Sheet metal flat length per DIN 6935
Calculate the flat pattern length of sheet metal parts right in your browser – either per DIN 6935 with the compensation value v or internationally with the K-factor, including multiple bends.
Flat length calculator
The DIN k formula applies to ductile flat steel products. For aluminium or stainless steel the K-factor method with a material guide value is recommended. r is always the inside radius.
Segments (legs and bends, outside/apex dimensions)
- Sum of leg dimensions
- 80 mm
- Sum of deductions
- −3.837 mm
For comparison with K-factor guide value: L = 76.335 mm
| Segment | Input | k | K | Bend allowance in mm | Compensation value v in mm | Contribution in mm |
|---|---|---|---|---|---|---|
| Leg 1 | a = 30 mm | +30 | ||||
| Bend 1 | r = 2 mm · β = 90° · r/s = 1 | 0.65 | 0.325 | 4.163 | 3.837 | −3.837 |
| Leg 2 | a = 50 mm | +50 | ||||
| Flat length L | 76.163 mm | |||||
Profile sketch (side view, radii simplified)
k table per DIN 6935 (k from r/s)
| r/s | 0.05 | 0.1 | 0.2 | 0.25 | 0.33 | 0.5 | 0.75 | 1 | 1.25 | 1.5 | 2 | 2.5 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| k | 0 | 0.15 | 0.3 | 0.35 | 0.41 | 0.5 | 0.59 | 0.65 | 0.7 | 0.74 | 0.8 | 0.85 | 0.89 | 0.95 | 1 |
Formulas and fundamentals
During cold bending the outside of the bend zone is stretched and the inside is compressed. The neutral axis, which keeps its length, therefore does not stay in the middle of the sheet but shifts towards the inside radius. As a result the flat pattern is shorter than the sum of the outside dimensions of the finished part – this correction is the bend shortening. DIN 6935 describes the position of the neutral axis with the correction factor k = 0.65 + 0.5 · log10(r/s), where r is the inside radius and s the sheet thickness. The factor is clamped to the range 0 to 1; for r ≥ 5·s or bend angles below 15° k = 1 applies and the axis is practically back in the middle of the sheet.
For each bend a compensation value v is subtracted from the sum of the leg dimensions. For opening angles β up to 90°, v = 2·(r + s) − π·((180° − β)/180°)·(r + k·s/2), with the legs measured as protruding corner dimensions over the outside faces. For opening angles above 90° up to 165°, v = 2·(r + s)·tan((180° − β)/2) − π·((180° − β)/180°)·(r + k·s/2), with apex dimensions to the theoretical intersection of the outside faces. At β = 90° both formulas give the same value; above 165° the shortening is negligible and v = 0.
For multiple bends, L = a₁ + a₂ + … + aₙ₊₁ − (v₁ + v₂ + … + vₙ): n bends with n+1 leg dimensions, where every bend gets its own compensation value from its radius, angle and the resulting k. The bending sequence in production has no influence on the flat length.
The internationally common K-factor method (CAD systems such as SolidWorks) works with the bend angle α = 180° − β and the bend allowance BA = π·(α/180°)·(r + K·s), the arc length on the shifted neutral axis. With the outside setback OSSB = (r + s)·tan(α/2) the bend deduction follows as BD = 2·OSSB − BA, which is subtracted from the outside dimensions. The simple bridge between both worlds is K = k/2: the DIN factor k = 0.65 corresponds to the ANSI K-factor 0.325. Mixing up the two scales is the most common source of error in flat pattern calculations.
The DIN formula applies to ductile flat steel products; for aluminium or stainless steel and for air bending, K-factor guide values by material and process (typically 0.30 to 0.50) are often closer to shop-floor reality. Real fabricators additionally use machine- and tool-specific bend tables – the calculated value is a solid starting point but does not replace measuring a test part for tight tolerances. Important: r is always the inside radius.
Worked example
An L-bracket from 2 mm sheet with inside radius r = 2 mm is bent by 90° (opening angle β = 90°); the outside dimensions of the legs are 30 mm and 50 mm. Because r/s = 1, k = 0.65 and the corrected neutral axis lies at r + k·s/2 = 2.65 mm. The compensation value is v = 2·(2 + 2) − (π/2)·2.65 = 8 − 4.163 = 3.837 mm. The flat length is therefore L = 30 + 50 − 3.84 = 76.16 mm. This also explains the well-known shop rule: with r = s you subtract just under two sheet thicknesses per 90° bend.
Second example with a large radius: s = 5 mm, r = 20 mm, β = 90°, legs of 100 mm each. From r/s = 4 follows k = 0.951, the compensation value v = 2·25 − (π/2)·(20 + 0.951·2.5) = 14.85 mm and the flat length L = 200 − 14.85 = 185.15 mm – matching the rounded handbook value v = 14.9 mm.
Frequently asked questions
Why is the flat pattern shorter than the sum of the outside dimensions?
During bending the outside is stretched and the inside is compressed. The length-preserving neutral axis moves towards the inside radius, so its arc length is shorter than the path over the outside corner. This difference is subtracted per bend as the compensation value v (DIN 6935) or bend deduction (K-factor method) from the outside dimensions.
What is the difference between opening angle β and bend angle α?
The opening angle β is the angle between the two legs (90° = right angle) and is used by DIN 6935. The bend angle α = 180° − β is the angle the sheet is folded by and is used in the K-factor world. Mixing up the two conventions is the most common mistake in flat pattern calculations – which is why this tool offers both inputs.
Is the DIN correction factor k the same as the K-factor in CAD?
No. DIN 6935 describes the neutral axis position as k·s/2 from the inside face (k from 0 to 1), CAD systems such as SolidWorks as K·s (K from 0 to 0.5). The relation is K = k/2: the DIN value k = 0.65 at r = s corresponds to a K-factor of 0.325. Confusing the scales produces significantly wrong blanks.
Is DIN 6935 still valid?
Yes. The standard was initially withdrawn in 2007 but republished in 2010 and is currently available as the revised edition DIN 6935:2011-10. The old 2007 status still circulates in forums but is outdated. Two supplements provide factors and precalculated compensation values.
Which K-factor should I use for my material?
Practical guide values range from 0.30 to 0.50, depending on material, bending process and the ratio r/s. For steel sheet in air bending with r between s and 3·s about 0.43 is common; the industry rule of thumb is K = 0.446. For large radii (r above 3·s) K approaches the limit of 0.5 and the neutral axis sits in the middle of the sheet. The tool suggests guide values by material and process; custom values can be entered.
Why does the finished part still deviate from the calculated value?
Fabricators use empirical bend tables per machine, tool and material that can deviate from the standard values – for air bending typically by a few tenths of a millimetre per bend. Springback also affects the achieved angle. For tight tolerances a test part is recommended; the actual K-factor can be back-calculated from its measured flat length.
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