Bend allowance, bend deduction and K-factor explained

What bend allowance and bend deduction actually are

When you lay out a flat blank for a bent part, the bend itself takes up more length on the outside of the bend than on the inside. The metal on the outside stretches, the metal on the inside compresses, and somewhere in between — the neutral axis — the length is unchanged. The flat pattern is the sum of the straight flange lengths plus a correction for that bend.

There are two ways to write that correction, and drawings use both:

• Inside dimensioning — the flanges are measured to the inside corner. Youadd the bend allowance (BA), the length of the neutral-axis arc, to get the flat length.
• Outside dimensioning — the flanges are measured to the outside corner. Yousubtract the bend deduction (BD) from the sum of the outside lengths.

BA and BD are two descriptions of the same physical correction. Pick the one your drawing uses and stay consistent; mixing them on one part is the classic cause of a blank that comes out a few millimetres long or short.

The formulas, and the intuition behind them

Three relationships carry most of the work. Angles are in degrees, lengths in inches, mild steel assumed:

Reading them left to right:

• BA is the arc length of the neutral axis. The term (r + k·t) is the neutral-axis radius — the physical inside radius r plus the neutral-axis offset, which is the K-factor times the thickness t. Multiply that radius by the bend angle in radians and you have the arc length.
• Setback (SB) is how far the bend tangent line sits from the corner. For a 90° bend it is simply r + t.
• BD follows from the geometry: two setbacks (one per leg) minus the arc you are already accounting for gives the total length to remove from the outside dimensions.

The K-factor is doing the heavy lifting inside BA, so the rest of this guide is really about understanding and pinning down K. The same math applies whether you are reading a k factor chart, a sheet metal bend allowance table in a handbook, running the press brake bend allowance formula by hand, or using a sheet metal bending calculator.

The K-factor: what it is and why it moves

K is the ratio of the neutral-axis distance from the inside surface to the total thickness:k = (distance from inside face to neutral axis) / t. In a perfectly symmetric elastic bend the neutral axis sits at the mid-plane, so k = 0.50. But press brake bending is not elastic — the inside of the bend is crushed and the outside is stretched, so the neutral axis shiftstoward the inside. That is why K is almost always below 0.50 in practice.

Where it lands depends mainly on the ratio of bend radius to thickness (r/t) and on the process. A widely used typical table:

Typical industry practice. The real value shifts with material, grain direction, springback and bending method. Verify on your own setup before production.

Worked example: 1/8 in mild steel, 90°, r = 1/8 in

This is the standard teaching case, and the numbers check cleanly. Material thicknesst = 0.125 in, inside radius r = 0.125 in, bend angle θ = 90°. That gives r/t = 1.0, so from the table k = 0.33.

Setback SB = r + t = 0.250 in, and the bend deduction:

Now lay out a simple L-bracket with two 2.000 in flanges and confirm both conventions give the same blank.

Inside dimensioning: flat length = 2.000 + 2.000 + BA = 4.000 + 0.261 =4.261 in.

Outside dimensioning: each outside flange is the inside flange plus the setback, 2.000 + 0.250 = 2.250 in. Flat length = 2.250 + 2.250 − BD = 4.500 − 0.239 =4.261 in.

Same blank, two routes. That is the whole point of BA and BD being interchangeable descriptions of one correction.

Pending input from the factory: KECMT tooling options (punch nose radii and V-die openings) available for small-tonnage machines, so readers can match a bend radius to their K-factor. This is the one place this guide needs factory input.

Air bending vs bottoming: which K to use

The K you pick depends on how the part is formed. In air bending the sheet is not forced flat against the die, so the neutral axis sits further out and K runs higher — typically around 0.33 to 0.43 for mild steel as r/t grows. In bottoming or coining the material is squeezed against the tools, the inside face is compressed more, and the neutral axis shifts inward, so K is smaller, often around 0.25 to 0.33. The same nominal radius can therefore carry different K values depending on the method, and that changes BA.

Rule of thumb: if your drawings are air-bent (the usual case on a CNC hydraulic press brake), use the higher K from the table. If the part is bottomed or coined, drop toward the lower end.

Minimum bend radius

Every material has a radius below which it cracks instead of bending. As a rule of thumb for mild steel, a 1t–2t inside radius is safe for most gauges. The interesting comparisons are aluminium and stainless:

• Aluminium — soft tempers (3003-O, 1100-O, 6061-O) bend extremely tight, sometimes close to 0t. Hardened tempers (6061-T6, 2024-T3) need roughly 1t–2t.
• Stainless (304/316) — less forgiving. Plan on roughly 1t–2t minimum, and more for thicker gauge, because stainless work-hardens and cracks at the outside of the bend.

Grain direction matters as much as the number. Bend perpendicular to the grain(bend line crosses the roll direction) and you get a clean radius. Bend parallel to the grain and stainless, in particular, will crack along the outside. When a drawing says "grain direction" it is not a suggestion.

These are rules of thumb for typical commercial alloys. Check the mill specification for critical parts, and always prove a tight radius on a sample before a production run.

Why every chart on the internet disagrees

If you have compared bend allowance tables, you have seen them diverge by noticeable amounts for the same material and thickness. That is not noise — it is because K is not a material constant. It moves with:

• bending method (air bend, bottoming, coining);
• tooling (punch nose radius, V-die opening, lubrication);
• material (grade, temper, actual thickness, grain);
• how the original table was measured and rounded.

A chart built for bottoming will not match your air-bent part. So the only K that is truly yours is the one you measure on your own press.

Deriving your own K from a test bend

Cut a flat blank of known length L_flat. Bend it once to your real angle and radius. Measure the two finished flange lengths (inside or outside, consistently) — call their sum L_flanges. The neutral-axis arc for inside dimensions is simply:

Then solve the BA formula backwards for k:

Check it against the example above:k = [0.261 × 0.6366 − 0.125] / 0.125 = [0.1661 − 0.125] / 0.125 = 0.33. That is exactly the table value — the table is just someone else's measured K, and now it is yours too.

Put it to work

Once you have a K you trust, the arithmetic is routine — but there is no reason to do it by hand for every part. Our bend allowance calculator runs the formula above for any angle, radius and thickness, and thetonnage calculator tells you whether your press has the force for the bend you are laying out. For matching a bend radius to a specific tool set, thetooling accuracy guide covers what punch noses and V-dies actually give you.

Questions we get asked

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