What the bend allowance is
The bend allowance is the length of the neutral axis through a bend. Add it to the two flat legs of a part and you get the length of the flat blank. The neutral axis keeps its length as the sheet bends, so its arc is the length the bend takes up in the blank.
A bent part ends up larger than the sum of its outside dimensions, unless the flat blank allows for the bend. Steve Benson explains this in The Fabricator: the neutral axis moves toward the inside of the bend, and the part elongates.
The bend allowance formula
BA = (pi / 180) x A x (R + K x T)
A is the bend angle in degrees, R the inside radius, K the K-factor and T the thickness. Benson writes the same formula as BA = [(0.017453 x R) + (0.0078 x T)] x A. In his version, 0.017453 is pi / 180, and 0.0078 is pi / 180 times a K-factor of 0.446.
The angle is the bend angle, the angle the flange turns through, which Benson calls the complementary angle. A part with a 135° included angle has a 45° bend angle. A flange bent back to a 30° included angle has a 150° bend angle.
The calculator also gives the outside setback, OSSB = tan(A / 2) x (R + T), and the bend deduction, BD = 2 x OSSB - BA. With them you can lay out the blank from either set of dimensions.
Flat blank length from the legs
- Take each flat leg from the drawing, from the edge of the part to the start of the bend.
- Work out the bend allowance for each bend.
- Add the legs and the bend allowances. That sum is the flat blank.
If your drawing gives the outside dimensions instead, the bend deduction calculator reaches the same blank from the dimensions to the apex.
Worked examples
From The Fabricator. Benson's example bends a 0.062 in sheet with a 0.062 in inside radius through 120°, with two 1.000 in legs. The article gives a bend allowance of 0.187 in and a flat blank of 2.187 in. The calculator, with Benson's average K-factor of 0.4468, returns 0.1879 in and 2.1879 in. The article drops the fourth decimal.
From Cincinnati Incorporated. Its bend allowance chart lists 0.6476 in for a 90° bend in 1/4 in mild steel over a 2 in vee die. The chart's inside radius is 0.3125 in, and its formula is BA = 1.57 (R + 0.4T). Enter 0.25, 0.3125, 90 and a K-factor of 0.4, and the calculator gives 0.6480 in. The chart rounds pi / 2 to 1.57.
In millimetres. Take a 1.5 mm sheet with a 1.5 mm radius, bent to 90° with a K-factor of 0.4468. Its bend allowance is 1.5708 x (1.5 + 0.4468 x 1.5) = 3.409 mm. With legs of 40 mm and 25 mm, the flat blank is 68.41 mm.
Bend allowance table for 90° bends
These values follow Cincinnati's rules for mild steel air bends. The vee die is 8 times the thickness, rounded up to the next 1/8 in. The inside radius is 5/32 of the vee opening. The K-factor is Benson's average of 0.4468. Your own radius and K-factor give different numbers, so use the calculator for a real part.
| Thickness | Vee die, 8 x T rounded up | Inside radius, 5/32 of V | Bend allowance, 90° |
|---|---|---|---|
| 20 gauge, 0.0359 in | 0.375 in | 0.0586 in | 0.1172 in |
| 18 gauge, 0.0478 in | 0.500 in | 0.0781 in | 0.1563 in |
| 16 gauge, 0.0598 in | 0.500 in | 0.0781 in | 0.1647 in |
| 14 gauge, 0.0747 in | 0.625 in | 0.0977 in | 0.2058 in |
| 12 gauge, 0.1046 in | 0.875 in | 0.1367 in | 0.2882 in |
| 10 gauge, 0.1345 in | 1.125 in | 0.1758 in | 0.3705 in |
| 3/16 in | 1.500 in | 0.2344 in | 0.4997 in |
| 1/4 in | 2.000 in | 0.3125 in | 0.6663 in |
The metric table uses a vee die of exactly 8 times the thickness.
| Thickness | Vee die, 8 x T | Inside radius, 5/32 of V | Bend allowance, 90° |
|---|---|---|---|
| 1 mm | 8 mm | 1.25 mm | 2.665 mm |
| 1.5 mm | 12 mm | 1.875 mm | 3.998 mm |
| 2 mm | 16 mm | 2.5 mm | 5.331 mm |
| 3 mm | 24 mm | 3.75 mm | 7.996 mm |
| 4 mm | 32 mm | 5 mm | 10.661 mm |
| 5 mm | 40 mm | 6.25 mm | 13.327 mm |
| 6 mm | 48 mm | 7.5 mm | 15.992 mm |
Which K-factor to use
A K-factor from a test bend on your own press brake is the most accurate. The K-factor calculator works it out from one bent strip. Without a test, Benson writes that 0.4468 comes close enough for everyday work. The link under the K-factor box fills in his estimate from the ratio of radius to thickness.
A part with several bends takes one bend allowance per bend. When a product family comes in many sizes, these rules produce each flat blank, and the same rules can price it. The guide to what CPQ means in a plant shows how that works in a quote.
Questions
What is the bend allowance formula?
What is the difference between bend allowance and bend deduction?
Do I use the included angle or the bend angle?
What K-factor should I use?
Does the bend allowance depend on the material?
How do I find the flat blank of a part with several bends?
Is anything I type sent anywhere?
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