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Machinery's Handbook

Manufacturing

Sheet Metal Bend Allowance & Deduction Calculator determines flat pattern length by computing bend allowance, bend deduction, and K-factor. Use the formula BA = (pi/180) x (R + K x T) x A where BA = bend allowance, R = inside radius, K = K-factor (0.33-0.50), T = thickness, A = bend angle. This calculator implements Industry Practice standard formulas.

Sheet Metal Bend Allowance & Deduction Calculator

Calculate bend allowance, bend deduction, outside setback, and minimum bend radius per Machinery's Handbook. Includes K-factor auto-selection by material and R/T ratio.

Unit System

Input Parameters

Material Preset

Auto K-factor: 0.33 (R/T = 1.00)

Sheet Thickness (T) — mm

Inside Bend Radius (R) — mm

Bend Angle (θ) — deg

K-factor (Neutral Axis Factor) (auto)

Calculation Summary

Input Parameters

Material	MILD STEEL
Thickness (T)	2.00mm
Inside Radius (R)	2.00mm
Bend Angle (θ)	90°
K-factor	0.330

Calculated Results

Bend Allowance (BA)	4.1783mm KEY
Bend Deduction (BD)	3.8217mm KEY
Outside Setback (OSSB)	4.0000mm
Min Bend Radius	2.0000mm
R/T Ratio	1.00

Mathematical Models & Equations

Bend Allowance

BA = (π/180) × 90° × (2 + 0.33 × 2) = 4.1783

Outside Setback

OSSB = (R + T) × tan(θ/2) = 4.00 × tan(45°) = 4.0000

Bend Deduction

BD = 2 × OSSB − BA = 3.8217

Verification Calculation Log

1Compute angle factor: π/180 × 90 = 1.570796
2Compute neutral axis radius: R + K×T = 2 + 0.33 × 2 = 2.6600
3Bend Allowance: BA = 1.570796 × 2.6600 = 4.1783
4tan(45°) = tan(0.785398 rad) = 1.000000
5Outside Setback: OSSB = (R + T) × tan(45°) = 4.0000 × 1.000000 = 4.0000
6Bend Deduction: BD = 2 × OSSB − BA = 2 × 4.0000 − 4.1783 = 3.8217
7R/T ratio = 2 / 2 = 1.00
8Min bend radius for material: 2.00 (factor 1.0×T)

Engineering Application Notes

Formulas per Machinery's Handbook (30th ed.) — bend allowance based on neutral axis arc length. K-factor represents neutral axis position as fraction of thickness from inside surface. K=0.33 typical for R < 2T (tight bends); K=0.5 typical for R ≥ 2T (open bends). Material presets auto-select K-factor based on R/T ratio per industry guidelines. Minimum bend radius varies by material: mild steel 1×T, aluminum 1.5×T, stainless 2×T, copper 1×T. Always calibrate K-factors using flat test cuts on your specific brake tooling and material batch. Bend deduction = material removed from flat pattern = 2×OSSB − BA. Springback not accounted — actual bent angle may differ from die angle; compensate in tooling.

Standard Citations & References

Machinery's Handbook, 30th Edition

Machinery's Handbook

Bending section — K-factor tables, bend allowance/deduction formulas, minimum bend radii by material.

SMACNA Sheet Metal Guidelines

SMACNA

Industry standard for HVAC and architectural sheet metal fabrication tolerances.

Domain of Validity

Valid for air bending of sheet metal 0.5-6 mm thick. K-factor values assume standard air bending.

Worked Example

90 deg bend, 2 mm steel, K=0.44, R=3 mm: BA = (pi/180) x (3 + 0.44 x 2) x 90 = 6.08 mm.

Verification

Formulas based on industry practice. K-factor from Miller (1994). Last verified: August 2026.

Accuracy and Uncertainty

Accuracy depends on K-factor. Typical plus/minus 5% with standard K-factors.

Frequently Asked Questions

What is bend allowance?

Bend allowance (BA) is the length of material consumed in the bend zone. It is added to the straight lengths to get the total flat pattern length.

What is the K-factor?

The K-factor is the ratio of the neutral axis offset to material thickness. It typically ranges from 0.33 to 0.50. For most materials, K is approximately 0.44 for air bending.

What is the difference between bend allowance and bend deduction?

Bend allowance (BA) is the arc length of the bend. Bend deduction (BD) is the amount subtracted from the sum of outside dimensions to get the flat length. BD = 2 x (R + T) - BA.

How does material type affect bend calculations?

Different materials have different K-factors due to varying ductility and springback. Soft materials (aluminum) have lower K-factors; hard materials (stainless steel) have higher K-factors.

What is the minimum bend radius?

The minimum bend radius depends on material type, thickness, and temper. For most steels, minimum radius is 1x thickness. For aluminum, it can be 0.5x thickness for soft temper.