A flat pattern is only correct when the bend allowance is right, and the bend allowance depends on where the neutral axis sits inside the material. That position is the K-factor, and it is the number that turns a drawing into a blank size. Get it wrong and the part is short or long by a fraction of a millimetre per bend - which is nothing on one bend and a scrapped frame on six.
What is the bend allowance formula?
Bend allowance is the length of the neutral axis through the bend: BA = π (R + K×T) × A / 180, where R is the inside bend radius, T is the material thickness, A is the bend angle in degrees and K is the K-factor, the position of the neutral axis as a fraction of thickness (typically 0.33–0.50). The flat length is the sum of the outside leg lengths minus the bend deductions, or the sum of the inside leg lengths plus the bend allowances. The bend deduction is BD = 2 × OSSB − BA, where the outside setback OSSB = (R + T) × tan(A/2). K-factor is not a constant: it moves with the R/T ratio, the material and the tooling, which is why the value in a CAD library should be confirmed against the first article rather than trusted for every job.
Why the neutral axis is not in the middle
When a sheet is bent, the outside of the bend stretches and the inside compresses. Somewhere between them is a surface that neither stretches nor compresses, and its length is the length the flat blank has to contain. In thin sheet with a generous bend radius that surface sits close to the middle (K near 0.5). In a tight bend, or in a material that work-hardens like stainless, it shifts toward the inside and K drops. That is why a 1 mm sheet bent to R1 behaves differently from a 3 mm sheet bent to R1, even in the same material.
The four terms that get mixed up
| Term | What it is | Where it is used |
|---|---|---|
| Bend allowance (BA) | Length of the neutral axis through the bend arc | Added to inside leg lengths, or removed from outside dimensions |
| Bend deduction (BD) | BA minus the setback, doubled | Subtracted from the sum of the outside leg lengths |
| Outside setback (OSSB) | Distance from the outside corner to the tangent point | Used to calculate the bend deduction and to check the flat pattern |
| K-factor | Neutral axis position as a fraction of thickness | The input that makes the allowance match the real part |
A worked example
Take a 2 mm steel sheet, inside bend radius R = 2 mm, bend angle A = 90°, K-factor 0.42. The bend allowance is BA = π (2 + 0.42 × 2) × 90 / 180 = 4.46 mm. The outside setback is OSSB = (2 + 2) × tan(45°) = 4.00 mm, so the bend deduction is BD = 2 × 4.00 − 4.46 = 3.54 mm. For a 90° bracket with outside legs of 50 mm and 30 mm, the flat blank is 50 + 30 − 3.54 = 76.46 mm. Change K to 0.33 and the blank becomes 76.22 mm - a quarter of a millimetre, which is the difference between a part that fits and a part that does not.
Where the K-factor actually comes from
- R/T ratio - as the inside radius grows relative to thickness, K moves toward 0.5; tight radii push it down toward 0.33.
- Material - work-hardening materials such as stainless behave differently from mild steel at the same R/T.
- Tooling - the die opening and the punch radius set the inside radius that actually forms, which may not be the radius printed on the drawing.
- Method - air bending, bottoming and coining produce different inside radii and different springback, so the same drawing needs different numbers on different brakes.
How we handle it in production
We calculate the flat pattern from the drawing, then confirm it on the first part and correct the K-factor before the batch runs. For a bracket with one bend that is a two-minute check; for a welded frame with twelve bends it is the difference between a straight frame and a frame nobody can assemble. Where the part is formed in a die rather than on a press brake, the forming is set by the tool and the flat pattern comes from the strip layout, so the two routes are never mixed in one calculation. Send the drawing and the material, and we will return the flat length we will actually cut.
Key point
Use BA = π(R + K×T)×A/180, subtract the bend deduction from outside dimensions, and treat K as a measured value rather than a constant. Confirm it on the first article, especially on stainless and on tight radii - after that the flat pattern is predictable for the whole programme.
Frequently asked questions
What is the bend allowance formula?
BA = π (R + K×T) × A / 180, where R is the inside bend radius, T the material thickness, A the bend angle in degrees and K the K-factor (neutral axis position as a fraction of thickness).
What is a typical K-factor?
Between 0.33 and 0.50. Tight bends and work-hardening materials sit near the bottom of that range, generous radii in soft materials near the top. It must be confirmed against the first article rather than copied from a table.
What is the difference between bend allowance and bend deduction?
Bend allowance is the neutral-axis length through the bend and is added to inside dimensions. Bend deduction is twice the outside setback minus the bend allowance, and is subtracted from outside dimensions. Both describe the same bend from different sides.
Do you build the flat pattern from the drawing?
Yes - we calculate it, cut the first part, check the formed dimensions and correct the K-factor before the batch runs. For die-formed parts the flat pattern comes from the strip layout instead.