When sheet metal bends, the outer surface stretches (tension) and the inner surface compresses. Somewhere between them is a zone that neither stretches nor compresses — the neutral axis. In theory it's at the exact center of the material. In practice it shifts inward because the compression zone (inside the bend) is constrained by the die and work-hardens, while the tension zone (outside) is less constrained and elongates more freely. The K-Factor (0 to 0.5) represents how far the neutral axis has shifted from the inner surface as a fraction of material thickness. K = 0 means the neutral axis is at the inner surface (all stretch, no compression — physically impossible). K = 0.5 means it's at the centerline (theoretical pure geometry). Real parts fall between 0.33 and 0.50, with tight radii pushing K lower and large radii pushing K toward 0.5.

Bend Allowance (BA) is the arc length of the bent region at the neutral axis — the material consumed by the bend. Flat length = Flange 1 + BA + Flange 2 (where flanges are measured from the tangent point of the bend, not the outside corner). Bend Deduction (BD) is a legacy shorthand used by older machining references that lets you work from outside corner dimensions: Flat length = Outside Dimension 1 + Outside Dimension 2 − BD. They describe the same bend but from different reference geometry. BD = 2 × (R + T) × tan(A/2) − BA. Most modern CAD systems use BA internally because it's geometrically cleaner. If your shop uses BD, convert: BD = OSSB × 2 − BA (where OSSB = outside setback). When in doubt, always verify against a first-article sample, regardless of which method your software uses.

Four causes account for >90% of first-run length errors: 1) Wrong K-Factor — the biggest variable. If the part is consistently too long or too short by a fixed amount at each bend, your K-Factor is wrong. Measure the error, divide by the number of bends, and adjust K until the formula matches your tooling reality. 2) Wrong thickness — using gauge nominal instead of micrometer-measured actual. 3) Wrong inside radius — using the punch tip radius as R when the actual formed inside radius may be larger (air bending result depends on die width, not just punch geometry). For air bending: actual inside radius ≈ 0.16 × die width [this is the Wuertz rule]. 4) Springback — the bend angle changed after the punch retracted, altering the geometry. Measure the actual final angle, not the programmed punch position, before diagnosing BA calculation errors.

Air bending uses only three points of contact (punch tip and two die edges) — the material floats freely over the die opening. The inside radius is set by the material's natural springback behavior and the die width, not by the punch radius. K-Factor typically 0.44–0.50 depending on die width ratio. Significant springback — you must overbend. Bottom bending drives the punch toward the die bottom until the material conforms more closely to the punch geometry, reducing springback. K-Factor typically 0.38–0.44. Requires 3–5× the tonnage of air bending. Coining drives the punch into the die under extreme pressure, fully plastically deforming the material at the bend zone — essentially zero springback. K-Factor approaches 0.30–0.38. Requires 5–10× the tonnage of air bending but produces repeatable, springback-free angles. Most production press brake work is air bending, and all modern press brake controllers use air bending K-Factor tables by default.