SizingKitInside dimensions
Bend allowance calculator
Bend allowance is the arc length of the neutral axis through a bend — BA = angle in radians × (R + K × t) — and it is the amount of flat blank a bend consumes. This page returns it in inches and millimeters, free and with no signup, together with the flat pattern for a two-leg part measured to the inside mold line, and a strip showing what that blank becomes across the whole physically possible range of K, which for 16 gauge steel on a 1/16 in radius is 0.0160 in of blank length.
- 100% free
- No signup
- Inches and mm
- K bands by R/t
- Sensitivity strip
The bend, and the legs measured on the inside
An inside leg runs from the end of the flange to where the two inside faces would meet if the bend were sharp. One bend, two legs — a part with several bends is laid out from the outside instead.
Measure it. A flat pattern built on a nominal gauge inherits the mill tolerance.
R/t = 1.05. In air bending this comes from the die opening, not the punch.
A square corner is 90 here, not 270 — this is how far the metal turns, not the angle you end up looking at.
Cold-rolled mild steel, half-hard copper and brass, annealed stainless, 5052-H32 and 6061-T4 aluminum.
To the inside mold line.
The other side of the same bend.
Prefilled from the band for 1t ≤ R < 2t in medium material: 0.38 to 0.43. These are starting values, not data about your coil — measure one and the guess goes away.
Bend allowance, inches
0.1362
Bend allowance, mm
3.460
| Step | Inches | mm |
|---|---|---|
| Neutral axis, from the inside faceK x t — where the metal is neither stretched nor squeezed | 0.0242 | 0.615 |
| Radius the neutral axis turns onR + K x t, and the arc above is this times the angle in radians | 0.0867 | 2.203 |
| Inside setback, each legtan(angle / 2) x R, from the inside mold line back to where the bend starts | 0.0625 | 1.587 |
| Flat portion of leg Aleg A minus that setback | 1.9375 | 49.212 |
| Flat portion of leg Bleg B minus that setback | 2.9375 | 74.613 |
| Flat blank lengthflat A + flat B + bend allowance | 5.0112 | 127.285 |
The blank comes out 0.0112 in longer than the 5.0000 in sum of the two inside legs. Which way it goes is not fixed: the arc adds material and the two setbacks take it away, so a tight radius leaves the blank long and a generous one leaves it short.
Bend allowance is the arc length of the neutral axis: BA = angle in radians × (R + K × t), with the angle taken as the movement of the metal rather than the corner you end up looking at. Everything else on this page is that one arc placed between two flats. The K it rests on is the one figure here that is a guess until you have measured it.
What the blank does if K is wrong
The same legs, the same radius and the same angle, at four K values spanning the whole physically possible range.
| K | Why this one | Allowance, in | Blank, in |
|---|---|---|---|
| 0.330 | a tight bend in soft material | 0.1292 | 5.0042 |
| 0.400 | a common shop default | 0.1357 | 5.0107 |
| 0.447 | implied by the handbook formula | 0.1402 | 5.0152 |
| 0.500 | the geometric ceiling | 0.1451 | 5.0201 |
End to end that is 0.0160 in — 0.406 mm — of blank length riding on a number nobody has measured. On a single bracket it is a rework; on a box with four bends it is four times that, all in the same direction. This is one formula's built-in assumption, not a measurement of your material. It sits at the top of the realistic range and suits generous radii in mild steel; tight bends run well below it.
How to get a flat blank out of an inside-dimensioned drawing
Three inputs decide the answer and only one of them is written on the drawing.
Measure the thickness rather than reading it off the gauge
A flat pattern is arithmetic on the actual metal. A gauge number is a nominal that mill product ships around, and the thickness enters the allowance twice — once through K × t in the arc and once through the setback that positions it — so a couple of thousandths of coil tolerance is a couple of thousandths of blank. Put a micrometer on the sheet you are going to cut, not on a sheet of the same order.
Use the radius the bend will actually have, not the one on the punch
In air bending the sheet never touches the punch nose, so the inside radius is set by the span between the die shoulders and comes out near 16% of the die opening in mild steel. Bottoming and coining are different — there the tool radius wins. Type what the finished part will have, because the allowance is a property of the geometry that exists after the ram goes up and not of the tooling that made it.
Take the K-factor as a starting point and then go and measure it
The field is prefilled from the band for your radius-to-thickness ratio and material class, and the button beside it refills that band's midpoint whenever the ratio changes. That is a guess with a range attached, which the sensitivity strip below the answer prices for you: the same bend across K from 0.33 to 0.50 moves the blank by a sixteenth of an inch on a five-inch part. Bend a coupon, measure it, and the guess turns into a number.
Technical specifications
| Formula evaluated | BA = θ × (R + K × t), with θ in radians. The arc of the surface that is neither stretched nor compressed, taken between the two tangent points. |
|---|---|
| Angle convention | The angle the metal is bent through, 1° to 179°. A square corner is 90 here. Press brake controls and bend tables use the same convention; the included angle you look at afterwards is 180 minus this. |
| Worked example | 0.0598 in sheet, 0.0625 in inside radius, 90°, K 0.405 gives BA 0.1362 in (3.460 mm) and a 5.0112 in blank from 2 in and 3 in inside legs. |
| K-factor default | The midpoint of the band for the entered R/t and material class — four ratio bands from under 1t to over 4t, three material classes. 0.405 for the example above, from the 0.38 to 0.43 band. |
| K-factor accepted | 0.05 to 0.50. The ceiling is geometric rather than conventional: the neutral axis can only move toward the inside of a bend, so K above 0.5 means a measurement is wrong. |
| Sensitivity strip | Blank length at K = 0.33, 0.40, 0.4469 and 0.50 — the last being the ceiling and the third being what the old handbook formula BA = (0.017453R + 0.0078t) × θ silently assumes. |
| Input ranges | Thickness 0.002 to 1 in, inside radius 0.002 to 6 in, legs 0.05 to 240 in. Each field takes a decimal, a fraction such as 3/64, a mixed number, or a metric figure with its unit. |
| Where it runs | In this tab. The dimensions you type are never uploaded, logged or kept, which matters when the drawing is somebody else's. |
Frequently asked questions
For a square corner, do I enter 90 or 270?
90 — this field is how far the metal turns, not the angle you end up looking at. The convention matters because the arc is proportional to it: entering 270 for a right angle triples the allowance and produces a blank three-quarters of an inch long on a part that needed a tenth. The rule that never fails is that a flat sheet is 0 and the metal folded back on itself is 180, so anything a brake can do lives between them. Acute bends are the case where people get this backwards most often: a bend that closes to a 30° included angle was bent through 150.
Why is the blank not simply the two legs added together?
Because the outside of a bend gets longer and the inside gets shorter, and the length that is preserved belongs to neither face. Somewhere between them is a surface that is neither stretched nor compressed, and the flat blank has to contain the length of that surface through the corner rather than the length of either edge. K says where it sits, as a fraction of thickness measured from the inside face, and it is always less than half because bending squeezes the inside harder than it stretches the outside. Which way the total goes depends on the radius: the arc adds material and the two setbacks remove it, so a tight bend leaves the blank longer than the sum of the inside legs and a generous one leaves it shorter.
What exactly is an inside mold line, and where do I measure it from?
It is the point where the two inside faces of the part would cross if the bend were a sharp corner with no radius at all. On a drawing dimensioned to the inside, that intersection is what the dimension runs to, and it is not a place you can touch on the finished part — the metal has curved away from it. From that dimension the page subtracts tan(θ/2) × R to reach the tangent line where the bend actually begins, and what is left is flat. If your drawing is dimensioned to the outside faces instead, which is how most shop drawings arrive, the bend deduction page linked below works from those directly and saves you the conversion.
My part has three bends. Can I multiply the allowance by three?
Only if all three are the same angle in the same radius, which is true of a channel and untrue of most brackets. The allowance is a property of one bend, so a part with a 90° in a 1/16 in radius and a 45° in a 1/8 in radius has two different allowances and they add rather than multiply. The safe habit is to work each bend on its own and sum, and for anything with more than two legs to lay out from the outside dimensions, where the same information arrives as one deduction per bend and there is nowhere for a leg to be double-counted.
The drawing does not state an inside radius. What do I put in?
Find out what the tooling will produce, because in air bending the drawing does not control it. The sheet bridges the two shoulders of the vee die and takes a radius set by that span, near 16% of the die opening in mild steel, more like 20% in stainless and nearer 14% in soft aluminum. So a 1/2 in vee produces about a 0.080 in inside radius whatever punch is in the holder, and if the flat pattern was calculated for 1/16 in it will be out. Ask the brake operator which die the job is running in before cutting the blank, or cut one part and check.
Does springback change the bend allowance?
Not directly, but it changes the geometry the allowance should be calculated on, which amounts to the same thing. Overbending to land on 90° is a change to what the ram does, not to the finished part, and the allowance follows the finished part. What does move the answer is that springback opens the radius as well as the angle: material released from a die relaxes to a slightly larger inside radius than the tooling suggested, and stainless and high-strength alloys relax further than mild steel. If you are compensating for springback by overbending, measure the radius on the finished coupon and use that.
Should I use the nominal gauge thickness or a measured one?
Measured, every time, and the difference is bigger than it looks because thickness enters the calculation in two places. It scales the neutral axis position through K × t and it sits inside the setback through R + t, so a sheet running 0.002 in over nominal shifts a 90° blank by roughly two thousandths per bend, all in the same direction. That is inside the mill tolerance and therefore not a defect in the material — it is simply why a flat pattern built on a gauge chart figure comes back a little wrong on a part with several bends. Look the nominal up when you are ordering; measure the coil when you are cutting.
About the neutral axis, and why K is the whole argument
Bending a sheet does two things to it at once. The material on the outside of the corner has further to travel and stretches; the material on the inside has less and is compressed. Between them lies a surface whose length does not change, and the flat blank has to be long enough to supply that surface — not the outside face, which would make it too long, and not the inside, which would make it too short. Bend allowance is simply the arc length of that surface, angle in radians times the radius it turns on, and the only reason the calculation is interesting is that nobody knows exactly where the surface is. K is the answer to that question, expressed as a fraction of thickness out from the inside face, and it can never reach 0.5 because compression on the inside always outruns tension on the outside. A tight bend crushes the inside hard and drives the neutral axis in toward it; a generous one leaves the strain nearly symmetric and lets K creep toward the half.
The second thing worth being careful about is where a leg is measured from, because three different points are all called the end of the leg. The inside mold line is where the two inside faces would meet with no radius; the outside mold line is the same construction on the outside; the tangent line is where the metal stops being flat and starts turning. Only the last of those is a real place on the part, and only the last of them adds up with a bend allowance directly. This page takes inside mold-line dimensions and steps back to the tangent line by subtracting tan(θ/2) × R from each leg, which is why the numbers in the table under the answer are worth reading rather than skipping. The bend deduction calculator makes the same journey from the outside, where the step back is tan(θ/2) × (R + t) — the extra thickness term being the entire difference between the two pages.
What other bend allowance calculators get wrong is not the formula, which everyone has right. It is presenting K as though it were known. A page that hard-codes 0.4469 because it fell out of the old handbook formula, or 0.33 because a supplier's chart said so, is reporting a blank length to four decimal places on an assumption worth one, and the strip under the answer here exists to make that visible instead of invisible. The honest sequence is to bend a coupon and back-solve, which is what the K-factor calculator is for. Two inputs feed this page from elsewhere: the thickness starts life as a gauge number that has to be converted in the right standard, and the inside radius comes out of the die the job runs in, which the press brake tonnage calculator works out along with the force. Once the blank length is settled, the plate weight calculator turns it and the width into what the nest will weigh.
Where the drawing dimensions go
Every number on this page is worked out by JavaScript running in the tab you are reading it in. Nothing you type — loads, lengths, nameplate ratings, the rates your utility charges you — is uploaded, logged or kept, which is also why the calculators carry on working in a mechanical room with no signal.
Nothing here is stored between visits either — reloading the page returns it to the worked example rather than to your last job, so a shared shop computer does not hand the next person your part dimensions.