Bend allowance, bend deduction and flat pattern length for sheet metal, plus springback angle, the overbend needed to compensate for it, and a minimum bend radius check against the material.
When sheet is bent, the outer surface stretches and the inner compresses. Between them lies the neutral axis, which keeps its original length. Its arc through the bend is the bend allowance — the material the bend consumes.
t sheet thickness (mm) ·
R inside bend radius (mm) ·
θ bend angle (degrees) ·
K K-factor ·
A, B flat leg lengths (mm) ·
Sy yield strength (MPa) ·
E Young's modulus (GPa)
A 2 mm mild steel bracket bent 90° over a 3 mm inside radius, with 50 mm flat legs each side.
Cut the blank at 106.1 mm and set the press brake to 90.5° so the part relaxes to 90°. The same geometry in aluminium 6061 would need a 8 mm minimum radius — the 3 mm radius here would crack it — and would spring back about 1.12°, roughly twice as much, because aluminium's elastic modulus is about a third of steel's.
| Quantity | Symbol | Unit | Accepted range |
|---|---|---|---|
| Sheet thickness | t | mm or in | > 0 |
| Inside bend radius | R | mm | ≥ 0 |
| Bend angle | θ | degrees | > 0, typically ≤ 180 |
| K-factor | K | — | 0.1 – 0.5 |
| Leg lengths | A, B | mm | ≥ 0 |
| Yield strength | Sy | MPa | > 0 |
| Young's modulus | E | GPa | > 0 |
| Bend allowance | BA | mm | output |
| Springback | — | degrees | output |
Thickness in inches is converted at 25.4 mm. Radius and leg lengths are always in millimetres. Note that E is entered in GPa, not MPa.
| Material | K | Sy (MPa) | E (GPa) | Rmin |
|---|---|---|---|---|
| Mild steel | 0.44 | 250 | 200 | 0.5 t |
| Stainless 304 | 0.44 | 310 | 193 | 1.0 t |
| Aluminium 6061 | 0.40 | 193 | 70 | 4.0 t |
| Copper | 0.44 | 210 | 117 | 1.0 t |
| Galvanised | 0.44 | 280 | 200 | 0.5 t |
Bend allowance is the arc length of the neutral axis through a bend. When sheet metal is bent the outside stretches and the inside compresses, and somewhere between them a layer neither stretches nor compresses. That neutral layer keeps its original length, so its arc length is the amount of material consumed by the bend. Adding bend allowance to the flat leg lengths gives the blank size needed.
The K-factor is the position of the neutral axis expressed as a fraction of material thickness measured from the inside surface. A K-factor of 0.44 means the neutral axis sits 44 % of the way through the thickness. It is always less than 0.5 because the neutral axis shifts toward the inside of the bend. Typical values are 0.44 for mild steel and stainless and about 0.40 for aluminium, though the true value depends on tooling, radius-to-thickness ratio and forming method.
They are two ways of reaching the same blank size from different measurements. Bend allowance is added to leg lengths measured from the bend tangent lines. Bend deduction is subtracted from leg lengths measured to the outside mould line, which is where the two flat faces would meet if extended. Using the wrong one with the wrong measurement is the most common cause of an incorrect flat pattern.
Springback grows with the ratio of yield strength to elastic modulus and with the bend radius to thickness ratio. Mild steel at a tight radius may spring back well under one degree, while aluminium at the same geometry springs back roughly twice as much because its elastic modulus is about one third that of steel. The tool must overbend by the springback amount so the part relaxes to the intended angle.
Minimum inside bend radius is the tightest radius a material tolerates before the outer surface cracks, and it scales with thickness. Common guidance is 0.5 × t for mild steel and galvanised sheet, 1.0 × t for stainless 304 and copper, and 4.0 × t for aluminium 6061. Bending across the grain direction allows tighter radii than bending along it.