What this calculator does
When sheet metal is bent, the outside stretches and the inside compresses, so the flat blank is not simply the sum of the finished legs. The bend allowance is the length the bend itself contributes, and for a 90 degree bend at 3 mm radius in 2 mm material with a K-factor of 0.44 it is 6.09 mm.
The K-factor locates the neutral axis, the layer that neither stretches nor compresses. It sits below the middle of the material, typically between 0.33 and 0.50 of the thickness from the inside face, and it depends on the material, the tooling and the radius. Getting it wrong is what makes a first article come out the wrong size.
The formula
The bend allowance is the bend angle in radians multiplied by the inside radius plus the K-factor times the thickness. That expression is the arc length of the neutral axis through the bend. The flat pattern is the sum of the flat legs plus the bend allowance for each bend.
| Term | Meaning |
|---|---|
| Bend allowance | The neutral axis arc length through the bend, added to the flat legs. |
| K-factor | Where the neutral axis sits, as a fraction of thickness from the inside face. |
| Neutral axis | The layer that neither stretches nor compresses during bending. |
| Bend deduction | An alternative convention subtracting from the outside dimensions rather than adding to the legs. |
The inputs explained
| Field | What to enter |
|---|---|
| Bend angle (°) | Bend angle in degrees, measured as the angle swept rather than the included angle. |
| Inside bend radius (mm) | Inside bend radius in millimetres, which is set by the tooling. |
| Material thickness (mm) | Material thickness. |
| K-factor | K-factor. 0.44 is a common default for mild steel; confirm it against a test bend for production work. |
When to use it
Developing a flat pattern
The blank size must account for what the bends consume, or the finished part is wrong.
Diagnosing an out-of-size part
A part consistently wrong by the same amount usually means the K-factor is off.
Changing material or tooling
Both affect the K-factor, so a proven pattern does not transfer unchanged.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does the bend angle change the allowance?
The same bend geometry across a range of angles.
| Bend angle | Bend allowance | Neutral axis offset from inside face | Outside radius |
|---|---|---|---|
| 45° | 3.05 mm | 0.88 mm | 5.00 mm |
| 90° | 6.09 mm | 0.88 mm | 5.00 mm |
| 135° | 9.14 mm | 0.88 mm | 5.00 mm |
| 180° | 12.19 mm | 0.88 mm | 5.00 mm |
Questions
What K-factor should I use?
0.44 is a reasonable default for mild steel bent with standard tooling, and values from 0.33 to 0.50 cover most situations. For production work, bend a test piece, measure the result and back-calculate the actual K-factor, since it depends on material, tooling and radius.
Why is the neutral axis not in the middle?
Because the material compresses more readily than it stretches, so the layer of zero strain shifts toward the inside of the bend. A K-factor of 0.5 would put it exactly in the middle, and real values are usually below that.
What is the difference between bend allowance and bend deduction?
Two conventions for the same correction. Bend allowance is added to the flat leg lengths measured to the bend tangent. Bend deduction is subtracted from the sum of the outside dimensions. Both give the same blank; mixing them gives a part that is wrong by roughly twice the error.
Does a tighter radius change things?
Yes, substantially. A tighter inside radius relative to thickness shifts the neutral axis further inward, lowering the K-factor, and increases the risk of cracking on the outside. A common minimum is an inside radius equal to the material thickness, though it varies by alloy and temper.
For punching forces, see the punch force calculator. For material weight, see the metal weight calculator.