About bend allowance
When a flat sheet of metal is bent, the material on the outside of the bend stretches and the material on the inside compresses. Somewhere between those two surfaces sits the neutral axis — a layer that neither stretches nor compresses, and whose length stays the same before and after the bend. Bend allowance (BA) is the arc length of that neutral axis through the bend, and it is the extra length of flat material a bend consumes. Fabricators add it to flange lengths when laying out a flat pattern so the finished, bent part comes out to the correct dimensions.
The formula
The standard bend allowance formula is:
BA = A × (π/180) × (R + K × T)
- A — the bend angle in degrees (the angle through which the sheet is bent, e.g. 90° for a right-angle bracket)
- R — the inside bend radius, in the same length unit as the output (this calculator uses millimeters)
- T — the material thickness
- K — the K-factor, the fraction of the thickness (measured from the inside surface) at which the neutral axis sits
The term (R + K×T) is the radius of the neutral axis itself, and A × (π/180) converts the bend angle to radians so the result is a true arc length. Multiplying an angle in radians by a radius always gives an arc length — that is the whole formula in one sentence.
K-factor, setback, and bend deduction
The K-factor is not a universal constant — it depends on the material, the bend radius-to-thickness ratio, and whether the part is air-bent, bottom-bent, or coined. Softer materials and larger radii push the neutral axis closer to the inside surface (lower K, around 0.33); harder materials and tighter radii push it closer to the middle (higher K, up to about 0.5). A K-factor of 0.446 is a widely used default for air-formed bends in mild steel when no better data is available.
Two related quantities help translate a bend allowance into a full flat-pattern layout. Setback is the distance from the bend's apex to the tangent point of the bend, measured along each flange: SB = (R + T) × tan(A/2). Bend deduction (BD) is what you subtract from flange lengths measured to the outside corners of a part, rather than adding bend allowance to flange lengths measured to the inside mold line: BD = 2 × SB − BA. Both are computed alongside the bend allowance above so you can work from whichever flange dimensions you already have.
Assumptions and limits
This formula assumes a single, uniform circular bend (not a series of small bends approximating a curve), a constant K-factor across the bend, and consistent units for R and T. It does not account for springback (the tendency of metal to relax slightly after the bending force is removed), which is a separate, material- and tooling-dependent correction fabricators add on top of the geometric bend allowance. For critical or high-volume work, verify the K-factor against a test bend or your press brake manufacturer's bend charts.