Sheet Metal Calculator — Bend Allowance, Springback & Forming (DIN 6935 / ISO 2768)
Governing standard: DIN 6935· DIN 6935:2011 (cold bending of flat steel, K-factor neutral-axis method) · ISO 2768 (general tolerances) · Gardiner springback relation · Sachs blank-development · Keeler-Brazier FLD
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 prediction and required overbend, punching and blanking force, deep drawing with blank-holder force, the Keeler-Brazier forming limit diagram (FLD) with safety-margin assessment, blank development for cups, boxes, cones and tubes, and multi-stage draw sequencing — all in a single ten-tab tool.
It is built for sheet-metal design engineers, press-tool designers and manufacturing process planners who need defensible, standards-cited numbers for a bend layout, press tonnage, or draw-reduction schedule — and who need to hand a reviewer a worked calculation rather than a shop-floor rule-of-thumb.
What this calculator does
- Bend allowance, bend deduction and flat blank length to DIN 6935 (K-factor neutral-axis arc method)
- Flat pattern layout for boxes and pans with corner relief (closed / open corner options)
- Springback angle and required overbend using the Gardiner elastic–perfectly-plastic relation with validity warnings
- Punching and blanking force (F = P · t · τ, τ = 0.8·UTS) plus stripping force and press tonnage for circles, rectangles and oblongs
- Deep drawing punch force and blank-holder force (Sachs), with draw ratio (DR) and required blank diameter
- Forming limit diagram (FLD) to the Keeler-Brazier / NADDRG model with safety-margin percentage and stretch/draw branch assessment
- Blank development for cylindrical cups, boxes, conical shells and tubes plus multi-stage draw sequence with annealing flags
- Built-in material library (mild steel, stainless, aluminium, copper, brass) with E, Sy, UTS and n values; 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.
Rn = R + K · twhere Rn = neutral-axis radius (mm); R = inside bend radius (mm); K = K-factor (0.33–0.50); t = sheet thickness (mm)
BA = (α · π / 180) · Rnwhere BA = bend allowance (mm); α = bend angle (°); Rn = neutral-axis radius (mm)
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 springback ratio αf/αi as a function of the dimensionless parameter x = Sy·R/(E·t): the cubic αf/αi = 1 − 3x + 4x³ is monotonically decreasing on the valid branch x ∈ [0, 0.5) where yielding occurs. 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.
αf / αi = 1 − 3x + 4x³, x = Sy · R / (E · t)where αf = final angle after springback (°); αi = intended/punch angle (°); x = dimensionless plasticity parameter; Sy = yield strength (MPa); E = elastic modulus (MPa); R = inside radius (mm); t = sheet thickness (mm). Valid for x < 0.5 (yielding occurs); at x ≥ 0.5 the sheet remains elastic and springs back to flat.
α_overbend = αi / (αf / αi)where α_overbend = punch angle needed to achieve the target final angle αf after springback; αi / αf ratio from the Gardiner relation 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 Sachs formula based on the blank-to-punch diameter ratio DR = D0/Dp. The required blank diameter for a cylindrical cup is found from the constant-thickness volume-conservation principle (Sachs formula). A limiting draw ratio of approximately 2.0 for mild steel defines when a redraw or annealing stage is needed.
F = P · t · τ, τ = 0.8 · UTSwhere 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).
D0_req = √(Dp² + 4 · Dp · H)where D0_req = required flat blank diameter (mm); Dp = punch (cup) diameter (mm); H = cup draw height (mm). Assumes constant sheet thickness.
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; use the springback tab to find the required overbend 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 steel — K-factor neutral-axis arc method), which is also consistent with ISO 2768 general-tolerance practice. Springback uses the Gardiner (1957) elastic–perfectly-plastic plane-strain model. Punching force uses the industry-standard τ = 0.8·UTS shear strength. Deep drawing and blank development use the Sachs formula. The forming limit diagram follows the Keeler-Brazier / NADDRG model. 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 relation αf/αi = 1 − 3x + 4x³ (x = Sy·R/(E·t)). 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 blank development tab supports cylindrical cups (Sachs formula D0 = √(Dp² + 4·Dp·H)), rectangular boxes (perimeter method), conical shells (surface-area equivalence for frustum geometry), and open-top tubes. The draw ratio DR = D0/Dp is compared to the material limiting draw ratio (LDR ≈ 2.0 for mild steel), and the multi-stage draw sequence tab computes the intermediate punch diameters and annealing stages automatically.
Is the sheet metal calculator free?
You can use every tab 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 part of a paid plan.
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