K-factor and bend deduction: sheet metal flat pattern

01 — PremiseThe flat pattern is a question of material physics.

When the sheet passes under the ram and is forced onto the V die, inner fibres compress and outer ones stretch. Somewhere across the thickness there is a line — the neutral axis — that does neither. The actual length of the arc travelled by that line through the curvature determines how much sheet the bend “consumes”. And that is exactly what you need to calculate the flat pattern blank to be cut at laser or shear before bringing it to the press brake.

The K-factor tells you where that neutral axis sits across the thickness. With the right K the flat pattern is correct to the millimetre. With the wrong K — or worse, with the CAD’s default 0.5 left in — the blank comes out too long or too short and the part misses its dimensions.

This page clarifies three things: which K values to use for steel, stainless and aluminium; how to compute bend allowance and bend deduction, the two formulas that translate K into flat pattern; and how to measure your shop’s actual K in five minutes. For V die, internal radius and force there is the PG bending force calculator: here we start from there and handle the next step.

02 — K-factorThe neutral axis, in numbers.

Definition: K = t / s, where t is the distance from the neutral axis to the inner surface of the bend and s is the thickness. K is dimensionless, between 0 and 0.5. If the neutral axis sat at the geometric centre, K would be 0.5; in reality it shifts toward the inside of the curvature, and the more so the tighter the radius compared to the thickness.

Two practical dependencies: K depends on the material (stiffer = higher K) and on the internal-radius / thickness ratio (R/s) — tight bends low K, wide bends K converging to 0.5. The reference table, adopted as standard by the main CAD/CAM systems (SolidWorks, Inventor, Creo, SolidEdge) for air bending which covers 90% of the work:

For mild steel with radius comparable to thickness — the most common case — K ≈ 0.43 is the correct value. For AISI 304/316 stainless K rises to 0.45 because the material is stiffer; for 5754 or 6082 aluminium it drops to 0.40 because it is more malleable. On tight bends (R smaller than thickness) all values fall by 4-5 hundredths; on wide radii (R over three times thickness) geometry takes over and K converges to 0.50 regardless of material. For coined bends (bottoming/coining) values rise by 0.02-0.06 points because coining symmetrically “crushes” the material and the neutral axis moves back toward the centre.

03 — Bend allowance and bend deductionTwo formulas, the same flat pattern.

Given K, the flat pattern can be computed in two equivalent ways. The CAD designer prefers one, the cutting department prefers the other.

Bend allowance (BA) — the actual arc length of the neutral axis:

BA = (π / 180) × α × (R + K × s)

α is the internal bend angle in degrees (90° for an L). Flat pattern = sum of legs measured to the tangent point with the radius + BA for each bend.

Bend deduction (BD) — the amount to subtract from the sum of outer legs (theoretical sharp corner):

BD = 2 × (R + s) × tan(α/2) − BA

Flat pattern = sum of outer legs − BD for each bend. BD is the shop-floor logic: you read the corner-to-corner dimension on the drawing and subtract the tabulated value. For a 90° bend on mild steel with R = s, BD is approximately 1.75 times the thickness — calculated from BD = 4·s − (π/2)·(1 + K)·s with K = 0.43. The old “rule of thumb” still circulating in shops (1.6×s) actually applies only for K = 0.5, typical of wide radii (R > 3s); on standard radius R = s the correct value is 1.7-1.75×s. The two formulas give the same flat pattern if K is correct: useful as a cross check.

04 — Three worked examplesSteel 90°, stainless 45°, aluminium 135°.

Case 1 — Mild steel S235, 90° bend. 3 mm sheet, L-bracket with outer legs 80 and 60 mm. V24 from the PG calculator, induced internal R ≈ 4 mm, R/s = 1.3, K = 0.43.
BA = (π/180) × 90 × (4 + 0.43 × 3) = 1.5708 × 5.29 ≈ 8.31 mm.
BD = 2 × (4 + 3) × tan(45°) − 8.31 = 14 − 8.31 = 5.69 mm.
Flat pattern = 80 + 60 − 5.69 = 134.31 mm. Cut at 134.3, bend at 90° with V24 and the legs come out clean at 80 and 60 mm.

Case 2 — AISI 304 stainless, 45° bend. 2 mm sheet, outer legs 60 and 40 mm. V16, R ≈ 3 mm, R/s = 1.5, K = 0.45.
BA = (π/180) × 45 × (3 + 0.45 × 2) = 0.7854 × 3.9 ≈ 3.06 mm.
BD = 2 × (3 + 2) × tan(22.5°) − 3.06 = 4.14 − 3.06 = 1.08 mm.
Flat pattern = 60 + 40 − 1.08 = 98.92 mm. A 45° bend “consumes” very little material: short arc, minimal BD.

Case 3 — 5754 aluminium, 135° bend. 4 mm thick. V32, R ≈ 5 mm, R/s = 1.25, K = 0.40.
BA = (π/180) × 135 × (5 + 0.40 × 4) = 2.3562 × 6.6 ≈ 15.55 mm.
BD = 2 × (5 + 4) × tan(67.5°) − 15.55 = 43.46 − 15.55 = 27.91 mm.
On obtuse bends — angles greater than 90° — BD grows quickly and in some combinations becomes negative: the blank is longer than the sum of the outer legs, not shorter. Never apply the “1.75×s rule” to angles other than 90° — it is valid as an approximation only for 90° bends on mild steel with R ≈ s.

05 — When K changes and how to actually measure it.

Three regimes to keep in mind. R smaller than thickness (thin sheet metal roofing, sharp bends): neutral axis sinks, K low 0.33-0.40. R comparable to thickness (everyday fabrication, from the DCA hydraulic to the electric machines): K 0.40-0.45. R over three times the thickness (soft radii, body panels): K → 0.5 for any material. Changing V die without updating K in the CAM means accepting flat pattern errors of 1-3 mm, enough to scrap a tight-tolerance part.

For ±0.5 mm tolerances on the blanks the values in §2 are enough. For tighter tolerances — multi-bend parts with critical dimensions, non-standard materials, large batches — you measure the actual K. Procedure: 100 mm flat blank, 90° bend with the production V and tools, callipers on the two outer legs. The sum minus 100 gives the empirical BD; reversing the §3 formula gives the K. You enter it in the CAM and from that moment the flat pattern is exact for that material/thickness/V combination. Five minutes that bypass any uncertainty on batch, tool wear and machine calibration. On the PG roofing line — long profiles, thin sheet, K always around 0.33-0.38 — an empirical K updated every two or three batches eliminates most of the first-piece scrap.

06 — Next stepsFrom K-factor to finished part.

07 — FAQQuick answers to recurring questions.