Sheet Metal Bend Allowance & Flat Pattern Calculator
Calculate bend allowance, bend deduction and flat length for up to four bends. Compare formed and flat views, edit K-factor, and estimate air-bending force and minimum flange.
This bend allowance calculator develops a constant-width sheet-metal strip into a rectangular blank. It is intended for engineers designing brackets and channels, students learning bend geometry, and fabricators estimating a first cut size. Enter one to four parallel bends, each with its own finished inside radius and signed turn angle. The formed section and flat pattern appear side by side, with the curved regions shaded on the blank.
Start with the sheet thickness and the blank width, measured parallel to the bend axes. Then choose how your flange lengths are dimensioned. Outside dimensions extend to the virtual sharp corners formed by the outside surfaces. Straight tangent lengths include only the uncurved material. An internal outside flange contains a setback at both ends. Mixing these two conventions is a common reason for an incorrect flat pattern.
Enter the flanges in order, beginning at edge 1. A positive angle turns counterclockwise along the section; a negative angle reverses the bend direction. The magnitude is the turn from flat, so a right-angle flange uses 90°. If a drawing specifies an included opening angle, subtract it from 180° first. Bend direction changes the drawing but does not change the developed allowance.
The K-factor sheet metal model places the neutral axis a fraction K of the thickness from the inside surface. The typical air-bending option selects a published starting value using the material family and each bend's radius-to-thickness ratio. These broad families are guidance rather than alloy specifications. Select the custom option to enter a K-factor established with your own material and tooling. The sensitivity chart shows how the cut length changes when a common K-factor is varied.
Results include bend allowance, outside setback and bend deduction for each bend, the total cut length, and bend-zone start, centre and end positions measured from edge 1. The zone centre is a geometric layout reference; it is not automatically the sight line or back-gauge setting for a particular brake.
For preliminary air-bending setup, enter the actual V-die opening and material tensile strength. The tool estimates force for one bend across the specified blank width and an approximate minimum outside flange near 90°. Sequential bends do not multiply the required press capacity. Force is also expressed in metric tonnes-force and US short tons-force.
This flat pattern calculator does not predict springback, cracking, minimum permissible bend radius, tool interference, bend sequence, corner reliefs, holes or hems. The drawings use independent fitting scales for the formed section and the blank. Check the supplier's material and tooling limits, including concentrated machine loading, and confirm production dimensions with a test bend before cutting a batch.
How it is calculated
For each bend, use the magnitude of the signed turn angle from flat. Convert degrees to radians explicitly, then calculate , and . The neutral-axis convention and equations follow SheetMetal.Me, Bend Allowance and Bend Deduction (sources s1, s2 and s7).
In outside-dimension mode, subtract one setback from each terminal flange and the two adjacent setbacks from each internal flange. In tangent mode the entered lengths already are the straight lengths. The flat length is , equivalently for outside dimensions. Bend-zone centres follow the cumulative straight lengths and allowances; they are not brake sight-line settings.
Typical K values use the three R/t bands in SheetMetal.Me's air-bending chart (s3). Each radius uses its own band; equality at 1 or 3 belongs to the smaller-radius band. Custom K replaces all bands with a common measured value.
The preliminary air-bending model is , with consistent force and length units (Daramco, s5). The 90° minimum outside flange is estimated as . The default approximates the WILA chart (s4, page 140), not its exact thickness- and tooling-dependent limits. See also the Bystronic capacity chart, s6, page 10. One metric tonne-force is 9.80665 kN; one US short ton-force is 2000 lbf.
Assumptions
- A constant-width, uniform-thickness strip with one to four circular, cylindrical bends and parallel bend axes.
- Each radius is the finished inside radius; uniform neutral-axis position through each bend.
- Outside flange dimensions use projected virtual sharp corners consistently, including at reverse bends.
- Typical K values are generic air-bending starting points. Material family changes K only; tensile strength remains an independent input.
- Force refers to one full-width air bend, without bottoming, coining, tooling wear or a user capacity margin.
- The formed drawing uses the actual mid-thickness geometry. The flat drawing shows neutral-axis developed lengths. Each panel is fitted separately; no physical quantity is exaggerated.
Where it applies
Use turn magnitudes from 1° to 170° and positive straight tangent lengths. End flanges must retain adequate die support; the editable 0.71 V estimate is for bends near 90° and does not guarantee tooling compatibility. The common V/t range of 6–12 is advisory, not a material-specific acceptance criterion.
No springback, thinning, anisotropy, minimum safe radius, cracking, bend sequence, self-intersection, punch/die collision, reliefs, cutouts, nonparallel bends or hems are modelled. A positive flat length does not prove a formable part. Confirm die shoulders, rated tool load, concentrated press capacity and the actual K-factor with the tooling supplier and test bends.
Published SheetMetal.Me table dimensions are rounded; reference tolerances allow their small differences from the exact circular-arc model. Manufacturer tonnage tables may use other empirical factors, so the force is a planning estimate rather than a certified machine setting.
References
- SheetMetal.Me — Bend allowance method and worked flat pattern: https://sheetmetal.me/formulas-and-functions/bend-allowance/
- SheetMetal.Me — Published bend allowance chart, page 1: https://sheetmetal.me/wp-content/uploads/2011/05/Bend-Allowance.pdf
- SheetMetal.Me — K-factor chart by radius/thickness and material family: https://sheetmetal.me/formulas-and-functions/k-factor/
- SheetMetal.Me — Bend deduction chart, page 1: https://sheetmetal.me/wp-content/uploads/2011/05/Bend-Deduction.pdf
- WILA Catalog USA, page 140 — air-bending tonnage and outside minimum flange: https://catalog.wilatooling.com/WILA-Catalog-USA/140/
- Daramco — Press Brake Tonnage Calculation Guide, 1 September 2026: https://www.daramco.com/press-brake-tonnage-calculation-guide/
- Bystronic Tools, Our Tools Euro-B, page 10 — manufacturer capacity chart: https://bystronic-mediacenter.picturepark.com/v/F0QFO88g/
Inputs
| Input | Symbol | Unit | Default |
|---|---|---|---|
| Number of bends A constant-width strip with parallel bend axes, followed from edge 1 to the far edge. | n_bends | 2 | |
| Flange measurement Outside mode: each leg reaches its outside virtual sharp corner. An internal leg includes one setback at each end. Tangent mode: enter only the straight material outside the curved bends. | dim_mode | Outside virtual apex dimensions | |
| Sheet thickness | t | mm | 2 |
| Bend length / blank width Dimension parallel to every bend axis. Force is for one bend across this width; sequential bends are not added together. | B_width | mm | 100 |
| Typical air-bending K-factor family Generic starting values, not material certification. This choice sets K only; enter tensile strength separately below. | family | Medium | |
| K-factor source | k_mode | Typical table, using each bend's R/t | |
| Custom K-factor Neutral-axis depth divided by thickness. Applied to every bend; calibrate with the same material, tooling and grain direction. | K_custom | 0.4 | |
| Flange 1 length Use the selected flange measurement consistently. Each internal outside dimension contains two setbacks. | A1 | mm | 30 |
| Flange 2 length Use the selected flange measurement consistently. Each internal outside dimension contains two setbacks. | A2 | mm | 60 |
| Flange 3 length Use the selected flange measurement consistently. Each internal outside dimension contains two setbacks. | A3 | mm | 30 |
| Flange 4 length Use the selected flange measurement consistently. Each internal outside dimension contains two setbacks. | A4 | mm | 40 |
| Flange 5 length Use the selected flange measurement consistently. Each internal outside dimension contains two setbacks. | A5 | mm | 30 |
| Bend 1 signed turn angle Turn from flat: +90° or −90° makes a right angle. Sign sets drawing direction only. For an included angle α, magnitude = 180° − α. | a1 | deg | 90 |
| Bend 1 inside radius Finished inside radius after springback, not automatically the punch radius. | R1 | mm | 2 |
| Bend 2 signed turn angle Turn from flat: +90° or −90° makes a right angle. Sign sets drawing direction only. For an included angle α, magnitude = 180° − α. | a2 | deg | 90 |
| Bend 2 inside radius Finished inside radius after springback, not automatically the punch radius. | R2 | mm | 2 |
| Bend 3 signed turn angle Turn from flat: +90° or −90° makes a right angle. Sign sets drawing direction only. For an included angle α, magnitude = 180° − α. | a3 | deg | -90 |
| Bend 3 inside radius Finished inside radius after springback, not automatically the punch radius. | R3 | mm | 2 |
| Bend 4 signed turn angle Turn from flat: +90° or −90° makes a right angle. Sign sets drawing direction only. For an included angle α, magnitude = 180° − α. | a4 | deg | -90 |
| Bend 4 inside radius Finished inside radius after springback, not automatically the punch radius. | R4 | mm | 2 |
| V-die opening The actual tool opening. These estimates apply to conventional air bending near 90°, not bottoming or coining. | V_die | mm | 16 |
| Material tensile strength Use the material certificate. The K-factor family above does not change this independent input. | R_m | MPa | 450 |
| Minimum-flange / die-opening ratio Approximate 90° outside flange: b ≈ 0.71 V. Replace with the tooling supplier's ratio; die shoulders and thickness matter. | c_flange | 0.71 |
Results
With the default inputs above, the calc gives:
| Result | Value |
|---|---|
| Flat-pattern cut length | 112.67 mm |
| Total bend allowance | 8.671 mm |
| Total bend deduction | 7.329 mm |
| Minimum outside flange — 90° estimate | 11.36 mm |
| Air-bending force — one bend, estimate | 15.98 kN |
| Air-bending tonnage — metric tonnes-force | 1.63 |
| Air-bending tonnage — US short tons-force | 1.8 |
Checked against sources
Each case below was calculated by this calc and agrees with the value from its source (within the tolerance where one is shown).
Published allowance: 16 gauge, 60°
Source: SheetMetal.Me Bend Allowance Chart (s2), page 1: 16 gauge, t = 0.060 in, R = 0.092 in, K = 0.33, 60° gives BA = 0.1170 in. Exact circular geometry gives about 0.11708 in; 0.0002 in absolute tolerance covers the published chart's rounded geometry. Formula is not adjusted to match.
Inputs: Number of bends = 1; Sheet thickness = 1.524 mm; Bend 1 inside radius = 2.337 mm; Bend 1 signed turn angle = 60 deg; K-factor source = Measured / custom K-factor; Custom K-factor = 0.33; Flange 1 length = 40 mm; Flange 2 length = 50 mm; the others as above.
| Result | Source | This calc |
|---|---|---|
| Bend allowances — neutral-axis arc lengths [1] | 2.972 ± 0.00508 mm | 2.974 mm |
Published deduction: 24 gauge, 90°
Source: SheetMetal.Me Bend Deduction Chart (s7), page 1: 24 gauge, t = 0.024 in, R = 0.020 in, K = 0.33, 90° gives BD = 0.0440 in. Exact geometry gives about 0.04414 in. Tolerance is 0.0002 in, allowing for rounded chart inputs; correct circular-arc physics is retained.
Inputs: Number of bends = 1; Sheet thickness = 0.6096 mm; Bend 1 inside radius = 0.508 mm; K-factor source = Measured / custom K-factor; Custom K-factor = 0.33; Flange 2 length = 40 mm; the others as above.
| Result | Source | This calc |
|---|---|---|
| Bend deductions from outside dimensions [1] | 1.118 ± 0.00508 mm | 1.121 mm |
Published outside-flange worked flat pattern
Source: SheetMetal.Me Bend Allowance worked example (s1): outside flanges 2 in and 3 in, radius 0.250 in; straight lengths 1.625 and 2.625 in imply t = 0.125 in. With its chart's nominal K = 0.33, the model gives BA 0.45749 in and flat 4.70749 in, consistent with published 0.457 and 4.707 in at 0.0006 in tolerance.
Inputs: Number of bends = 1; Sheet thickness = 3.175 mm; Bend 1 inside radius = 6.35 mm; K-factor source = Measured / custom K-factor; Custom K-factor = 0.33; Flange 1 length = 50.8 mm; Flange 2 length = 76.2 mm; V-die opening = 25.4 mm; the others as above.
| Result | Source | This calc |
|---|---|---|
| Flat-pattern cut length | 119.6 mm | 119.6 mm |
| Bend allowances — neutral-axis arc lengths [1] | 11.608 ± 0.01524 mm | 11.62 mm |
Daramco worked 6 mm air-bending force
Source: Daramco Press Brake Tonnage Calculation Guide (s5), Calculation Example: 6 mm mild steel, tensile strength 450 MPa, 2000 mm bend, 48 mm V-opening gives 958.5 kN and approximately 97.7 metric tonnes-force. The source rounds gravity to 9.81; this tool uses exact standard gravity 9.80665.
Inputs: Sheet thickness = 6 mm; V-die opening = 48 mm; Bend length / blank width = 2,000 mm; Bend 1 inside radius = 8 mm; Bend 2 inside radius = 8 mm; Flange 1 length = 70 mm; Flange 2 length = 100 mm; Flange 3 length = 70 mm; the others as above.
| Result | Source | This calc |
|---|---|---|
| Air-bending force — one bend, estimate | 958.5 kN | 958.5 kN |
| Air-bending tonnage — metric tonnes-force | 97.7 ± 0.1 | 97.74 |
Independent Bystronic air-bending chart comparison
Source: Bystronic Tools Euro-B (s6), page 10: t = 2 mm, V = 16 mm, Rm = 420 N/mm², 1 m bend: F = 160 kN, minimum flange 12 mm. The simple 1.42-coefficient estimate gives 149.1 kN (6.8% lower); 12 kN absolute tolerance is an explicit 7.5% engineering comparison, not exact chart reproduction. Approximate 0.71 V flange differs by 0.64 mm; tolerance 1 mm. Use manufacturer limits for actual setup.
Inputs: Bend length / blank width = 1,000 mm; Material tensile strength = 420 MPa; the others as above.
| Result | Source | This calc |
|---|---|---|
| Air-bending force — one bend, estimate | 160 ± 12 kN | 149.1 kN |
| Minimum outside flange — 90° estimate | 12 ± 1 mm | 11.36 mm |
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