Bend Allowance & K-Factor Calculator
Flat patterns for sheet metal — bend allowance, deduction, tonnage and springback, with the K-factor tracking your radius instead of being guessed once.
How the K-factor moves with your radius
Same material, same thickness — only the inside radius changes. This is why one number copied into a CAD template is right at exactly one radius.
Two reasons flat patterns come out wrong
The K-factor is not a material constant. People look up "0.44 for aluminium" once, put it in the template and use it forever. It is not a property of the material — it is a property of how tightly you are bending. At R/T = 1 it is about 0.33, at 2 about 0.40, at 3 about 0.44, and only above about R/T = 5 does it settle near 0.50. The neutral axis physically migrates: bend tightly and the inside face is compressed hard, pushing the plane of zero strain toward it; bend gently and there is little compression, so it sits near the middle.
And the inside radius is not the punch radius. This one is worse, because it invalidates the K-factor you just looked up. In air bending — how most parts are made — the sheet touches the punch tip and the two die shoulders, and the radius it forms is set by the die opening, at roughly 16% of the vee width in mild steel. The punch tip is irrelevant as long as it is sharper than the radius being formed. So a drawing that says "1 mm inside radius" run in a 16 mm vee produces 2.6 mm, and every flat length derived from the drawing was wrong before the arithmetic started. Bottoming and coining are different — there the punch really does set the radius, which is exactly why they cost four to nine times the tonnage.
- 6061-T6 cracks. In the T6 temper it wants three to four thicknesses of inside radius, not the half-thickness people attempt. If a part has to bend tight, 5052 is the answer and 6061 is not — that single substitution fixes more sheet metal problems than any calculation here.
- Bend across the grain. Rolling direction is worth roughly a factor of two on cracking. A bend that splits along the grain will often form perfectly at ninety degrees to it.
- The angle is the angle bent through. A 90° bend uses 90 in the formula, not the 90° of included angle left between the flanges. Those coincide at ninety degrees and diverge everywhere else, which is why shop rules that quietly assume 90° fall apart at 30.
- Force goes with thickness squared. Doubling the thickness quadruples the tonnage, and opening the die is the only lever that brings it back down — at the cost of a larger formed radius, which changes your K-factor again.
- Springback rises with R/T. A gentle bend springs back much more than a tight one, and it scales with yield over modulus — which is why 6061-T6 recovers several times as much as mild steel and annealed copper barely moves. Stainless is worse than any formula says, because it work-hardens while it forms.
- One measurement beats every chart, including this one. Bend a test piece in the actual material on the actual machine, measure the flanges, and back-calculate the K-factor from what came out. Every brake has its own tooling wear, crowning and habits.
How to use
- Pick the material and enter the thickness and bend angle.
- Enter the die opening, and leave the radius blank so the die sets it.
- List the flange lengths measured to the outside corner.
- Read the flat length, then check the radius against the cracking minimum.
Frequently asked questions
Why does my K-factor keep being wrong?
Because it is almost certainly one number copied off a chart, and the K-factor is not a material constant. It is a property of how tightly you are bending, and it moves with the ratio of inside radius to thickness: roughly 0.33 at R/T of 1, 0.40 at 2, 0.44 at 3, and only settling near 0.50 above about 5. A single figure in a CAD template gives flat patterns that are right at exactly one radius and progressively wrong everywhere else, which is why the same template works on one job and is millimetres out on the next.
What actually sets the inside bend radius?
In air bending, the die opening — at roughly 16 per cent of the vee width in mild steel. The sheet spans the two die shoulders rather than wrapping the punch, so the punch tip radius is irrelevant as long as it is sharper than the radius being formed. This is the one that quietly ruins flat patterns: a drawing calls out a 1 mm inside radius, the part runs in a 16 mm vee, it forms at 2.6 mm, and every length derived from the drawing was wrong before any arithmetic happened.
When does the punch radius matter then?
When you bottom or coin, because those press the sheet against the punch face rather than letting it span the die. That is precisely why they cost four to nine times the tonnage of air bending: you are paying for the punch to dictate the radius instead of the die. Air bending dominates production work because one set of tooling covers a wide range of angles and radii, and the tonnage is manageable.
What is the difference between bend allowance and bend deduction?
They answer the same question from two directions. Bend allowance is the arc length of the neutral axis, which you ADD to flange lengths measured to the tangent point. Bend deduction is what you SUBTRACT from flanges measured to the outside mould line. Shops use deduction because a flange is measured to the outside corner with a rule, and the tangent point is invisible. Both must give the same flat length, and if they do not, one of the formulas is wrong.
Why does my 6061 crack when I bend it?
Because 6061-T6 needs three to four thicknesses of inside radius and people routinely try half a thickness. It is the least formable alloy in common use, and no amount of care in the brake fixes it — the material is simply in the wrong temper for bending. If a part has to bend tight, 5052-H32 is the answer: it forms cleanly at about one thickness and is far more predictable. That single substitution solves more sheet metal problems than any calculation.
Does grain direction really matter?
Yes, and by roughly a factor of two on cracking. Rolling elongates the grain structure, and a bend running along that direction is trying to split the material the easy way. The same bend at ninety degrees to the grain will often form perfectly where the first one cracked. On a part with bends in two directions you cannot always win, which is when a larger radius on the awkward one is the cheapest fix available.
How much should I overbend for springback?
It depends on the radius as much as the material: springback rises with the ratio of radius to thickness, and with the ratio of yield strength to elastic modulus. That is why 6061-T6 recovers several times as much as mild steel and annealed copper barely moves at all. The figure here comes from the standard elastic-recovery model, which understates anything that work-hardens while forming — 304 and 316 stainless most of all — so use it as a starting overbend and measure a test piece.
What is the most reliable way to get a flat pattern right?
Bend a test piece in the actual material on the actual machine, measure the flanges that came out, and back-calculate the K-factor from the difference. One measurement beats any chart, including this one, because every brake has its own tooling wear, its own crowning and its own habits. Once you have a measured K for a given material, thickness and die, it is good for every part you run that way.
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