K-Factor Calculator uses $BA=A_{rad}(R+K\times T)$ to find sheet metal bend allowance, bend deduction, setbacks, neutral axis depth, and radius from thickness, inside radius, angle, and K-factor.
What the K-Factor Means in Sheet Metal Bending
When sheet metal bends, the material on the inside of the bend compresses and the material on the outside stretches. Somewhere through the thickness there is a layer that neither compresses nor elongates — this is the neutral axis. The K-factor is the ratio that locates that neutral axis as a proportion of the total material thickness.
A K-factor of 0.50 places the neutral axis exactly at mid-thickness. A lower K-factor, such as 0.33, shifts the neutral axis closer to the inside of the bend, which is typical of air-bending softer materials or tight-radius bends. Higher K-factors, approaching 0.50 or above, indicate the neutral axis has moved outward and are associated with bottoming, coining, or stiffer material grades.
Typical published K-factor ranges are approximately 0.33–0.50 for most sheet metal applications, but the actual value depends on material type and temper, inside bend radius relative to thickness, bending method (air bending, bottoming, coining), tooling geometry, grain direction, and how a specific shop's press brake and tooling perform in practice. No calculator can determine K-factor for you — it must be sourced from material data, CAD system defaults, tooling manufacturer data, or shop-calibrated test bends.
Sheet Metal Bend Formulas Used in This Calculator
BABend AllowanceBDBend DeductionOSSBOutside SetbackISSBInside SetbackTMaterial ThicknessRInside Bend RadiusKApplied K-FactorABend Angle (degrees)A_radBend Angle in radiansBend Allowance (BA)
Bend allowance is the arc length along the neutral axis through the bend zone. It represents how much flat material is consumed by the bend itself. BA is added to the two flat leg lengths to get the total flat pattern length. The formula converts the bend angle to radians and multiplies by the neutral-axis radius \( R + K \times T \).
Bend Deduction (BD)
Bend deduction is the shortcut value used in flat layout when working from outside flange dimensions. It equals the total outside setback (both legs) minus the bend allowance. In practice: Flat Length = Leg A + Leg B − BD, where leg dimensions are measured to the outside of the bend.
Outside Setback (OSSB) and Inside Setback (ISSB)
Setback is the distance from the start of the bend arc to the theoretical sharp outside (or inside) corner. OSSB uses the outside mold line radius \( R + T \); ISSB uses the inside radius \( R \) alone. For a 90° bend, \( \tan(45°) = 1 \), so both setback values equal their respective radii — a useful sanity check.
Neutral Axis Depth, Radius, and Y-Factor
The neutral axis depth is the physical distance from the inside surface of the bend to the neutral layer. The neutral axis radius is what the bend allowance formula actually uses. The Y-factor is a conversion of K-factor used in some CAD systems and older bend-table methods — it is mathematically equivalent to K-factor for the same bend allowance result.
Calculator Inputs Explained
Measurement System
Switch between US Customary (inches) and Metric (millimetres). All dimensional inputs and outputs update to the selected unit. K-factor and bend angle are dimensionless and do not change between unit systems.
Material Thickness (T)
The nominal material thickness of the flat sheet. For sheet metal, use the actual measured thickness from the material cert or a micrometer reading rather than a nominal gauge, since gauge-to-decimal conversions vary by standard and material type.
Inside Bend Radius (R)
The radius of the inner curved surface of the bend, measured from the bend centre to the inside of the material. This is normally set by the punch tip radius and the die opening in air bending, or by the tooling geometry in bottoming and coining.
Bend Angle
The included angle of the bend in degrees — not the complementary angle. A standard 90° press brake bend produces a 90° bend angle. Values must be greater than 0° and less than 180°. The calculator converts the entered degree value to radians internally for all arc-length formulas.
Applied K-Factor
The ratio locating the neutral axis, entered by the user. This calculator requires a known K-factor — it does not derive one. Source your K-factor from the material supplier's bend data, your CAD system's sheet metal defaults, the tooling manufacturer's tables, or test-bend calibration data. Valid range is above 0 and below 1.0.
Understanding the Calculator Results
The four main output cards mirror the calculator display. The explanations below describe each result, what it is used for, and what the sub-values in each card represent.
Bend deduction is the dimension subtracted from the sum of two outside flange measurements to get the flat pattern length. It is the result most commonly used when programming a press brake from outside-dimension drawings. The sub-rows show the total setback (both legs combined) and the BA that was subtracted from it.
OSSB is the distance from the bend tangent line to the theoretical sharp outside corner. It is used in bend deduction and setback-based flat layout methods. ISSB is the corresponding value at the inside surface. For the default 90° bend, the tangent of half the angle is exactly 1.00, which is why OSSB numerically equals \( R + T = 0.125 + 0.125 = 0.25 \) in.
The neutral axis depth is the physical location within the material cross-section that experiences zero strain during bending. With K = 0.44 and T = 0.125 in, it sits 0.06 in from the inside surface — slightly below mid-thickness at 0.0625 in, hence the offset of 0.01 in. The Y-factor (0.69) is the equivalent ratio used in bend allowance tables that express neutral-axis location in Y-factor terms rather than K-factor terms.
The neutral axis radius \( R + (K \times T) \) is the exact radius the bend allowance formula uses. For the default example: \( 0.125 + (0.44 \times 0.125) = 0.180 \) in. The Radius / Thickness severity ratio of 1.00 means the inside bend radius equals the material thickness — a moderately tight bend. Ratios below 1.00 indicate tight bends that risk outer-face cracking and should be confirmed against material minimum bend radius specifications.
Worked Example — Default Calculator Values
The following example uses the pre-loaded default inputs. All values match the calculator's output exactly.
| Parameter | Symbol | Value |
|---|---|---|
| Material Thickness | T | 0.125 in |
| Inside Bend Radius | R | 0.125 in |
| Bend Angle | A | 90° |
| Applied K-Factor | K | 0.44 |
Step 1 — Convert angle to radians: \( A_{rad} = 90 \times \pi / 180 = 1.5708 \) rad.
Step 2 — Bend Allowance: \( BA = 1.5708 \times (0.125 + 0.44 \times 0.125) = 1.5708 \times 0.180 = 0.28 \) in.
Step 3 — Setbacks: \( \tan(45°) = 1.00 \). \( OSSB = (0.125 + 0.125) \times 1.00 = 0.25 \) in. \( ISSB = 0.125 \times 1.00 = 0.13 \) in (rounded from 0.125).
Step 4 — Bend Deduction: \( BD = 2 \times 0.25 - 0.28 = 0.50 - 0.28 = 0.22 \) in.
Step 5 — Neutral Axis: Depth \( = 0.44 \times 0.125 = 0.055 \approx 0.06 \) in. Radius \( = 0.125 + 0.055 = 0.18 \) in. Severity \( = 0.125 / 0.125 = 1.00 \).
| Output | Result |
|---|---|
| Bend Allowance (BA) | 0.28 in |
| Bend Deduction (BD) | 0.22 in |
| Outside Setback (OSSB) | 0.25 in |
| Inside Setback (ISSB) | 0.13 in |
| Neutral Axis Depth | 0.06 in |
| Neutral Axis Radius | 0.18 in |
| Radius / Thickness | 1.00 |
When to Use This Sheet Metal K-Factor Calculator
Assumptions and Limitations
- This calculator requires a known, user-supplied K-factor. It does not reverse-calculate or derive K-factor from flat length measurements, test coupons, or finished part dimensions.
- The calculator does not account for material-specific springback. Press brake operators must apply overbend compensation separately based on material and tooling behaviour.
- The calculator does not select or recommend die opening, punch tip radius, punch angle, or any tooling parameter.
- K-factors above 0.50 are atypical for standard air bending. Results in this range should be treated with caution and verified against measured shop data or tooling manufacturer specifications.
- A Radius / Thickness ratio below 1.00 indicates a tight bend and raises risk of cracking on the outer face of the material. Confirm minimum bend radius against the material certificate or supplier's forming data sheet before proceeding.
- All formulas assume a simple single-radius bend. Complex multi-radius or curved forms are outside the scope of this calculator.
References
- Oberg, E., Jones, F. D., Horton, H. L., and Ryffel, H. H. Machinery's Handbook. Industrial Press. Sheet metal and plate bending — bend allowance, bend deduction, and setback formulas. Multiple editions. industrialpress.com
- Autodesk. Sheet metal K-factor and bend allowance in Autodesk Inventor. help.autodesk.com — Inventor Sheet Metal
- Dassault Systèmes. SOLIDWORKS sheet metal — K-factor and bend allowance documentation. help.solidworks.com — Sheet Metal K-Factor
- Protolabs. Sheet metal design guide: bend radius, K-factor, and flat pattern considerations. protolabs.com — Sheet Metal Design Guide
- The Fabricator. Understanding the K-factor in sheet metal bending. thefabricator.com — Understanding the K-Factor
- The Fabricator. Bend allowance and bend deduction: the two most confused terms in sheet metal. thefabricator.com — Bend Allowance and Bend Deduction