Bend allowance is the developed length of the neutral axis through a bend. It converts bend angle, inside radius, material thickness, and K-factor into the arc length that belongs in a flat-pattern calculation.
BA = (π ÷ 180) × A × (R + K × T)
A = bend angle in degrees · R = inside radius · T = thickness · K = neutral-axis ratio.
Bend allowance formula
The radius of the neutral axis is R + K × T. Multiplying that radius by the bend angle in radians produces its arc length. The formula works in millimeters or inches as long as radius and thickness share the same unit.
Worked 90-degree example
For thickness 2.0 mm, inside radius 2.0 mm, bend angle 90°, and K-factor 0.40:
- Neutral-axis radius:
2.0 + 0.40 × 2.0 = 2.8 mm. - Angle in radians:
90 × π ÷ 180 = 1.5708. - Bend allowance:
1.5708 × 2.8 = 4.398 mm.
| Variable | Example |
|---|---|
| Thickness T | 2.0 mm |
| Inside radius R | 2.0 mm |
| K-factor K | 0.40 |
| Angle A | 90° |
| Bend allowance | 4.398 mm |
How bend allowance enters flat length
When flange dimensions are measured to tangent points, flat length is the sum of the straight tangent lengths plus bend allowance. When dimensions are outside mold-line dimensions, bend deduction is usually the more direct workflow. Do not add bend allowance to outside dimensions without first accounting for setbacks.
Why the calculated value is a starting point
K-factor and the achieved inside radius depend on material, grain direction, thickness, tensile properties, punch radius, V-opening, bending method, and tooling condition. A generic table cannot capture every combination. For repeat production, make a controlled test bend, measure the finished part, calculate the observed deduction or allowance, and store the validated value with the exact material and tooling setup.
- Confirm whether the drawing angle is included or bent angle.
- Use the achieved radius, not merely the punch-tip label.
- Keep the K-factor convention between 0 and 0.5 for the standard definition used here.
- Separate air bending, bottoming, and coining data.
- Revalidate after changing V-opening, material batch, temper, or grain direction.
Technical references
Published and formula-checked by MfgWorkbench. Last reviewed September 15, 2026. See our editorial method.
A 120° included angle is a 60° bend
The angle A in the K-factor bend-allowance equation is the angle through which the material bends from flat. For the simple single-bend geometry here, A = 180° − included angle. A right-angle example hides this distinction because both numbers happen to be 90°.
Use an illustrative thickness T = 1.5 mm, inside radius R = 3 mm and K = 0.40. The neutral-axis radius is 3.6 mm. For A = 60°, BA = (π/3) × 3.6 = 3.7699 mm. With straight tangent lengths of 25 mm and 35 mm, flat length = 25 + 35 + 3.7699 = 63.7699 mm.
Entering the 120° included angle directly would instead give BA = 7.5398 mm, overstating this flat length by 3.7699 mm. Check the software’s field definition before concluding that its result disagrees with the formula.
Keep full precision during the calculation and round the final manufacturing dimension according to the drawing. These inputs are mathematical examples, not a tested K-factor. If the drawing supplies outside mold-line legs instead of tangent lengths, use the bend-deduction workflow rather than adding allowance directly.
Content updated October 8, 2026. Sources and numerical examples are explained above; examples are not production test results. Editorial method · Report a correction.