About

Incorrect bend allowance calculations cause scrap parts. Every bend in sheet metal stretches the material along the neutral axis. The neutral axis shifts inward from the geometric center depending on material hardness, grain direction, tooling radius, and thickness. The K-factor quantifies this shift as a ratio from 0 to 1, where 0.5 places the neutral axis at the geometric center and real-world values for cold-rolled steel typically fall between 0.3 and 0.45. This calculator computes bend allowance BA, bend deduction BD, outside setback OSSB, and flat pattern length using the standard arc-length formula from machinery handbooks. Results assume uniform thickness and a single-axis bend without springback compensation.

Tooling wear, anisotropy in rolled stock, and operator technique introduce variance of ±0.05mm or more. Always verify against a test coupon before production runs. The K-factor presets provided here follow Machinery's Handbook (31st ed.) guidelines for air bending. Bottom bending and coining operations shift K lower. Pro tip: if your inside radius is less than the material thickness, expect cracking in hard alloys - the formula still computes but physics will object.

Formulas

The bend allowance represents the arc length of the neutral axis through the bend zone. It is the foundational value from which bend deduction and flat pattern dimensions derive.

BA = π180 × θ × (R + K × T)

Where BA = bend allowance (arc length of neutral axis), θ = bend angle in degrees, R = inside bend radius, K = K-factor (neutral axis position ratio, 0 - 1), T = material thickness. All linear dimensions share the same unit.

The outside setback is the distance from the tangent point to the apex of the bend measured along the outside surface.

OSSB = (R + T) × tan(θ2)

Bend deduction is the difference between twice the outside setback and the bend allowance. It represents the material removed from the total flange lengths to yield the correct flat pattern.

BD = 2 × OSSB − BA

The flat pattern length for a single-bend part with two legs:

L_flat = L₁ + BA + L₂

Where L₁ and L₂ are the flat leg lengths measured from the inside bend tangent points to the edge of the part. Equivalently, L_flat = F₁ + F₂ − BD, where F₁ and F₂ are the outside flange dimensions.

Reference Data

Material	Condition	Typical K-Factor	Min Bend Radius / Thickness	Tensile Strength MPa
Mild Steel (A36)	Annealed	0.33	0.5t	400 - 550
Mild Steel (A36)	Half-Hard	0.38	1.0t	400 - 550
Stainless Steel 304	Annealed	0.35	0.5t	515 - 690
Stainless Steel 304	Half-Hard	0.41	1.5t	860 - 1100
Aluminum 3003-H14	Half-Hard	0.33	1.0t	150 - 200
Aluminum 5052-H32	Quarter-Hard	0.35	1.0t	230 - 280
Aluminum 6061-T6	Tempered	0.40	1.5t	290 - 340
Copper C110	Soft	0.30	0.3t	210 - 240
Copper C110	Hard	0.38	1.0t	310 - 380
Brass C260	Soft	0.32	0.5t	300 - 365
Brass C260	Hard	0.39	1.5t	435 - 525
Titanium Grade 2	Annealed	0.38	2.0t	345 - 510
Titanium Grade 5 (Ti-6Al-4V)	Annealed	0.42	3.0t	895 - 1000
Inconel 625	Annealed	0.40	2.0t	827 - 1035
Spring Steel 1095	Hardened	0.45	3.0t	1200 - 1500
Galvanized Steel	Standard	0.36	1.0t	340 - 480
Zinc Sheet	Soft	0.30	0.5t	100 - 150
Magnesium AZ31B	Annealed	0.38	5.0t	240 - 290
Beryllium Copper C172	Solution Treated	0.36	1.5t	480 - 620
Monel 400	Annealed	0.37	1.5t	517 - 620

Frequently Asked Questions

In air bending the material floats above the die, and the neutral axis sits closer to the inside surface - typical K-factor range is 0.3-0.45. In bottom bending (bottoming), the punch forces the material fully into the die, compressing the inner zone more aggressively. This pushes the neutral axis further inward, reducing K to roughly 0.25-0.35. Coining operations compress the material even further, driving K below 0.25 in some cases. Always calibrate K against test bends for your specific die set and tonnage.

A systematic error in flat pattern length almost always traces back to an incorrect K-factor or measuring convention mismatch. If you measure flange dimensions to the outside mold line but the calculator expects inside dimensions (tangent-to-tangent), every bend adds an error equal to the material thickness. Verify whether your CAD system uses inside dimensions or outside dimensions, and adjust inputs accordingly. Also confirm your inside radius matches the actual punch tip radius, not the nominal die opening.

When R < T (a tight-radius bend), the outer fibers stretch beyond their elongation limit in hard materials, causing surface cracking or fracture. The bend allowance formula remains mathematically valid, but the physical result may be a cracked part. For mild steel, a minimum inside radius of 1.0T is typical; for aluminum 6061-T6, use at least 1.5T; for titanium Grade 5, use 3.0T or more. If you must use a tighter radius, consider annealing the material or switching to a softer temper before bending.

Grain direction does not change the geometric formula, but it changes whether the part survives the bend. Bending parallel to the rolling direction (with the grain) requires a larger minimum radius because elongation across grain boundaries is lower. Bending perpendicular to the grain (across the grain) allows tighter radii. For critical parts, orient bends perpendicular to the grain and add 0.5T to your minimum radius when bending parallel. The K-factor itself can shift by ±0.02 depending on grain orientation in anisotropic alloys.

The bend allowance formula calculates the geometry at the die - not after the punch retracts. Springback opens the bend angle by 1° - 5° depending on material yield strength, R/T ratio, and tooling. High-strength steels and stainless spring back more than mild steel or soft aluminum. To compensate, over-bend by the springback angle. This calculator outputs the nominal BA at the programmed angle. If your final part angle must be exactly 90°, you may need to program 92° - 94° on the press brake. Test bends are the only reliable way to determine the exact springback offset for a given setup.

Yes. Calculate the bend allowance independently for each bend using its own angle, radius, and K-factor (the K-factor can differ if radii or tooling change between bends). Sum all flat leg lengths and all individual bend allowances to get the total flat pattern length. Ensure that leg dimensions between bends are measured consistently from tangent point to tangent point - not from bend apex to bend apex - to avoid double-counting the bend zone.