.

Two more cautions. $\theta$ is the angle of bend, not the included angle between the flanges — supplementary, equal only at 90°, and the acute case above is what exposes a mix-up. And the tangent goes to infinity as $\theta$ approaches 180°, which is the arithmetic telling you that a hem is not an ordinary bend: the flanges have folded flat against one another, the apex has run off to infinity and setback has stopped meaning anything. Hems are laid out from a measured allowance, found by folding a coupon and measuring the blank it took.

Because the deduction is built out of the bend allowance, everything true of the K-factor is true here. Measure your own on your own press with your own tooling, and re-measure after any tooling change. And as everywhere in bending, nothing on this page knows anything about springback — a deduction computed for a 90° bend describes a part that leaves the tool at 90°, and if it springs back to 92° the pattern was developed for a bend that did not happen.