Key Takeaways
- Bend allowance (BA): the arc length of material consumed by the bend. Flat length = leg 1 + leg 2 + BA.
- K-factor: the ratio t_neutral/t — where the neutral axis sits within the thickness. Typical range 0.30–0.50; most mild steel air bends: 0.44.
- Bend deduction (BD): an alternative approach — Flat length = (leg 1 + leg 2) − BD. Easier to apply manually but BA is more accurate for programming.
- Using the wrong K-factor is the most common cause of first-part-wrong flat patterns in sheet metal CAD/CAM.
Why Flat Pattern Calculation Matters
When you bend sheet metal, material in the bend zone stretches on the outside and compresses on the inside. The neutral axis — where length stays constant — sits somewhere in the material thickness. If you unfold the part as if the bend were on the outer surface, you'll cut a blank that's too long. If you unfold from the inner surface, it'll be too short.
The K-factor and bend allowance formulas define exactly where the neutral axis is and how much arc length to add back to the flat pattern. Using the correct values means your first-article part hits the dimension — not your fifth after test-bending your way to the answer.
Bend Allowance Formula
Where:
- BA = bend allowance (mm)
- Ri = inside bend radius (mm)
- K = K-factor (unitless, 0.30–0.50)
- t = material thickness (mm)
- A = bend angle (degrees)
Flat length = Leg 1 + Leg 2 + BA (where Leg 1 and Leg 2 are measured from the mold line — the theoretical intersection of the two flat faces)
K-Factor Reference Values
| Material | Ri / t ratio | K-Factor | Notes |
|---|---|---|---|
| Mild Steel (air bend) | 0.5–1.0 | 0.44 | Most common production value |
| Mild Steel (air bend) | 1.0–2.0 | 0.45–0.47 | Softer radius, neutral axis migrates outward |
| Stainless 304 | 0.5–1.0 | 0.48 | Work hardens in bend zone |
| Aluminium 5052 | 0.5–1.0 | 0.40–0.42 | Softer alloy, neutral axis closer to inside |
| Aluminium 6061-T6 | 0.5–1.0 | 0.43–0.44 | Harder temper |
| Copper | 0.5–1.0 | 0.38–0.40 | Very ductile; soft K-factor |
| Brass | 0.5–1.0 | 0.42–0.44 | Similar to mild steel |
K-factor values vary with die width, punch radius, and material hardness. Always verify with a physical test bend before production. Values above are starting points for air bending.
Worked Example
Part: 3 mm mild steel, 90° air bend, inside radius 3 mm (1×t), Leg 1 = 50 mm, Leg 2 = 30 mm. K-factor = 0.44.
BA = 0.01745 × (3 + 1.32) × 90
BA = 0.01745 × 4.32 × 90
BA = 6.78 mm
Flat length = 50 + 30 + 6.78 = 86.78 mm
Bend Deduction Method
Some shops use bend deduction (BD) instead of bend allowance. BD is the amount subtracted from the sum of the two legs measured from the outside (mold line) dimensions:
BD is often tabulated in press brake manuals for common thickness/die combinations and is faster to apply manually. However, BA is more accurate for CNC flat-pattern programming because it relates directly to the arc length.