Bend Allowance Calculator
Work out bend allowance, bend deduction and the flat pattern length for sheet metal, with the K-factor taken from the radius-to-thickness ratio.
How to use this calculator
- 1Enter the inside radius the part will actually get, not the punch nose radius. On an air bend they are different, and the die opening is what governs.
- 2Leave the K-factor on automatic unless you have measured one. The automatic figure comes from the radius-to-thickness ratio, which is what really drives it.
- 3Enter the flange dimensions as they are drawn - outside dimensions are the normal convention, and the bend deduction is what converts them.
- 4Do one test bend and back out your own K-factor before running a batch. It is worth more than any chart.
How the calculation works
BA = (pi / 180) x angle x (R + K x T)
OSSB = tan(angle / 2) x (R + T)
BD = 2 x OSSB - BA
Flat = sum of outside dimensions - (number of bends x BD)- R
- Inside bend radius - what the part actually gets, which in air bending comes from the die opening rather than the punch
- T
- Material thickness
- K
- Where the neutral axis sits, as a fraction of thickness from the inside face. Moves with R/T, not just with material
- OSSB
- Outside setback - from the apex where the two outside faces would meet, back to the tangent point of the bend
Bend allowance is the arc length of the neutral axis: the radius to that axis is R + K T, and the arc is that radius times the angle in radians.
Bend deduction exists because parts are dimensioned to their outside faces, which meet at a theoretical apex that the real bent part never reaches. Subtracting BD converts from that apex geometry back to real material.
Add BA when working from inside dimensions; subtract BD when working from outside dimensions. Both are correct and they are not interchangeable - confusing them costs about two material thicknesses per bend.
Worked example
A right-angle bracket in 1/8 in steel
- 1.R/T is 1.0, which puts K at 0.44 - the neutral axis a little inside the middle.
- 2.BA = (pi/180) x 90 x (0.125 + 0.44 x 0.125) = 1.5708 x 0.180 = 0.2827 in.
- 3.OSSB = tan(45) x (0.125 + 0.125) = 0.250 in, so BD = 2 x 0.250 - 0.2827 = 0.2173 in.
- 4.Two 2 in outside legs sum to 4 in, less one deduction, gives a 3.7827 in blank.
Result: Cut the blank 3.783 in - not 4 in, and not 3.75
A five-sided enclosure, where the K-factor matters
- 1.16 gauge steel is 0.0598 in, bent on a 1/16 in inside radius - R/T is 1.05, so K is 0.44.
- 2.BD comes out at 0.105 in per bend, and there are four bends.
- 3.The outside dimensions total 18 in, so the blank is 18 - 4 x 0.105 = 17.58 in.
- 4.Had 0.33 been used for K the blank would come out 0.04 in shorter - a lower K means a shorter arc through the bend and therefore a larger deduction - and across four bends that is enough to put the last flange visibly out.
Result: About 17.58 in, and the K-factor is worth 0.04 in across four bends
A generous radius, where K returns to the middle
- 1.A 3/8 in radius in 1/16 in material is an R/T of 6 - a very generous bend.
- 2.At that ratio the neutral axis has moved back to essentially mid-thickness, so K is 0.50.
- 3.BA is 1.5708 x (0.375 + 0.5 x 0.0625) = 0.6381 in, and OSSB is 0.4375, so BD is 0.2369.
- 4.The blank is 6 - 0.2369 = 5.763 in. Using 0.42 for K here would have made it 0.008 in too short.
Result: 5.763 in, with K back at 0.50
What actually happens in a bend
Wrap a strip of metal around a radius and the outside surface has further to travel than the inside one. The outside stretches, the inside compresses, and somewhere between them lies a surface whose length is unchanged. That surface is the neutral axis, and its length through the bend is exactly the amount of material the bend consumes.
If the neutral axis stayed at mid-thickness the whole subject would be trivial. It does not. Compression is easier for metal than tension, so as the bend tightens the neutral axis migrates towards the inside face, and the bend consumes less material than the mid-thickness assumption predicts. The K-factor is simply that position, expressed as a fraction of the thickness measured from the inside.
This is why K is not a material constant. A 0.060 inch sheet bent on a 0.030 radius and the same sheet bent on a 0.375 radius have different K-factors, and they will be different by enough to matter on a multi-bend part. Charts that give one number per alloy are giving an average over a range they do not state.
Allowance, deduction, and which one you want
Bend allowance is the arc length of the neutral axis: how much flat material disappears into the bend. If a part is dimensioned to the inside faces of its legs, you add the bend allowance to the sum of those legs and get the blank.
But parts are almost never dimensioned that way. They are drawn to outside faces, and two outside faces meeting at a corner meet at a theoretical apex the real part never reaches - the bend rounds the corner off well before it. The outside setback measures how far back from that apex the bend actually starts, and the bend deduction combines the two effects: subtract it from the sum of the outside dimensions and you get the blank.
Both are right. Which one to use is decided by how the drawing is dimensioned, and the failure mode is using the wrong one, which is out by roughly two material thicknesses per bend. On a bracket that is visible. On a five-bend enclosure it is a scrapped part.
- Bend allowance — Add to inside dimensions. The arc length of the neutral axis.
- Bend deduction — Subtract from outside dimensions. The usual case, because that is how parts are drawn.
- Outside setback — Apex to tangent point. The geometric bridge between the two.
- K-factor — Where the neutral axis sits. Moves with R/T, and worth measuring rather than assuming.
The test bend that beats every chart
The genuinely reliable way to get a K-factor is to make one. Take a strip of the exact material, measure it, bend it on the exact tooling at the exact angle, and measure the result. The difference between what you started with and what the outside dimensions now sum to is the bend deduction, and K falls out of it by rearranging the equations.
That number applies to that material, that thickness, that die and that angle - and it will be right, which no published figure can promise. Shops that do a lot of forming keep a book of them, and the good ones re-measure when the material supplier changes, because temper varies between mills more than it has any right to.
It is also worth understanding why the radius is uncertain in the first place. In air bending - the way most shop work is done - the punch does not touch the bottom of the die, and the inside radius that results is set by the die opening rather than the punch nose. A common approximation is about one sixth of the vee width in mild steel. Enter the punch radius instead and the whole calculation is built on a number the part never had.
What this assumes, and where it stops
Assumptions
- Air bending or bottoming with a consistent inside radius, uniform along the bend.
- The K-factor from the radius-to-thickness ratio uses the standard air-bending bands for mild steel, adjusted for temper.
- Flange dimensions are outside dimensions, which is the usual drawing convention.
- Every bend on the part uses the same radius, angle and material.
Limitations
- It does not model springback. The angle a part holds after release is not the angle it was formed to, and how much it recovers depends on material, temper, radius and tooling.
- Hems, folds and bends past 180 degrees have their own allowances and are not covered.
- Coining - where the punch fully forms the material into the die - drives the neutral axis differently from air bending, and K runs lower.
- Bends across the grain crack at radii that bends with the grain survive. Nothing here sees grain direction.
- Very tight radii cause thinning at the outside of the bend, which changes the geometry the equations assume.
Common questions
What K-factor should I use?
One you measured, if you possibly can. Failing that, use the radius-to-thickness ratio rather than a material constant: about 0.42 where the inside radius is less than the thickness, 0.44 between one and three times, and 0.50 above that. Any single number quoted for a whole alloy is an average across a range that is not stated.
What is the difference between bend allowance and bend deduction?
Bend allowance is what you add to inside dimensions; bend deduction is what you subtract from outside dimensions. They describe the same bend from opposite directions and are related by the outside setback. Which you need depends on how the drawing is dimensioned - and mixing them up is out by roughly two material thicknesses per bend.
Why does my part come out short?
Most often the K-factor is too low for the bend, or the inside radius entered was the punch radius rather than what the part actually got. On an air bend the radius comes from the die opening, and it is frequently larger than people assume - roughly a sixth of the vee width in mild steel. Bend a test piece, measure it, and back the real numbers out of it.
How short can a flange be?
Roughly four times the material thickness plus the inside radius, on a conventional press brake - below that the material does not sit properly across the die shoulders and tends to slip in or roll over. Shorter flanges are possible with special tooling, or by forming long and trimming afterwards.
Does the grain direction matter?
For cracking, very much. Bending across the rolling grain is far more likely to crack the outside of the bend than bending along it, and the difference shows up first on tight radii and hard tempers. It does not change the allowance arithmetic, but it decides whether the part survives - which is why sheet metal drawings on critical parts call out the grain.
Sources
- Sheet metal bending - bend allowance and K-factor fundamentals — The Fabricator
Formula and content last reviewed on .
Results are estimates for information only, not professional advice.
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