01 — K-factorThe neutral axis, in one number.
When you bend sheet metal the outer face stretches and the inner face compresses. Between them sits a fibre whose length doesn't change: the neutral axis. The K-factor says where it is, as a fraction of the thickness measured from the inner face:
At rest the neutral axis is in the middle (K = 0.5); under bending it shifts inward, so the real K typically lies between 0.33 and 0.50 (lower on tight radii). The smaller the radius relative to thickness, the lower K. It's the one number you need to develop the part correctly: get it wrong and you cut the blank too long or too short and end up with finished dimensions out of tolerance.
02 — BA and BDAllowance and deduction.
Two quantities come from the K-factor. The bend allowance (BA) is the real length of the neutral arc inside the bend; the bend deduction (BD) is how much to subtract from the sum of the sides measured to the outside to get the flat. The formulas (β = bend angle = 180° − part angle, in degrees):
OSSB = (Ri + S) · tan(β / 2)
BD = 2 · OSSB − BA
OSSB is the setback: the distance from the theoretical outside apex to the bend tangent line. For a 90° bend on Ri = 2, S = 2 and K from DIN ≈ 0.33: BA ≈ 4.16 mm, OSSB = 4.00 mm, BD ≈ 3.84 mm.
03 — DevelopmentThe blank length.
The flat development (flat pattern) is the length of the unfolded sheet, before bending. For a single bend with sides A and B measured to the outside dimensions:
With several bends you subtract each BD. Example: outside sides 50 and 50 mm, 90° bend, Ri 2, S 2, K from DIN ≈ 0.33 → BD ≈ 3.84 → flat ≈ 96.16 mm. The calculator above does exactly this, in real time.
04 — DIN 6935K from the geometry.
When you don't have a measured value, the German standard DIN 6935 estimates the neutral-fibre position from the Ri/S ratio alone, via the correction factor k:
k equals 1 (i.e. K = 0.5, axis in the middle) for Ri/S ≥ 5, and drops toward 0.65 (K ≈ 0.33) on tight radii. It's the value the calculator uses by default in DIN mode.
| Ri / S | k (DIN) | K-factor |
|---|---|---|
| 0.5 | 0.65 | 0.33 |
| 1 | 0.65 | 0.33 |
| 2 | 0.80 | 0.40 |
| 3 | 0.89 | 0.44 |
| ≥ 5 | 1.00 | 0.50 |
05 — Your real KMeasure it once.
Tables give an estimate; the real K depends on your machine, tooling and material. You measure it once and reuse it. With the Sample → real K mode:
1. Cut a blank of known length and bend it to 90° with your tooling. 2. Measure the two outside sides A and B on the finished part and the inner radius Ri. 3. Enter A, B, Ri, S and the flat (the starting blank length). The calculator derives the real BD and, from it, your K-factor — comparing it with the DIN estimate. From then on you design with the right number.
06 — LimitsWhen to validate.
DIN values are indicative for air bending on mild steel. Coining, high-strength materials, very large radii (bump bending) and acute angles move the neutral axis: in those cases measure the real K or validate it with our engineering department. This tool supports design; it doesn't replace verification on the part.
