Bend allowance answers the flat-pattern question: how much sheet does the corner itself use up? It is the arc length along the neutral axis, BA = θ·(π/180)·(R + K·T), with the K-factor placing that axis within the thickness. Its companion works from the other dimensioning convention: parts on a print are usually dimensioned to the outside mold lines, whose two flange dimensions overlap at the corner, and the bend deduction BD = 2·OSSB − BA (with outside setback OSSB = (R+T)·tan(θ/2)) is exactly what that overlap overstates the flat by — so flat length = flange A + flange B − BD.
A bracket makes the stakes concrete: 2 mm mild steel bent 90° over a 3 mm inside radius with two 50 mm outside flanges gives BA = (π/2) × (3 + 0.44×2) = 6.095 mm, OSSB = 5 mm, BD = 3.905 mm, and a blank cut at 96.095 mm. Cut at the naive 100 mm and both finished legs come out nearly 2 mm long, because the corner only consumes 6.1 mm of material while the outside dimensions overlap by 10.
Two geometry cautions guard the result. In air bending the inside radius is set by the die opening, not the punch tip — roughly 1/6 of the V-die width for mild steel — and since the radius feeds both BA and OSSB, an assumed radius off by a millimetre moves the flat pattern visibly. And past 90° the tan(θ/2) setback convention diverges (racing to infinity at 180°), so obtuse bends get the bend allowance only — still exactly the neutral-axis arc at any angle — with the deduction left to the CAD system’s obtuse-bend convention.