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Neutral-Axis Bend Allowance and Deduction

Find sheet-metal bend allowance and deduction from angle, inside radius, thickness and K-factor, with consistent degree, radian and length units.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

A 90° bend with inside radius 2 mm, sheet thickness 1 mm and K = 0.4 gives allowance 3.769911184 mm and deduction 2.230088816 mm.

BA = θ(rad)(R + KT); BD = 2(R + T)tan(θ/2) − BA.

Worked example

Enter these known values and leave the other values blank.

Angle bent from flat
90 deg
Finished inside bend radius
2 mm
Sheet thickness
1 mm
Neutral-axis depth / thickness
0.4
Neutral-axis bend allowance
3.77 mm
Outside-dimension bend deduction
2.23 mm

Assumptions and limitations

  • The angle is the amount bent from a flat sheet, not the finished included angle. A flat sheet corresponds to 0° and a right-angle bend to 90°.
  • Allowance is the developed arc length along the neutral axis. Deduction relates the sum of outside flange dimensions to developed length; it is not the allowance itself.
  • K is neutral-axis distance from the inside face divided by sheet thickness. Use a value calibrated for the material and forming setup; this calculation does not predict K.
  • Inside radius and thickness must be positive. The retained geometric domain uses 0 < K < 1 and 0° < angle < 180°; these bounds do not establish manufacturability.
  • All lengths use consistent SI or international customary conversions. Angle may be entered in degrees or radians.
  • The four geometry inputs remain editable. Bend allowance and deduction retain the captured output-only controls; their unit selectors remain usable. The local calculation graph preserves the captured mathematical inverses without exposing those outputs as input controls.
  • The constant-radius neutral-axis model does not account for springback or tool-specific forming effects. Verify the selected K against a test bend before using a flat pattern.

Common questions

Which bend angle should I enter?

Enter the angle bent from flat. For a finished included angle of 120°, the bend from flat is 60°.

How do I choose K?

Use a measured or process-specific neutral-axis factor. Material, tooling and bend radius affect it.

Are allowance and deduction interchangeable?

No. Allowance is neutral-axis arc length; deduction is subtracted from a sum of outside flange dimensions.

References

Use exact-sign tests for positive radius, thickness and angle; keep angle strictly below 180° and K strictly between zero and one. Neutral-axis allowance must be positive.

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