Bend Allowance Calculator

What the bend allowance calculator does

When you bend a piece of sheet metal, the flat blank you start with is not simply the sum of the finished sides, because the metal stretches and compresses around the bend. This calculator works out the bend allowance and the bend deduction, the corrections you need to cut the flat pattern to the right size, from the bend angle, the inside radius, the material thickness, and the K-factor.

Below is why bending changes the length, what the K-factor captures, the equations behind the answers, and a worked example.

How to use it

1. Enter the bend angle, the inside radius of the bend, and the material thickness.
2. Enter the K-factor, a number between 0 and 1 that locates the neutral axis.
3. Press Calculate for the bend allowance and bend deduction, or Reset to clear it.

Why bending changes the length

Bending sheet metal does something subtle to the material. On the outside of the bend, the metal is stretched and gets a little longer; on the inside, it is squeezed and gets a little shorter. Somewhere in between is a layer that is neither stretched nor compressed, and keeps its original length. Because of this, the total length of metal in the finished part is not the same as adding up the outside dimensions of the flat sides.

If you cut a blank by simply adding the finished leg lengths, the bent part comes out wrong, because that ignores what happens in the curved region. Getting the flat pattern right means accounting for the true length of metal that wraps through the bend, which is exactly what the bend allowance does.

The neutral axis and the K-factor

The layer that keeps its length through the bend is called the neutral axis, and where it sits inside the thickness is the heart of the calculation. It does not stay in the middle. Because the metal resists compression more than stretching, the neutral axis shifts toward the inside of the bend, and how far it shifts depends on the material, the radius, and the angle.

The K-factor is the number that captures this. It is the position of the neutral axis as a fraction of the material thickness, measured from the inside surface, so it runs between 0 and 1 and in practice sits roughly between 0.3 and 0.5. A precise K-factor is what makes a flat pattern come out accurate, and shops often refine it from test bends on their own material and tooling.

The equations it uses

The bend allowance, the length of the neutral axis through the bend, is the bend angle in radians times the radius out to the neutral axis. With the angle θ, inside radius r, thickness T, and K-factor K:

BA = (θ × π ÷ 180) × ( r + K T )

The bend deduction, how much to subtract from the summed outside dimensions, follows from the geometry of the outside setback:

BD = 2 ( r + T ) tan(θ ÷ 2) − BA

Both give a length, in the units you choose. The bend allowance is added to the flat sides to get the blank length; the bend deduction is subtracted from the outside dimensions to the same end.

Bend allowance and bend deduction

The two outputs are two routes to the same flat pattern, suited to how the part is dimensioned. The bend allowance is used when you build up the blank from the flat lengths of the sides plus the metal in the bend: you add the bend allowance for each bend. It is the actual arc of material wrapping through the bend.

The bend deduction is used when you work from the overall outside dimensions of the finished part, the way a drawing is often dimensioned. You add the outside lengths and subtract the bend deduction for each bend to get the blank. Either approach lands on the same blank length when applied correctly, so you use whichever matches the numbers you have in hand.

Units and precision

You can enter the radius and thickness in millimetres, inches, and other length units, and read the results in any of them, with the calculator converting internally. The bend angle can be given in degrees or radians, and is the angle through which the sheet is bent, which cannot exceed 180 degrees. The K-factor is a pure fraction between 0 and 1. Results carry several figures, finer than sheet-metal work usually needs, so round to your tooling's practical tolerance.

A worked example

Take a 90-degree bend with an inside radius of 3 mm in material 2 mm thick, using a K-factor of 0.4.

The bend allowance is (90 × π ÷ 180) × (3 + 0.4 × 2) = 1.571 × 3.8 ≈ 5.97 mm. The bend deduction is 2 × (3 + 2) × tan(45°) − 5.97 = 10 − 5.97 ≈ 4.03 mm. So for this single bend you would add about 5.97 mm of arc to the flat legs, or subtract about 4.03 mm from the outside dimensions, to size the blank.

Questions people ask

What is bend allowance?

It is the length of material that wraps through a bend, measured along the neutral axis. You add it to the flat side lengths to find the size of the flat blank before bending.

What is the K-factor?

It is the position of the neutral axis as a fraction of the material thickness, from the inside of the bend. It usually lies between about 0.3 and 0.5 and is what makes a flat pattern accurate.

What is the difference between bend allowance and bend deduction?

Both correct the flat pattern. Bend allowance is added to the flat side lengths; bend deduction is subtracted from the summed outside dimensions. They give the same blank when used correctly.

Why not just add the side lengths?

Because the metal stretches and compresses around the bend, so the length through the curve is not captured by the outside dimensions. Ignoring it makes the finished part the wrong size.

References

A quick note on where this comes from. The bend allowance and bend deduction formulas, and the role of the neutral axis and K-factor, are standard sheet-metal fabrication, set out by SheetMetal.me and in manufacturing references such as Machinery's Handbook. The SI units follow the US National Institute of Standards and Technology.

1. SheetMetal.me, Bend Allowance and the K-factor. https://sheetmetal.me/tools-and-resources/bend-allowance/
2. Machinery's Handbook, Industrial Press, sheet-metal bending.
3. National Institute of Standards and Technology (NIST), Special Publication 811, Guide for the Use of the International System of Units (SI). https://www.nist.gov/pml/special-publication-811