Sheet Metal Calculator — Bend Allowance, Flat Pattern & Springback (DIN 6935)

Governing standard: DIN 6935· DIN 6935:2011 (cold bending of flat rolled steel — K-factor neutral-axis method, incl. its k = 0.65 + 0.5·lg(r/s) correlation) · Gardiner springback relation · Sachs blank development · Kalpakjian/Siebel draw force · Keeler-Brazier FLD (engineering estimates, badged in-product)

Page last updated 12 October 2026

How DIN 6935 works — the method explained

Video walkthrough (4:11)

Read the transcript

Here's a 90° bend in 2 mm mild steel, with a 4 mm inside radius. The tool says it's OK.

Now make the exact same bend in aluminium 6061-T6. It fails. The outside of the bend will crack.

This is the MechanixCalc sheet metal calculator. It works out the flat blank you need to cut, and it checks the bend radius and the springback. It also covers punching and deep drawing. Let's go through it, step by step.

When sheet metal bends, the outside is stretched and the inside is squeezed. Somewhere in between, one layer keeps its length. That is the neutral axis.

It sits at K times the thickness from the inside, and its length is your flat blank. If the bend is too tight for the material, the stretched outside cracks.

Step one is the material. Mild steel, 2 mm thick. The material sets the stiffness and the strength, and that drives the springback.

The temper matters most. It isn't picked yet, so the tool assumes full-hard, the strictest case. The verdict is CHECK, in amber.

Set the temper to soft, annealed. Now the sheet can bend as tight as half its thickness, and the verdict turns green. It's OK.

Step two is the bend itself. A 4 mm inside radius, bent to 90°. The K-factor of 0.4 puts the neutral axis at 40 % of the thickness.

The two flanges are 50 and 80 mm long. So the flat blank you cut is 125.54 mm. That's shorter than the two flanges added up.

Step three shows the checks. The radius over the thickness, R over t, is 2, and soft steel only needs 0.5. Springback is just 0.54°. So this bend is OK.

Now switch the material to aluminium 6061-T6, and keep the same 4 mm radius.

This alloy needs a radius of at least 3 times its thickness. At R over t of 2, it FAILS, too tight. The outside of the bend will crack.

So open the radius up to 6 mm. R over t is now 3, exactly on the minimum. The verdict is CHECK, in amber. Right on the limit.

Go to 9 mm, and the verdict turns green. The flat blank gets a little shorter, at 123.39 mm.

Step four is springback. With the bigger radius, the part springs back 4.42° when the press opens. So you bend it to 94.64°, to land on 90°.

Springback and the minimum radius are engineering estimates. And the page labels them that way.

DIN 6935 gives a K-factor for this R over t, 0.488. Apply it, and the flat blank becomes 123.67 mm.

Punching is its own module. A 20 mm hole in 2 mm steel needs 4.1 tonnes of press force. On a 200 tonne press, that's only 2 %.

Put the same hole on a small 4 tonne press, and it needs 103 % of its rating. That's OVER CAPACITY. Don't run it.

Deep drawing turns a flat blank into a cup. A 60 mm cup, 30 deep, from a 108 mm blank, draws in a single hit. The draw ratio is 1.8, under the limit of 2.1.

Make the cup 40 deep, and the same blank comes up 6.89 mm short. The tool says BLANK TOO SMALL.

What the tool does not check is listed too: hole-to-bend distance, press-brake force, grain direction and more. So silence never reads as a pass.

Every input, every formula and every check goes into a PDF report. A report your reviewer can follow.

That's a bent part, checked. Try it on your own parts, on MechanixCalc.com.

The MechanixCalc sheet metal calculator covers the full forming workflow from flat blank to finished part — bend allowance and flat-pattern layout to DIN 6935 (K-factor neutral-axis method), Gardiner springback and the required over-bend, punching and blanking force with press tonnage, deep drawing from blank development through draw-ratio feasibility to a multi-stage sequence, and the Keeler-Brazier forming limit diagram — in four modules, each with its own step-by-step checks.

It is built for sheet-metal design engineers, press-tool designers and manufacturing process planners who need a traceable worked calculation for a bend layout, press tonnage, or draw-reduction schedule. Only the bend allowance uses a standard relation (the DIN 6935 K-factor); the minimum bend radius, springback, punching, deep-drawing and forming-limit panels are labelled engineering estimates.

What this calculator does

Bend allowance, bend deduction and flat blank length by the K-factor neutral-axis arc method, with the standard's own k = 0.65 + 0.5·lg(r/s) correlation offered as a one-click K
Feasibility judged against MechanixCalc's typical minimum inside bend radius (an estimate, not a DIN 6935 value) for the ACTUAL material and temper you selected — not a fixed R/t rule; with no temper selected it is graded at the hardest listed temper and says so
Flat pattern layout for boxes and pans with corner relief (closed / open corner options)
Springback angle, final radius and required over-bend on the same panel as the bend itself (Gardiner elastic–perfectly-plastic relation, with validity warnings)
Punching and blanking force (F = P · t · τ, τ = 0.8·UTS) with press tonnage, stripping force, cut energy and punch compressive stress computed on the TRUE punched area for circles, rectangles and obrounds
Deep drawing punch force and blank-holder force, with the required blank compared against the blank you intend to cut
Blank development for plain AND flanged cylindrical cups, rectangular pans (graded on the corner quarter-cups that actually govern), conical shells and tubes
Multi-stage draw sequence with intermediate annealing, single-sourced to the same limiting draw ratio the feasibility check uses
Forming limit diagram (FLD) to the Keeler-Brazier / NADDRG model, with an explicit warning when the selected alloy sits outside the low-carbon-steel data the correlation was fitted on
Built-in material library (mild steel, stainless 304, aluminium 6061-T6 and 5052-H32, DP 980, copper, brass) with E, Sy, UTS and n; custom material entry
Branded PDF engineering report showing the full method, substituted formulas and results

Method & formulas

Bend allowance — DIN 6935 K-factor method

The flat blank length is found by locating the neutral axis at a fraction K of the sheet thickness from the inside surface, computing the arc length at that radius (the bend allowance BA), and subtracting the bend deduction BD from the sum of the two flange lengths. DIN 6935 formalises this K-factor approach for cold bending of flat steel. Typical K values range from 0.33 (tight bends, soft material, air bending) to 0.50 (large radii, coining), with 0.38–0.40 for standard press-brake work.

The outside setback (OSSB) is the distance from the flange outside-mould-line intersection to the edge of the bend zone. The bend deduction BD = 2·OSSB − BA captures the material 'used up' in the bend, so the flat blank is shorter than the sum of the formed dimensions.

Neutral-axis radius

Rn = R + K · t

where Rn = neutral-axis radius (mm); R = inside bend radius (mm); K = K-factor (0.33–0.50); t = sheet thickness (mm)

Bend allowance (arc at neutral axis)

BA = (α · π / 180) · Rn

where BA = bend allowance (mm); α = bend angle (°); Rn = neutral-axis radius (mm)

Flat blank length

L_flat = L1 + L2 − BD, BD = 2 · OSSB − BA, OSSB = tan(α / 2) · (R + t)

where L_flat = flat blank length (mm); L1, L2 = flange lengths (mm); BD = bend deduction (mm); OSSB = outside setback (mm)

Springback — Gardiner elastic–perfectly-plastic relation

When the punch is withdrawn, the bent sheet partially recovers elastically. The Gardiner (1957) plane-strain model for air bending gives the radius ratio Ri/Rf as a function of the dimensionless parameter x = Sy·Ri/(E·t): the cubic Ri/Rf = 1 − 3x + 4x³ is monotonically decreasing on the valid branch x ∈ [0, 0.5) where yielding occurs. The angle then follows because the bend allowance (the neutral-fibre length) is unchanged by springback: αf/αi = (Ri + K·t)/(Rf + K·t), on the same K-factor the bend allowance uses (Kalpakjian & Schmid's springback factor writes it on the mid-surface, K = ½, which gives the least springback). At x ≥ 0.5 the sheet bends elastically and springs back flat (no permanent set). The calculator returns the final angle αf, the springback loss Δα, and the required overbend angle — and warns when the operating point leaves the model's valid domain.

Gardiner springback — radius and angle

Ri / Rf = 1 − 3x + 4x³, x = Sy · Ri / (E · t); αf / αi = (Ri + K·t) / (Rf + K·t)

where Ri, Rf = inside radius before / after springback (mm); αf = final angle after springback (°); αi = intended/punch angle (°); x = dimensionless plasticity parameter; Sy = yield strength (MPa); E = elastic modulus (MPa); t = sheet thickness (mm). K = the bend's K-factor. The angle ratio conserves the neutral-fibre length through springback. Valid for x < 0.5 (yielding occurs); at x ≥ 0.5 the sheet remains elastic and springs back to flat.

Required overbend angle

α_overbend = αi / (αf / αi)

where α_overbend = punch angle needed to achieve the target final angle after springback; αf / αi is the angle ratio (Ri + K·t)/(Rf + K·t) above.

Punching force and deep drawing

The blanking force to punch a hole or blank a part is the product of the cut perimeter, the sheet thickness and the shear strength of the material. The shear strength is taken as 0.8 times the ultimate tensile strength (UTS) — using yield strength under-predicts press tonnage and is unsafe for press sizing.

The deep drawing punch force follows the Kalpakjian & Schmid empirical relation (of the Siebel family) based on the blank-to-punch diameter ratio DR = D0/Dp; it is an empirical correlation rather than a code rule, and is badged as an engineering estimate in the tool. The required blank diameter is found from constant-thickness area equivalence — the classical Sachs blank development — which for a FLANGED cup is D = √(Df² + 4·Dp·h) and reduces to √(Dp² + 4·Dp·h) when there is no flange. The draw ratio is compared against the material's limiting draw ratio (about 2.0–2.2 for mild steel) to decide whether a redraw and an intermediate anneal are needed. The limiting draw ratio is physically governed by the sheet's normal anisotropy r̄, which this calculator does not hold, so treat the limit as shop guidance and confirm against supplier data.

Punching force

F = P · t · τ, τ = 0.8 · UTS

where F = blanking force (N); P = cut perimeter (mm); t = sheet thickness (mm); τ = shear strength (MPa); UTS = ultimate tensile strength (MPa). Press tonnage = F / 9806 (kN → tonnes).

Blank development for a cup (Sachs / area equivalence)

D_blank = √(Df² + 4 · Dp · H)

where D_blank = required flat blank diameter (mm); Df = outside flange diameter (mm), equal to Dp for a cup with no flange; Dp = punch (cup) diameter (mm); H = cup draw height (mm). Assumes constant sheet thickness.

Deep drawing: maximum punch force (Kalpakjian/Siebel)

F = π · Dp · t · UTS · (D0/Dp − 0.7)

where F = peak punch force (N); Dp = punch diameter (mm); t = sheet thickness (mm); UTS = ultimate tensile strength (MPa); D0 = blank diameter (mm). Empirical — the 0.7 lumps friction and bending over the die radius.

Worked example

Calculate the flat blank length for a 90° air bend in 2 mm mild-steel sheet with inside radius R = 4 mm, K-factor 0.40, and flange lengths L1 = 50 mm and L2 = 80 mm.

Given

Sheet thickness t2 mm
Inside bend radius R4 mm
Bend angle α90°
K-factor0.40
Flange L150 mm
Flange L280 mm

Result

Neutral-axis radius Rn4.80 mm
Bend allowance BA7.540 mm
Bend deduction BD4.460 mm
Flat blank length L_flat125.54 mm

Find the neutral-axis radius: Rn = R + K·t = 4 + 0.40 × 2 = 4.80 mm.
Compute the bend allowance: BA = (90 × π/180) × Rn = (π/2) × 4.80 = 2.4π ≈ 7.540 mm.
Compute the outside setback: OSSB = tan(α/2) × (R + t) = tan(45°) × (4 + 2) = 1.000 × 6 = 6.000 mm.
Compute the bend deduction: BD = 2 × OSSB − BA = 12.000 − 7.540 = 4.460 mm.
Flat blank length: L_flat = L1 + L2 − BD = 50 + 80 − 4.460 = 125.54 mm.

Illustrative example — verify against your actual material K-factor and bend radius. Springback is not included here; open the Springback & charts step of the Bending module to find the required over-bend angle for the actual punch angle.

Frequently asked questions

Which standard does this sheet metal calculator use?

Bend allowance and flat-pattern layout follow DIN 6935 (cold bending of flat rolled steel — the K-factor neutral-axis arc method), and the standard's own k = 0.65 + 0.5·lg(r/s) correlation is offered as a one-click K-factor. Everything else is a named engineering correlation rather than a standard, and each is badged as such in the tool: springback uses the Gardiner (1957) elastic–perfectly-plastic plane-strain model; punching force uses the industry τ = 0.8·UTS shear basis; blank development uses Sachs area equivalence; the deep-draw punch force uses the Kalpakjian/Siebel empirical relation; and the forming limit diagram uses the Keeler-Brazier / NADDRG regression, which was fitted on low-carbon steel and is flagged as extrapolated for any other alloy. The governing method is shown in the generated PDF report.

What is the K-factor and how do I choose it?

The K-factor positions the neutral axis as a fraction of the sheet thickness from the inside of the bend: K = 0.33 for tight bends in soft material with air bending; 0.38–0.40 for typical press-brake work; 0.50 for large-radius bends and coining. The material library pre-fills a default K per material. Entering an incorrect K is the most common source of flat-blank length error, so the tool displays the resulting R/t ratio alongside the minimum-bend-radius table as a sanity check.

How does the springback calculator work, and when is it inaccurate?

It uses the Gardiner elastic–perfectly-plastic cubic Ri/Rf = 1 − 3x + 4x³ (x = Sy·Ri/(E·t)) for the radius, and the angle ratio αf/αi = (Ri + K·t)/(Rf + K·t), which keeps the neutral-fibre length (the bend allowance) constant through springback. This is accurate for air bending of isotropic sheet in the valid range x < 0.5 (the sheet yields). At x ≥ 0.5 the sheet bends elastically and springs back flat — the calculator warns explicitly in this region. The model also becomes conservative for highly strain-hardened AHSS or for bottoming/coining, where the contact pressure changes the neutral-axis location.

Can it calculate the required blank for a deep-drawn cup or conical shell?

Yes. The Deep Drawing module develops plain and flanged cylindrical cups (area equivalence, D = √(Df² + 4·Dp·H)), rectangular pans (blank (L + 2H) × (W + 2H), with severity taken from the corner quarter-cups that actually govern a drawn box), conical shells and open-top tubes. The draw ratio is compared to the material's limiting draw ratio — about 2.1 for mild steel, 2.2 for brass — and when it is exceeded the same panel lays out the intermediate diameters and the annealing stages. Because the tool computes the blank the part needs AND takes the blank you intend to cut, it also tells you when the two disagree.

Is the sheet metal calculator free?

You can use all four modules (bending, punching, deep drawing, forming limit) for a 30-minute preview with no sign-up required. A free 14-day account trial (no credit card needed) gives unlimited access to all calculators. The branded PDF engineering report and the ability to save and reload calculations are included in the free 14-day trial and in every paid plan.

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