Formula and method
With θ the angle bent from flat: BA = (πθ/180)(R + KT); OSSB = (R + T)tan(θ/2); BD = 2OSSB − BA. For an inside included angle, θ = 180° − α. All lengths are in mm; trigonometric evaluation converts degrees to radians.
Worked example
For thickness 2 mm, inside radius 2 mm, a 90° bend from flat and K = 0.42: BA ≈ 4.461 mm, OSSB = 4 mm and BD ≈ 3.539 mm.
Assumptions and limits
- The angle must be strictly between 0° and 180°; 90° is a right-angle bend. Closed hems, rolled shapes and multiple bends are outside this model.
- Here K is neutral-axis depth from the inside face divided by thickness, accepted from 0 to 0.5. Do not directly enter the doubled coefficient used by some DIN tables. The default 0.42 is an example only.
- OSSB and BD use outside dimensions to the virtual sharp formed by extending the outer faces. For outside legs A and B, flat length = A + B − BD. For straight lengths to bend tangencies, use a + b + BA; do not mix the conventions.
- Use finished radius and angle after springback, with K calibrated by trial bends for the same sheet, tools, direction and machine. Minimum bend radius, cracking, springback, tonnage and manufacturability are not checked; zero inside radius is a geometric limit only.
Frequently asked questions
How do BA and BD differ?
BA is the neutral-axis arc through the bend and joins straight lengths measured to tangencies. BD is subtracted from the sum of outside dimensions to the virtual sharp. They are not interchangeable.
How do I enter a 120° inside included angle?
Select inside included angle and enter 120; the tool uses a 60° bend from flat. In angle-bent mode, enter 60 directly.
Can material name alone determine K?
No. Thickness, radius, tooling and bending process affect the result. Use manufacturer-approved data or measured trial parts rather than treating the example K as universal.