Sheet metal does not bend at a sharp corner. It curves around the punch over the bend radius, and the metal on the outside stretches while the inside compresses. Getting a flat blank to fold up to the right finished size means accounting for that behaviour, which is exactly what bend allowance describes.
How it works
The neutral axis is the layer inside the bend that neither stretches nor compresses. Its position is set by the K-factor, and its arc length through the bend is the bend allowance.
angle_rad = bend_angle x pi / 180
BA = angle_rad x (IR + K x T)
OSSB = tan(angle_rad / 2) x (IR + T)
BD = 2 x OSSB - BA
flat = leg1 + leg2 - BDHere IR is the inside bend radius, T is material thickness, and K is the K-factor. The bend angle is the angle the metal turns through, so a part folded into a right angle uses 90 degrees. The flat-pattern length is the sum of the outside flange legs minus the bend deduction, which is what you cut before forming.
Worked example
A 90-degree bend in 1.5 mm mild steel with an inside radius of 2 mm and a K-factor of 0.42:
- Angle in radians: 90 × π/180 = 1.5708 rad
- Bend allowance: 1.5708 × (2 + 0.42 × 1.5) = 1.5708 × 2.63 = 4.13 mm
- OSSB: tan(45°) × (2 + 1.5) = 1.0 × 3.5 = 3.50 mm
- Bend deduction: 2 × 3.50 − 4.13 = 2.87 mm
If the outside flanges measure 50 mm and 30 mm, the flat blank is 50 + 30 − 2.87 = 77.13 mm.
K-factor by forming method and material
The K-factor is the ratio of the neutral-axis distance from the inside surface to the material thickness. It shifts depending on how the part is formed:
| Method | Aluminium | Mild steel | Stainless |
|---|---|---|---|
| Air bend | ~0.33 | ~0.42 | ~0.43 |
| Bottom bend | ~0.38 | ~0.44 | ~0.46 |
| Coin bend | ~0.42 | ~0.50 | ~0.50 |
Air bending is the most common press-brake operation; coining and bottoming seat the metal into the die and push the neutral axis outward, increasing the K-factor. Tighter radii (IR less than 1× thickness) also tend to increase the effective K-factor.
Tips for accurate flat patterns
- Calibrate with a test bend. Cut a test coupon from the same material batch and form a 90-degree bend. Measure the finished outside dimensions and back-calculate the true BA or BD. That measured value is more reliable than a textbook K-factor for your specific tooling.
- Multi-bend parts. Calculate the deduction for each bend separately, then subtract all deductions from the sum of all outside dimensions to find the full flat blank length.
- Springback is separate. This calculator gives the correct blank size for the stated K-factor and radius but does not model springback. If your part springs open after bending, compensate by over-bending — typically 1–4 degrees for mild steel air bends — rather than changing the blank length.
- Grain direction. Bending across the grain (perpendicular to the rolling direction) generally gives a slightly smaller effective K-factor and less springback than bending parallel to the grain.