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Neutral axis method · K-factor · springback compensation

Bend Allowance Calculator

Bend allowance, bend deduction and flat pattern length for sheet metal, plus springback angle, the overbend needed to compensate for it, and a minimum bend radius check against the material.

K-factor method Bend deduction Springback Min bend radius

Calculate bend allowance and flat pattern

Material & Bend Geometry
Set by material. Override with a measured value if you have one.
Minimum 1.0 mm for this material and thickness.
Angle through which the sheet turns, not the included angle.
Measure legs from the tangent lines. A and B are the flat lengths from each edge to where the bend starts — not to the outside corner. Flat pattern is then A + B + bend allowance.

Enter your values and select Calculate.

Bend allowance formulas

When sheet is bent, the outer surface stretches and the inner compresses. Between them lies the neutral axis, which keeps its original length. Its arc through the bend is the bend allowance — the material the bend consumes.

BA = (π/180) × θ × (R + K·t) — bend allowance, mm BD = 2(R + t)·tan(θ/2) − BA — bend deduction, mm Flat = A + B + BA — legs measured from tangent lines (equivalently A′ + B′ − BD, with legs to the outside mould line) — Springback — Kf = Sy · R / (E · t) θfinal = θ × (1 − 3Kf + 4Kf³) springback = θ − θfinal overbend = θ + springback — set the tool to this angle — Formability — Rmin = factor × t — 0.5t steel · 1.0t SS/Cu · 4.0t aluminium

t sheet thickness (mm) · R inside bend radius (mm) · θ bend angle (degrees) · K K-factor · A, B flat leg lengths (mm) · Sy yield strength (MPa) · E Young's modulus (GPa)

The most common flat-pattern error. Bend allowance and bend deduction are not interchangeable — each belongs with a different way of measuring the legs. Add BA to legs measured from the tangent lines; subtract BD from legs measured to the outside corner. Mixing them produces a blank wrong by roughly BA + BD, about 10 mm on the example below.

Worked example

A 2 mm mild steel bracket bent 90° over a 3 mm inside radius, with 50 mm flat legs each side.

Given
Material
Mild steel — K = 0.44, Sy = 250 MPa, E = 200 GPa
Thickness t
2 mm
Inside radius R
3 mm
Bend angle θ
90°
Legs A / B
50 mm / 50 mm (from tangent lines)
Step 1 — neutral axis and bend allowance
Neutral axis offset = K·t = 0.44 × 2
0.88 mm
Neutral arc radius = R + K·t = 3 + 0.88
3.88 mm
BA = (π/180) × 90 × 3.88
6.095 mm
Step 2 — deduction and blank size
BD = 2 × (3 + 2) × tan 45° − 6.095
3.905 mm
Flat = 50 + 50 + 6.095
106.095 mm
Step 3 — springback
Kf = 250 × 3 / (200 000 × 2)
0.001875
θfinal = 90 × (1 − 0.005625 + …)
89.49°
Springback
0.51°
Overbend target
90.5°
Step 4 — formability
Rmin = 0.5 × 2
1.0 mm — 3 mm radius is well clear
Blank 106.095 mm · BA 6.095 · BD 3.905 · overbend to 90.5° → bend acceptable

Cut the blank at 106.1 mm and set the press brake to 90.5° so the part relaxes to 90°. The same geometry in aluminium 6061 would need a 8 mm minimum radius — the 3 mm radius here would crack it — and would spring back about 1.12°, roughly twice as much, because aluminium's elastic modulus is about a third of steel's.

Units and input ranges

QuantitySymbolUnitAccepted range
Sheet thicknesstmm or in> 0
Inside bend radiusRmm≥ 0
Bend angleθdegrees> 0, typically ≤ 180
K-factorK0.1 – 0.5
Leg lengthsA, Bmm≥ 0
Yield strengthSyMPa> 0
Young's modulusEGPa> 0
Bend allowanceBAmmoutput
Springbackdegreesoutput

Thickness in inches is converted at 25.4 mm. Radius and leg lengths are always in millimetres. Note that E is entered in GPa, not MPa.

Material properties and minimum bend radius

MaterialKSy (MPa)E (GPa)Rmin
Mild steel0.442502000.5 t
Stainless 3040.443101931.0 t
Aluminium 60610.40193704.0 t
Copper0.442101171.0 t
Galvanised0.442802000.5 t
K-factor is not a constant. The tabulated values are reasonable defaults for air bending at moderate R/t. The true neutral axis position shifts with radius-to-thickness ratio, tooling and forming method — bottoming and coining push it higher than air bending. For production work, back-calculate K from a test bend and use that.

Frequently asked questions

What is bend allowance?

Bend allowance is the arc length of the neutral axis through a bend. When sheet metal is bent the outside stretches and the inside compresses, and somewhere between them a layer neither stretches nor compresses. That neutral layer keeps its original length, so its arc length is the amount of material consumed by the bend. Adding bend allowance to the flat leg lengths gives the blank size needed.

What is the K-factor in sheet metal bending?

The K-factor is the position of the neutral axis expressed as a fraction of material thickness measured from the inside surface. A K-factor of 0.44 means the neutral axis sits 44 % of the way through the thickness. It is always less than 0.5 because the neutral axis shifts toward the inside of the bend. Typical values are 0.44 for mild steel and stainless and about 0.40 for aluminium, though the true value depends on tooling, radius-to-thickness ratio and forming method.

What is the difference between bend allowance and bend deduction?

They are two ways of reaching the same blank size from different measurements. Bend allowance is added to leg lengths measured from the bend tangent lines. Bend deduction is subtracted from leg lengths measured to the outside mould line, which is where the two flat faces would meet if extended. Using the wrong one with the wrong measurement is the most common cause of an incorrect flat pattern.

How much springback should I expect?

Springback grows with the ratio of yield strength to elastic modulus and with the bend radius to thickness ratio. Mild steel at a tight radius may spring back well under one degree, while aluminium at the same geometry springs back roughly twice as much because its elastic modulus is about one third that of steel. The tool must overbend by the springback amount so the part relaxes to the intended angle.

What is the minimum bend radius?

Minimum inside bend radius is the tightest radius a material tolerates before the outer surface cracks, and it scales with thickness. Common guidance is 0.5 × t for mild steel and galvanised sheet, 1.0 × t for stainless 304 and copper, and 4.0 × t for aluminium 6061. Bending across the grain direction allows tighter radii than bending along it.

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