Bending and forming
Bend allowance and bend deduction (K-factor method)
- where
- bend allowance (mm)
- bend angle (°)
- inside bend radius (mm)
- K-factor
- material thickness (mm)
- outside setback (mm)
- bend deduction (mm)
Explain this equation
Works out the bend allowance and bend deduction for sheet or plate bent on a press brake. Use them to get flat blank sizes right first time.
When metal bends, the inside squashes and the outside stretches; somewhere in between a neutral line keeps its length. K says where that line sits as a fraction of the thickness from the inside. The bend allowance is the length of that line through the bend: the angle in radians (θπ/180) times its radius R + KT. The outside setback is how far each flange's outside line runs past the tangent to the corner. Two setbacks minus the bend allowance is how much shorter the blank is than the outside dimensions.
Arc length equals radius times angle in radians; the setback follows from the tangent geometry.
Sense check: a 90° bend in 2 mm sheet with a 2 mm inside radius and K = 0.41 gives BA ≈ 4.43, OSSB = 4 and BD ≈ 3.57 mm.
Watch out: K depends on material, tooling and radius. Bend a test piece and adjust K to match your brake.
Length of material consumed by a bend (bend allowance), and how much to subtract from the sum of the outside dimensions (bend deduction) when working out a blank.
Enter your values to see the result.
Good to know
The K-factor is the position of the neutral axis as a fraction of the thickness from the inside face. Machinery's Handbook 90° bend tables correspond to K ≈ 0.35 for soft brass and copper, 0.41 for soft (mild) steel and aluminium, and 0.45 for cold-rolled steel, bronze and spring steel. For air bending on a press brake the inside radius is set mainly by the V-die opening (roughly one-sixth of it for mild steel); use your own test bends to refine K for your tooling.
Common mistake
Entering the included angle (e.g. 135° for a 45° bend) instead of the angle bent through. A right-angle bend is 90° bent through.
Limits
Assumes a constant K and a circular bend. Very tight radii (R < T) and thick plate shift the neutral axis further; always confirm with a test piece for critical parts.
Sources
- Oberg et al., Machinery's Handbook (Industrial Press): Sheet metal – allowances for bends
- PTC Creo help: bend tables from Machinery's Handbook (90° bend L = (π/2)R + Y·T; Y 0.55/0.64/0.71, K 0.35/0.41/0.45 for soft brass–copper / soft steel–aluminium / cold-rolled steel)
- Design Fusion: Machinery's Handbook bend formula (L = 0.64T + 1.57R for soft steel and aluminium; 0.71T + 1.57R for cold-rolled steel)
Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow the welding procedure specification (WPS), BS EN ISO 15614/9606, BS EN 1090, BS EN 1993 and manufacturers’ data. Structural welds need qualified welders and engineered designs.