Bend deduction calculator

What the bend deduction is

The bend deduction is the length you take off the outside dimensions of a part to get its flat blank. The Fabricator defines it as the value subtracted from the flat blank for each bend, and a part can have several.

A drawing can give each flange to the apex of the bend, where the outside surfaces of two flanges would meet. The bend deduction turns those dimensions into a cut length.

The bend deduction formula

• Outside setback: OSSB = tan(A / 2) x (R + T)
• Bend allowance: BA = (pi / 180) x A x (R + K x T)
• Bend deduction: BD = 2 x OSSB - BA
• Flat blank: flange 1 + flange 2 - BD

These are the formulas in Steve Benson's calculation basics article. T is the thickness, R the inside radius, A the bend angle and K the K-factor. The outside setback runs from the tangent point of the bend to the apex. At 90°, tan 45° equals 1, so the outside setback is the radius plus the thickness.

Flat blank from outside dimensions

1. Take each flange from the drawing, from its edge to the apex of the bend.
2. Enter the thickness, the inside radius, the bend angle and the K-factor.
3. Read the bend deduction and the flat blank.

For a part with several bends, add every dimension along the profile and subtract one bend deduction for each bend. If your drawing gives the flat legs instead, use the bend allowance calculator.

Worked examples

From The Fabricator. Benson's example bends a 0.250 in plate with a 0.250 in inside radius through 160°. Each flange measures 3.836 in from its edge to the apex. The article gives an outside setback of 2.836 in, a bend deduction of 4.662 in and a flat blank of 3.010 in. The calculator, with a K-factor of 0.4468, returns 2.836 in, 4.661 in and 3.011 in. The last digits differ because the article rounds each step.

In millimetres. Take a 3 mm plate with a 3 mm radius, bent to 90°, with flanges of 80 mm and 50 mm to the apex. The outside setback is 6 mm. The bend allowance is 1.5708 x (3 + 0.4468 x 3) = 6.818 mm. The bend deduction is 12 - 6.818 = 5.182 mm, and the flat blank is 130 - 5.182 = 124.82 mm.

In inches. A 1/4 in plate over a 2 in vee die forms about a 0.3125 in radius, by Cincinnati's 5/32 rule. With flanges of 3 in and 2 in, the outside setback is 0.5625 in and the bend deduction 0.4587 in. The flat blank is 4.541 in.

Bend deduction table for 90° bends

These values take the inside radius equal to the thickness and a K-factor of 0.4468.

A different radius or K-factor changes every column, so check your own setup in the calculator.

Negative bend deductions

Benson notes a catch with parts bent past 90°. If you take the outside setback from the included angle, the bend deduction can come out negative. Subtracting a negative deduction adds length, and the flat blank comes out the same. This calculator always uses the bend angle, the angle the flange turns through. For a flange closed to a 20° included angle, you enter 160°.

Bend deductions in a quote

An estimator needs the flat blank to price the material and the cutting. When a product comes in many sizes, the bend deductions sit inside the rules that size every blank. The guide to general arrangement drawings covers the drawing that travels with a configured product.