Inputs
Both leg lengths a and b (measured on the outside up to the apex), sheet thickness s, inner radius r and the opening angle β of the finished part.
Manufacturing · DIN 6935
Bend allowance and developed length
Calculate the developed (flat-pattern) length of a bent sheet-metal part to DIN 6935: L = a + b − v. The calculator returns the correction value v, the k factor of the neutral fibre shifted towards the inside, the arc length and the straight portions used as back-gauge dimensions.
Per DIN 6935 the legs are measured on the outside up to the apex. The k factor k = 0.65 + 0.5 · log₁₀(r/s) applies to ductile, medium-strength steels; springback, rolling direction and tooling effects are not included.
LDIN 6935
02
Flat pattern
Set the dimensions and calculate.
Inputs and method
Developed length to DIN 6935
Calculate the flat-pattern length of a bent sheet-metal part from the leg lengths, thickness, inner radius and opening angle.
Calculation
DIN 6935 computes L = a + b − v. The correction value v = 2 · (r + s) · tan(α/2) − α·π/180 · (r + s·k/2) replaces the two outer corners with the neutral fibre arc, where α = 180° − β is the bend angle. The k factor k = 0.65 + 0.5 · log₁₀(r/s) shifts the neutral fibre from mid-thickness towards the inside and is clamped to 0…1. For β < 90° the standard caps the corner allowance at its 90° value (r + s), because the apex would otherwise run to infinity.
Example
a = b = 50 mm, s = 2 mm, r = 2 mm and β = 90° give k = 0.65, a neutral fibre at 2.65 mm, an arc length of 4.16 mm, v = 3.84 mm and therefore L = 96.16 mm.
Sources and limits: DIN 6935 (cold bending of flat steel products); only the published closed-form relations are evaluated, no standard table is reproduced. Valid for ductile, medium-strength steels; springback, rolling direction, tooling and coatings are not covered.
Developed length to DIN 6935 in detail
Calculate the flat-pattern length of a bent sheet-metal part from the leg lengths, thickness, inner radius and opening angle.
What is the developed length?
During folding the material in the bend zone is stretched on the outside and compressed on the inside. Because the tool supports the inner radius, stretching dominates: the sheet becomes thinner in the bend zone and longer overall. The blank must therefore be shorter than the sum of the later leg dimensions. That blank dimension is the developed length; the difference from the sum of the legs is the correction value, or bend deduction.
Formula and variables
L = a + b − v
90° ≤ β ≤ 165°: v = 2 · (r + s) · tan(α/2) − α·π/180 · (r + s·k/2)β < 90°: v = 2 · (r + s) − α·π/180 · (r + s·k/2)β > 165°: v = 0k = 0.65 + 0.5 · log₁₀(r/s), clamped to 0 ≤ k ≤ 1
| Symbol / input | Meaning |
|---|---|
| a, b | Leg lengths of the finished part, measured on the outside up to the apex. |
| s, r | Sheet thickness and inner bend radius. |
| β, α | Opening angle of the finished part and the resulting bend angle α = 180° − β. |
| k | Correction factor that places the neutral fibre at radius r + s·k/2. |
| v, L | Correction value (bend deduction) and developed length of the blank. |
Choose the inputs correctly
Both leg lengths a and b (measured on the outside up to the apex), sheet thickness s, inner radius r and the opening angle β of the finished part.
How to use the calculator
Enter both leg lengths exactly as dimensioned on the drawing – per DIN 6935 on the outside, up to the apex of the extended outer faces. Add sheet thickness and inner radius (not the outer radius) and the opening angle of the finished part. The calculator returns the blank length, the correction value and additionally the straight portions used as back-gauge dimensions when folding.
Worked example
a = b = 50 mm, s = 2 mm, r = 2 mm and β = 90° give k = 0.65, a neutral fibre at 2.65 mm, an arc length of 4.16 mm, v = 3.84 mm and therefore L = 96.16 mm.
How should the result be used?
The developed length is the dimension the blank is cut to. The correction value v alone says little about the quality of the calculation – the neutral fibre radius is more informative, because it is exactly what can be compared with any other flat-pattern method and any CAD system, regardless of how the k factor is defined there. The additionally reported straight portions a′ and b′ are the dimensions set at the back gauge when folding.
All lengths in millimetres (optionally cm or inches), the opening angle in degrees. The k factor and the ratio r/s are dimensionless.
Typical applications
Work preparation and blank sizing in sheet-metal fabrication, checking a flat pattern produced by a CAD system, determining back-gauge dimensions on folding machines and press brakes, and estimating material demand for bent parts.
Assumptions, limits and common mistakes
DIN 6935 (cold bending of flat steel products); only the published closed-form relations are evaluated, no standard table is reproduced. Valid for ductile, medium-strength steels; springback, rolling direction, tooling and coatings are not covered.
Common mistake: Do not confuse the opening angle β with the bend angle α: a right-angled bend has β = 90° and α = 90°, while a shallow part with β = 150° is bent by only 30°. Do not enter the outer radius instead of the inner one. In air bending the actual inner radius is not the punch radius but follows from die width and material – an underestimated radius corrupts both the arc length and the k factor. And do not measure the legs to the start of the radius when calculating to DIN 6935; the separately reported straight portions serve that purpose.
Frequently asked questions
Why is the developed length shorter than a + b?
Two effects combine. First, the outer corner up to which the legs are measured is longer than the arc it replaces in the bent part – that is pure geometry. Second, during bending the material is stretched on the outside more than it is compressed on the inside, so the neutral fibre moves towards the inside and the developed arc length shrinks further.
What exactly does the k factor mean?
It states at what fraction of half the sheet thickness the calculated neutral fibre lies: its radius is r + s · k/2. k = 1 is exactly mid-thickness, k = 0.5 is a quarter of the thickness above the inner radius, k = 0 is right on the inner surface. Per DIN 6935 it follows from k = 0.65 + 0.5 · log₁₀(r/s) and reaches 1 at r ≥ 5 · s.
Above which angle does bend deduction stop mattering?
Above an opening angle of 165°, i.e. a bend angle below 15°, DIN 6935 treats the deduction as negligible. The calculator then reports a correction value of zero and the developed length equals the sum of the legs.
Why does my CAD system give a different value?
Many CAD systems use a k factor with a different definition (neutral fibre offset as a fraction of the full thickness rather than of half of it), so roughly 0.33 there corresponds to a DIN value of 0.65. CAD systems also often use the machine manufacturer's bend tables. The neutral fibre radius reported here allows a direct comparison independent of the k definition.
Is the result ready for production?
It is a very good starting value for ductile, medium-strength steels. Springback, rolling direction, tool geometry, coatings and high-strength grades all have additional effects; for series parts the flat pattern should be confirmed on a sample part.