K-Factor Calculator for Sheet Metal

Estimate sheet metal K-factor from material thickness, inside bend radius, and material type. Returns K-factor, R/T ratio, neutral axis location, and material category.

Mild steel base K

0.40

Soft aluminum base K

0.33

Stainless 304 base K

0.45

Output clamp

0.25–0.50

Units Switches thickness and radius inputs

Material thickness T (mm) Sheet nominal thickness

Inside bend radius R (mm) Punch tip or specified inside radius

Material type Sets the base K-factor

K-factor

0.409

Mild steel, R/T = 1.50

R/T ratio

1.50

Neutral axis location

0.818mm

Material category

Medium

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Tip This model is a first-pass estimate. Cut a test coupon on your production brake, measure the finished part, and back-solve K. The empirical value becomes your shop standard for that material–tooling combination.

Worked example

T = 2 mm, R = 3 mm, mild steel (base K = 0.40).

1. R/T ratio R/T = 3 / 2 = 1.50 2. Adjustment term adj = log10(max(R/T, 0.1)) × 0.05 adj = log10(1.50) × 0.05 adj = 0.176 × 0.05 ≈ 0.0088 3. Clamp to practical range K = clamp(0.40 + 0.0088, 0.25, 0.50) K ≈ 0.409 4. Neutral axis location offset = K × T = 0.409 × 2 offset = 0.818 mm from inside face

Where K-factor comes from

K-factor is the ratio (distance from the inner surface to the neutral axis) divided by sheet thickness. In a tight bend (R/T < 1), the inner fibers compress and the outer fibers stretch heavily — the neutral axis migrates inward and K is small (≈ 0.33). As R/T grows, the strain field becomes more symmetric and the neutral axis moves outward toward the geometric centerline; K approaches 0.5 in the limit. This is why K depends on R/T rather than absolute size: a 1 mm bend on 1 mm sheet behaves the same as a 10 mm bend on 10 mm sheet. For soft-tooled mild steel air bending, K is clamped to the 0.33–0.45 band — the upper bound 0.5 is a theoretical ceiling that air bending never reaches.

Why K-factor scales with R/T K-factor is the ratio of the neutral-axis location to the material thickness. As inside bend radius R approaches the thickness T, the neutral axis shifts outward (away from the inside of the bend) because compression on the inner fiber is bounded by yield — the inner fiber cannot keep accepting strain once it goes plastic in compression, so additional bend strain is absorbed by the outer fiber in tension and the neutral axis migrates with it. Empirically the relationship is roughly logarithmic in R/T over the working range R/T = 0.5 to 5. For sharp bends (R/T < 0.5) the metal cracks before the neutral-axis model holds; for gentle bends (R/T > 5) K asymptotes near 0.5 (true neutral axis at mid-thickness).

Typical-K reference (cross-check) Compare the calculator output against published bend-test data:

R/T	Soft (annealed)	Medium	Hard (cold-rolled)
0.5	0.33	0.33	0.38
1.0	0.38	0.41	0.43
2.0	0.42	0.44	0.45
3.0+	0.45	0.46	0.47

Source: Protocase Bend Allowance Guide (2023) and Wilson Tool published bend-test data.

K vs R/T cross-check (soft-tooled mild steel)

R/T ratio	Typical K	Neutral-axis behavior
R/T < 1.0	≈ 0.33	Tight bend; neutral axis pulled toward inner face by compressive strain.
R/T 1.0–3.0	≈ 0.40	Standard air-bend window; neutral axis between inner third and centerline.
R/T > 3.0	≈ 0.45	Generous radius; neutral axis approaches geometric centerline (K → 0.5 limit).

Piecewise values from Protocase and Wilson Tool published design guides for soft-tooled air bending. Use as a sanity check against the calculator above.

K-factor reference by material

Material	Soft (R < T)	Medium (R ~ T–3T)	Hard (R > 3T)
Aluminum 1100	0.32	0.36	0.42
Aluminum 5052	0.33	0.38	0.44
Aluminum 6061	0.36	0.41	0.46
Mild Steel	0.35	0.40	0.46
Stainless 304	0.38	0.43	0.48
Copper	0.32	0.37	0.43
Brass	0.33	0.38	0.44
Titanium	0.39	0.44	0.49

Full tooling-method breakdown (air bend / bottoming / coining) in the K-factor reference.

Common mistakes

Treating K as a material constant. K changes with R/T, tooling (V-die opening), and bending method. It is empirical, not physical.
Using K = 0.50 by default. K = 0.5 is the upper theoretical bound (neutral axis at mid-thickness). Air-bent sheet almost never reaches it.
Parallel-to-grain bends. Cracking risk increases and K shifts. For minimum-radius bends, align the bend transverse to the rolling direction.
Forgetting the die opening. The "8× rule" says achievable inside radius ≈ 0.16 × V-die width for mild steel. Picking R on paper that the die cannot produce wastes K-factor math.

Warn The same 0.090" mild steel on two press brakes with different V-dies can yield K values 0.03 apart — on a 12" blank that is 0.030" of flat-pattern error. Calibrate with test coupons for any tolerance ≤ ±0.010".

FAQ

What is K-factor in sheet metal?

The fractional position of the neutral axis through sheet thickness during bending, measured from the inside face. It lets you convert a real bend geometry into a flat-pattern length.

How is K-factor related to bend allowance?

Directly — BA = (π/180) × angle × (R + K × T). Larger K increases the effective neutral-axis radius and the arc length assigned to the bend.

What is a typical K-factor value?

Air-bent sheet usually falls between 0.33 and 0.46. Bottoming and coining push the value higher (typically 0.40–0.50).

Does K-factor change with bend angle?

Angle has secondary effect. R/T ratio, material temper, and bending method dominate. But if changing angle also changes springback or penetration, the effective K shifts.

How do I measure K-factor empirically?

Cut a coupon of known length, bend on production tooling, measure leg lengths and included angle, and back-solve K until the calculated bend allowance matches the measured flat. Average 3–5 coupons.

Sources

Ind. Press Machinery's Handbook — Sheet Metal Protocase K-Factor design guide Xometry K-Factor Sheet Metal Wilson Tool Press brake tooling references

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