Bend Deduction Calculator

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Walk-through

How to Use This Calculator

4 steps

1

Enter your bend angle, radius, and thickness

Enter the included bend angle in degrees, the inside radius of the bend, the sheet's material thickness, and a K-factor (0.44 is a common air-bend estimate — edit it if your shop uses a measured value for the tooling and material). Pick a preset chip for a quick starting point, or use the unit toggle to switch between inches and millimeters.

2

Read the bend deduction

The headline number is the bend deduction (BD) — the amount to subtract from the sum of your mold-line flange lengths to get the correct flat-pattern length. The stat grid below it shows the setback and bend allowance values BD is built from.

3

See how the setback is derived

Open the Setback tab for a step-by-step breakdown of tan(angle / 2) x (R + t) — the geometric distance from the mold line back to the tangent point where the bend radius begins.

4

Apply it to a real flat pattern

Open the Flat Pattern (Mold Line) tab, enter your two mold-line flange lengths, and read the developed flat-pattern length. The K-factor comparison table there also shows how sensitive that flat length is to the K-factor you chose.

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Reference

Formula & Methodology

3 formulas

Bend Deduction

BD = 2 x Setback - BA

Bend deduction is the amount subtracted from the sum of a bend's two mold-line flange lengths to get the correct flat-pattern (developed) length. It equals twice the setback minus the bend allowance.

Setback

Setback = tan(angle / 2) x (R + t)

Setback is the distance, measured along each flange, from the mold line (where the flange faces would intersect if extended) back to the tangent point where the curved bend radius begins. angle is the included bend angle in degrees, R is the inside bend radius, and t is the material thickness.

Bend Allowance (used inside BD)

BA = angle x (pi / 180) x (R + K x t)

Bend allowance is the length of material consumed by the curved region of the bend, measured along the neutral axis. This is the same formula the Bend Allowance calculator uses, so the two tools stay numerically consistent for the same inputs. K is the K-factor — the fractional distance of the neutral axis from the inside face of the material (0.44 is a common estimate for air bending).

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Glossary

Key Terms Explained

7 terms

Bend deduction The amount subtracted from the sum of a bend's two mold-line flange lengths to get the flat-pattern (developed) length: BD = 2 x setback - BA.

Setback The distance from the mold line back to the tangent point where a bend's curved radius begins, measured along each flange: setback = tan(angle / 2) x (R + t).

Mold line The theoretical line where two flat flange faces would intersect if the bend radius were removed and the flanges extended to a sharp corner. CAD models often dimension flanges to the mold line rather than to the tangent point.

Bend allowance The length of material consumed by the curved portion of a bend, measured along the neutral axis: BA = angle(rad) x (R + K x t). Bend deduction is derived from bend allowance.

Flat pattern The two-dimensional, unbent (developed) shape of a sheet-metal part — the shape you'd cut from flat stock before forming the bends. Bend deduction (or bend allowance) is what lets you calculate flat-pattern dimensions from a bent part's finished dimensions, or vice versa.

K-factor A ratio describing where the neutral axis (the layer of material that neither stretches nor compresses during bending) sits between the inside and outside faces of the sheet, as a fraction of the material thickness. Typical values range from about 0.33 to 0.50 depending on the bending method, material, and tooling; 0.44 is a common general-purpose estimate for air bending.

Inside radius The radius of the bend measured on the inside (concave) face of the material. It's set by the tooling (die opening and punch nose radius) and material properties, not by the operator directly.

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Scenarios

Real-World Examples

3 worked examples

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Standard 90° bend

Typical shop case

Bend angle 90° Inside radius 0.125 in Thickness 0.060 in K-factor 0.44

Setback = tan(45°) x (0.125 + 0.060) = 0.1850 in. Bend allowance = (π/2) x (0.125 + 0.44 x 0.060) = 0.2378 in. Bend deduction = 2 x 0.1850 - 0.2378 = 0.1322 in — subtract this from the sum of the two mold-line flange lengths to get the flat-pattern length.

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Setback-only check

Verifying a mold-line dimension by hand

Bend angle 90° Inside radius 0.125 in Thickness 0.060 in

For a 90° bend, tan(angle / 2) = tan(45°) = 1, so setback simplifies to R + t = 0.185 in. That's the distance back from the mold line to the tangent point on each flange — useful for laying out where the flat blank's straight sections end and the curved bend region begins.

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Mold-line flat pattern

Two flanges dimensioned to their mold line

Flange 1 (mold line) 2.000 in Flange 2 (mold line) 1.500 in Bend deduction 0.1322 in (from example 1)

Flat pattern length = 2.000 + 1.500 - 0.1322 = 3.3678 in. Because the mold-line dimensions already include the corner the bend radius replaces, you subtract bend deduction once per bend rather than adding an allowance.

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Deep Dive

Understanding Bend Deduction for Sheet Metal Flat Patterns

4 chapters · 5 min read

Bend deduction is one of two standard methods (alongside bend allowance) for converting a finished sheet-metal part's bent dimensions into the flat pattern needed to cut the blank before forming. It's the method that matches how most CAD packages dimension flanges by default — to the mold line — which makes it the natural fit for programming a laser, punch, or CNC blank from a drawing that already carries mold-line dimensions.

How bend deduction works

When a flat sheet is bent, the corner doesn't stay sharp — it becomes a curved radius, and the material along that curve neither fully stretches nor fully compresses at every layer. Bend allowance quantifies how much material length that curved region consumes, measured along the neutral axis. Setback quantifies the geometric distance from the theoretical sharp corner (the mold line) back to where the curve actually begins.

Bend deduction combines the two: BD = 2 x setback - BA. Because CAD models typically dimension flanges to the mold line (the sharp-corner intersection point), and mold-line dimensions overstate the true flat length by exactly the bend deduction, subtracting BD once per bend converts mold-line dimensions directly into the flat-pattern length.

Bend deduction vs. bend allowance

Bend allowance and bend deduction solve the same underlying problem — relating bent dimensions to a flat pattern — but they start from different reference dimensions. Bend allowance is added to the sum of a part's flange lengths measured to the bend's tangent points. Bend deduction is subtracted from the sum of flange lengths measured to the mold line. Both approaches, applied consistently, produce the same flat-pattern length; the one to use depends on how your drawing dimensions the flanges.

Because most parametric CAD tools (SolidWorks, Fusion 360, Inventor, and similar) report flange lengths to the mold line by default, bend deduction is usually the more directly useful figure for programming a flat blank from an existing 3D model.

Why K-factor matters

K-factor sets where the neutral axis sits within the material thickness, and it feeds directly into the bend allowance term inside the bend-deduction formula. A higher K-factor increases bend allowance, which decreases bend deduction (and therefore increases the resulting flat-pattern length) for the same angle, radius, and thickness. K-factor varies with bending method (air bending vs. bottoming vs. coining), material, tooling, and thickness — 0.44 is a reasonable general-purpose starting point, but shops that cut and bend the same material and gauge repeatedly often measure and record their own K-factor for tighter tolerance.

Limits and edge cases

This calculator assumes a single, simple air bend with a constant inside radius and thickness along the bend line — it does not account for springback, work-hardening at tight radii, or multi-radius/compound bends. Very tight inside radii relative to material thickness (sharp or coined bends) can behave differently from the linear K-factor model this formula assumes. For production tolerance work, validate the K-factor against test bends on your actual material, gauge, and tooling rather than relying on the 0.44 default alone.

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Questions

Frequently Asked Questions

6 questions

What is the bend deduction formula?+

BD = 2 x Setback - BA, where Setback = tan(angle / 2) x (R + t) and BA (bend allowance) = angle(rad) x (R + K x t). Subtract BD from the sum of a bend's two mold-line flange lengths to get the flat-pattern length.

What's the difference between bend deduction and bend allowance?+

They're two different methods for the same goal. Bend allowance is added to flange lengths measured to the bend's tangent points; bend deduction is subtracted from flange lengths measured to the mold line (the theoretical sharp-corner intersection). Applied consistently with the matching dimension style, both produce the same flat-pattern result.

What is the mold line?+

The mold line is the theoretical intersection point of two flange faces if the bend radius were removed and the flat faces extended to a sharp corner. Most CAD tools dimension flange lengths to the mold line by default, which is why bend deduction — built around mold-line dimensions — is often the more directly usable figure.

When should I use bend deduction instead of bend allowance?+

Use bend deduction when your flange dimensions come from the mold line (the common default in most 3D CAD software). Use bend allowance when your dimensions are measured to the bend's tangent points instead. Check how your drawing or model dimensions the flanges before picking a method.

What K-factor should I use?+

0.44 is a common general-purpose estimate for air bending and is this calculator's default, but the true value depends on your material, thickness, bending method, and tooling. Shops that repeatedly bend the same material and gauge often measure their own K-factor from test bends for tighter accuracy.

What units does this calculator use?+

Enter the inside radius, thickness, and mold-line flange lengths in inches or millimeters using the unit toggle — the calculator converts your existing entries when you switch. The bend angle is always entered in degrees.

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