Formula
The neutral axis neither stretches nor shrinks during bending, so its length equals the flat length. It lies K·T from the inside surface.
BA = θ(rad) · (R + K·T) bend allowance: neutral axis length in the bend OSSB = tan(θ/2) · (R + T) outside setback BD = 2·OSSB − BA bend deduction Flat length = A + B − BD
Choosing a K-factor
The K-factor depends on the material, thickness, tooling and bending method. The most reliable value comes from a test bend with the same material and tooling, worked backwards. Without test data, start from these typical values.
| R / T | Estimated K | Situation |
|---|---|---|
| Below 1 | 0.33 | Tight bends |
| 1 to under 3 | 0.40 | Typical air bending |
| 3 and above | 0.50 | Large radius, neutral axis at mid-thickness |
Worked example
Thickness 2 mm, inside radius 2 mm, 90° bend, K 0.40, outside dimensions 50 × 30 mm:
- BA = π/2 × (2 + 0.40 × 2) ≈ 4.40 mm
- OSSB = tan 45° × (2 + 2) = 4.00 mm
- BD = 2 × 4.00 − 4.40 ≈ 3.60 mm
- Flat length = 50 + 30 − 3.60 ≈ 76.40 mm
With K 0.33 the flat length becomes 76.18 mm. A 0.2 mm difference matters on tight-tolerance parts, so confirm K with a test bend before production.
Limitations
- For parts with several bends, subtract BD for each bend. This calculator handles one bend.
- As the bend angle increases, the outside setback grows quickly and outside dimensions become impractical. Angles up to 150° are accepted.
- A flange shorter than the outside setback cannot actually be bent. Also check the minimum flange length for your tooling.
References
- Machinery's Handbook, Industrial Press, sheet metal bend allowance formula
- Dassault Systèmes SOLIDWORKS Help, definitions of Bend Allowance, Bend Deduction and K-Factor