Bend Allowance vs Bend Deduction: Formulas and Worked Examples

Bend allowance vs bend deduction comes down to the starting measurements: allowance adds the curved length to straight tangent lengths; deduction subtracts the corner correction from outside flange dimensions. Both give the same flat length when the angle, radius and measurement convention agree.

For the hypothetical right-angle example below, outside flanges of 40 mm and 30 mm produce a flat length of 66.40 mm under the stated assumptions. Adding bend allowance directly to those outside dimensions would use the wrong starting measurements. Define where each dimension ends before calculating a blank.

Define the bend and the dimension endpoints

Use a simple planar bend with constant thickness and a circular bend region. Let R be the inside radius, T the sheet thickness and K the neutral-line depth divided by T. The neutral-line radius in this model is R + K × T; K must be chosen for the actual forming conditions.

Let θ be the bend rotation measured from flat and α the final inside included angle. For this ordinary corner, θ = 180° − α. A drawing that specifies an inside included angle of 120° therefore uses a bend rotation of 60° in the equations below.

The virtual corner is the intersection obtained by extending the straight outside faces. It is not a point on the rounded metal surface. Mark that construction on the drawing so the designer, programmer and inspector use matching endpoints.

Where the formulas come from

The FAA Airframe & Powerplant Mechanics—Airframe Handbook, AC 65-15A, Chapter 5, printed pages 146–150, explains neutral-line arc length, tangent geometry and setback. Page 147 discusses the limitation of a midpoint approximation; pages 148–149 cover setback. This is a geometry reference, not a universal material K table.

The following equations are our algebraic derivation using that geometry and the symbols defined here. Substituting the chosen neutral-line radius into circular arc length gives BA; a right triangle at the virtual corner gives SB. Our K denotes neutral-line position, distinct from the handbook’s angular setback multiplier.

Bend allowance: BA = (π × θ / 180) × (R + K × T)

Outside setback: SB = (R + T) × tan(θ / 2)

Angles in these displayed equations are in degrees. When using software that expects radians, convert the angle before evaluating the trigonometric function. Keep radius, thickness, flange dimensions and the resulting lengths in the same length unit.

For this bend, s₁ = a − SB and s₂ = b − SB. Add the straight lengths and the curved length: L = s₁ + s₂ + BA. Substitution gives L = a + b − 2 × SB + BA.

Bend deduction: BD = 2 × SB − BA

Flat length from outside dimensions: L = a + b − BD

Worked example: a right-angle bend

This is hypothetical geometry, not a material or machine capability claim. Assume θ = 90°, α = 90°, T = 2 mm, R = 2 mm, K = 0.40, a = 40 mm and b = 30 mm. The K value is chosen only to illustrate the calculation; it is not a recommended value for a material grade.

The neutral-line radius is 2 + 0.40 × 2 = 2.8 mm. At this angle the outside setback reduces to SB = R + T = 4 mm.

• BA: (π × 90 / 180) × 2.8 = 4.398229715… mm
• BD: 2 × 4 − 4.398229715… = 3.601770285… mm
• L: 40 + 30 − 3.601770285… = 66.398229715… mm

Check through tangent lengths: s₁ = 40 − 4 = 36 mm and s₂ = 30 − 4 = 26 mm. Then 36 + 26 + 4.398229715… = 66.398229715… mm, matching the deduction method.

Displayed to 0.01 mm, the results are BA = 4.40 mm, BD = 3.60 mm and L = 66.40 mm. Keep unrounded intermediate values in the calculation. The display precision is not a manufacturing tolerance or a promise about the finished part.

Worked example: an obtuse inside angle

Assume α = 120°, so θ = 180° − 120° = 60°. Use T = 1.5 mm, R = 3 mm, K = 0.40, a = 50 mm and b = 40 mm. These are another set of illustrative inputs, with no material grade implied.

The neutral-line radius is 3 + 0.40 × 1.5 = 3.6 mm. The setback uses half the bend rotation: SB = (3 + 1.5) × tan(30°) = 2.598076211… mm.

• BA: (π × 60 / 180) × 3.6 = 3.769911184… mm
• BD: 2 × 2.598076211… − 3.769911184… = 1.426241238… mm
• L: 50 + 40 − 1.426241238… = 88.573758762… mm

Rounded for display, BA = 3.77 mm, SB = 2.60 mm, BD = 1.43 mm and L = 88.57 mm. Subtract the unrounded setback from each outside flange, then add the unrounded BA, to check the same flat length by the tangent method.

The angle conversion is part of the calculation, not a naming preference. Entering the included angle where the equation requires bend rotation changes both the arc and setback. Label the angle on the input sheet before copying it into CAD or a worksheet.

Calibrate with a measured coupon

A proposed shop check starts with a known blank length L, then measures the formed outside dimensions a and b using the same virtual-corner construction. Their relationship gives BD = a + b − L. Record the actual inside radius, thickness and finished angle as well.

From the measured geometry, calculate SB and recover BA = 2 × SB − BD. Rearranging the allowance equation gives K = [BA × 180 / (π × θ) − R] / T. This is a derived calibration relation; no shop trial is claimed here.

Keep the record with its material, tooling and forming method. Changing those conditions requires checking whether the calibration still applies. Springback, setup and backgauge referencing also affect the finished part; the flat-length equation does not control the finished angle by itself.

Limits before releasing a flat pattern

The setback expression is unsuitable for a closed hem: at a bend rotation of 180° its tangent term is singular. Noncircular bends and changing thickness also fall outside the stated model. Use a method appropriate to those geometries rather than forcing their dimensions into this corner formula.

Check that the assumed tangent regions exist within the flanges and that adjacent bends do not invalidate the simple construction. Material cracking at a tight radius is a formability question; adjusting K does not establish that the material can survive the bend.

Machine selection and forming force are separate checks. See how to choose a press brake for the equipment enquiry and the press brake tonnage calculator for force sizing. Neither replaces the dimension convention used to develop the blank.

Questions about allowance and deduction

Which method should a drawing use?

Use the method that matches its dimension endpoints. Outside flanges to a virtual corner use deduction; straight lengths to tangent points use allowance. Document the convention with the drawing revision.

Is K = 0.40 a standard material value?

No. It is the assumed neutral-line factor in these examples. Confirm the applicable value or deduction through the shop’s material, tooling and process calibration.

Can a correct formula still give the wrong blank?

Yes. An incorrect angle convention, radius, K value or dimension endpoint can produce an unsuitable result. Check the input definitions and compare a trial part with the drawing before releasing production blanks.

Send BEIGEMA the part drawing and bend requirements, or contact WhatsApp +86 18005147868. Include material, thickness, radius, angle convention and flange dimensions for the equipment discussion.