Definitions before dimensions
Give each bend quantity its own job.
A bend allowance, a bend deduction and an outside leg are different measurements. The ideal flat-length equation works only when those definitions agree.
Bendnote models one constant-radius, constant-thickness bend in a plane. You enter two outside legs, an assumed final inside radius, thickness, a dimensionless K-factor and a direction change from flat. The tool is useful for checking the arithmetic of a stated drawing model. It does not choose a process, infer a material factor or generate machine instructions.
Start at the virtual sharp
Extend the two outer straight faces until their tangent lines meet. Their intersection is the virtual sharp, labelled V in the schematic. Outside leg A runs from one free end to V. Outside leg B runs from the other free end to that same V. Neither measurement stops at the curved part's tangent point. Neither is automatically an overall width or height of the finished part's bounding box.
The two outside leg dimensions overlap the region replaced by the bend. Setback SB is the distance from V to each outer tangent point, along its outer face. Subtracting SB from A and B leaves the two straight tangent legs. A negative result means that the supplied leg is too short for this geometric definition. Bendnote rejects that input rather than hiding it with a rounded zero.
Describe the angle consistently
The input angle θ is the change in direction from a flat sheet. A right-angle turn is 90°. The angle between the two legs at the opening is 180° − θ. A 45° direction change therefore corresponds to a 135° opening. This tool shows that opening for clarity, but it does not use a second angle-entry mode.
The supported direction change is 1° through 90°. Foldback shapes, hems, rolled forms and multiple bends are outside this one-bend model. Do not enter a 135° opening as a 135° bend direction change; it exceeds this calculator's scope and has a different meaning.
Place the assumed neutral axis
The inside radius R is measured from the centre of the bend to its inner face. Thickness t separates that inner face from the outer face. The outer radius is R + t. In the entered linear model, K places the neutral axis a distance Kt from the inner face. Its radius is R + Kt. K has no unit and is entered between 0 and 1.
The example value 0.4 is illustrative. It is not selected for your material, thickness, tooling or machine. A real forming process may need measured calibration or a different model. Specifying a factor in this calculator does not establish that the neutral axis actually follows it.
Follow the allowance, setback and deduction
The bend allowance BA is the neutral-axis arc length: θ × π / 180 × (R + Kt). It is the curved contribution to the model's developed length. The outside setback is (R + t) × tan(θ / 2), with the trigonometric angle converted to radians internally. At exactly 90°, the setback simplifies to R + t, and Bendnote keeps that special case exact from the entered rational values.
The bend deduction is BD = 2SB − BA. It adjusts the sum of the two outside legs to the developed length. Calling BD the allowance would reverse the meaning of the adjustment. Bendnote displays both quantities and keeps their labels in local exports.
There are two consistent routes to the same conditional flat length. First, add the two straight tangent lengths and the allowance: (A − SB) + (B − SB) + BA. Alternatively, subtract the deduction from the outside sum: A + B − BD. Both use the same input assumptions.
A 90° example
Enter A = 30 mm, B = 40 mm, R = 2 mm, t = 1 mm, K = 0.4 and θ = 90°. The neutral radius is 2 + 0.4 × 1 = 2.4 mm. The setback is exactly R + t = 3 mm. The straight legs are therefore 27 and 37 mm.
The allowance is (π / 2) × 2.4 = 1.2π ≈ 3.769911 mm. The deduction is 6 − 1.2π ≈ 2.230089 mm. The ideal flat length is 27 + 37 + 1.2π ≈ 67.769911 mm. The outside-leg route gives 30 + 40 − 2.230089, the same rounded result.
Change only the direction to 45°
Keep the same lengths and K, then enter θ = 45°. The opening is 135°. The setback is 3 × tan(22.5°) = 3(√2 − 1) ≈ 1.242641 mm. The allowance is 0.6π ≈ 1.884956 mm.
The straight lengths are approximately 28.757359 and 38.757359 mm. The deduction is approximately 0.600326 mm. Adding the straight lengths and allowance gives approximately 69.399674 mm, matching 70 minus the deduction. This is a different geometric turn with the same entered neutral-axis assumption.
Boundary states do not certify a part
At 90°, A = R + t produces one zero straight tangent leg. That is mathematically allowed by this model. The result includes a note because it does not demonstrate that a physical part can be made or supported by tooling. A leg below the unrounded setback is rejected. Radius zero with K zero is also rejected because the assumed neutral-axis radius would be zero; radius zero with positive K can remain within the stated mathematical scope.
Software bounds keep the calculation domain explicit. A, B and R are no greater than 1,000,000 mm equivalent. Thickness ranges from 0.000001 through 10,000 mm equivalent. Those limits do not identify acceptable material dimensions or process capabilities. Invalid, missing, nonfinite or exponent-form text clears the result and schematic and disables exports.
Keep exact inputs separate from rounded outputs
The input accepts plain decimals with at most 12 fractional places. Physical lengths are stored as exact rational millimetre values, with an international inch equal to exactly 25.4 mm. Switching between millimetres and inches retains those values. Visible conversion text may round to 12 places; it is not reinterpreted until you edit that individual field.
π and tangent results are numerical approximations. Displayed outputs round to six decimal places in the selected unit. Small positive values may consequently appear as approximately zero. Six decimal places describe display precision, not a manufacturing tolerance or a measurement resolution. The text and CSV reports retain the original exact canonical inputs and the definitions used to produce the numerical outputs.
Read the schematic as an explanation
The illustration follows the entered angle, marks the outer tangent points T1 and T2, distinguishes the virtual sharp V and shows an illustrative neutral arc. Its other proportions are exaggerated to make the definitions visible. It is not a scaled drawing or a cutting template. Use the numerical inputs and output definitions for your model rather than measuring pixels from the screen.
What remains outside the model
The tool does not model springback, material grade, tooling, tonnage, collision, bend relief, corner features, variable thickness, thermal effects or process tolerances. It provides no strength, safety, fit or standards assessment and no promise of a suitable shop blank. A different unfolding method may be needed when a linear K assumption does not match the actual process.
References
Official Autodesk documentation defines the linear neutral-axis allowance model and radius and K-factor parameters. Its bend-table context explains why measured process behaviour can matter. NIST provides the exact inch conversion. The setback geometry, worked examples, illustration, interface and implementation here are original.