SizingKitMeasured, not tabulated
K-factor calculator
K is where the neutral axis sits inside a bend, as a fraction of thickness out from the inside face, and the honest way to get it is to bend a coupon and work backwards from what you measure. This page does that, free and with no signup: give it the blank length, the outside legs after bending, the angle, the radius and the thickness, and it returns K along with the bend allowance and deduction that follow from it. It refuses anything outside 0 to 0.5, because the neutral axis cannot go there, and tells you which measurement is at fault.
- 100% free
- No signup
- From a real coupon
- 0.50 hard ceiling
- Error sensitivity shown
The coupon you bent, measured six ways
Cut a strip, measure it, bend it, measure it again. Every figure below comes off the same piece of metal, and the answer is the K your machine, your tooling and your coil produced between them.
Measure this one with a caliper. It is the figure the answer is most sensitive to.
Measured on the coupon, not read off a gauge chart — K is a fraction of this number.
R/t = 1.05 on the finished coupon, after springback has opened it.
The finished angle after springback, measured with a protractor on the coupon.
More bends in one coupon divides your measuring error by the count. This is the cheapest accuracy available here.
Only used to say where your measurement landed. It changes nothing.
Outside legs, measured after bending
To the outside corner, summing to 4.1080 in — 0.1080 in more than the blank you started with.
Measured K-factor
0.4091
Neutral axis from the inside face
0.0245 in · 0.621 mm
That lands inside the 0.38–0.43 band the table suggests for this ratio in medium material — but it is now a measurement rather than a band, and it is the one to use.
| What it gives you | Inches | mm |
|---|---|---|
| Deduction your coupon actually lost(sum of outside legs − blank) ÷ number of bends — the raw measurement | 0.1080 | 2.743 |
| Setback in this toolingtan(angle / 2) × (R + t), which does not depend on K at all | 0.1223 | 3.106 |
| Bend allowance at this Kwhat to add to flat legs on the next part | 0.1366 | 3.470 |
| Bend deduction at this Kwhat to subtract from outside dimensions on the next part | 0.1080 | 2.743 |
At these dimensions a 0.005 in error on the blank length moves K by 0.0532, because the whole measurement is a difference between two lengths that are nearly equal. That is the argument for the bend count above: putting four identical bends in one coupon divides the same caliper error by four, which is free accuracy no better instrument can buy you.
The bands, for before you have measured anything
Every figure in this table is a starting value, not data about your material. The one relationship that is not in dispute is the trend: K rises with the ratio of inside radius to thickness, and harder material sits higher at a given ratio.
| Inside radius vs thickness | Soft | Medium | Hard |
|---|---|---|---|
| R < 1t (tight) | 0.30–0.35 | 0.32–0.38 | 0.33–0.40 |
| 1t ≤ R < 2t | 0.35–0.40 | 0.38–0.43 | 0.40–0.45 |
| 2t ≤ R < 4t | 0.40–0.45 | 0.43–0.47 | 0.45–0.48 |
| R ≥ 4t (generous) | 0.45–0.50 | 0.46–0.50 | 0.47–0.50 |
Representative K-factor bands, arranged on the one relationship that is not in dispute: K rises with the ratio of inside radius to thickness, from roughly a third at a tight bend toward the geometric limit of 0.5 at a generous one, and harder material sits higher at a given ratio than soft. Bounded above by MAX_K_FACTOR, which is a geometric certainty, and anchored near the top by HANDBOOK_K_FACTOR = 0.4469, which is arithmetic on a published formula.
These are starting values, not data about your material. Real K depends on the alloy and temper, the grain direction, the die opening, the tooling radius, the friction and the machine — which is why the honest workflow is to bend a test coupon, measure it, and back-solve K with kFactorFromMeasuredBend. A shop that has done that for its own material and tooling should use its own number and ignore this table. Air bending and bottoming give different K on the same material because the die opening sets the effective radius in air bending.
- The ceiling: K = 0.5
- Geometric limit: K is the neutral axis position as a fraction of thickness from the inside face. Bending compresses the inside and stretches the outside, so the neutral axis can only move inward from the mid-thickness — K ≤ 0.5 always, and 0.5 is approached only at very generous radii.
- The inherited default: K = 0.4469
- Implied by the traditional bend-allowance formula BA = (0.017453 × R + 0.0078 × t) × angle, printed in Machinery's Handbook and in shop layout tables for decades: 0.0078 ÷ (π/180) = 0.4469. 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 measure the K-factor of your own material
Twenty minutes with a strip of offcut replaces every K table on the internet, for that material on that machine.
Cut a coupon and measure the blank before it goes anywhere near the brake
Take a strip of the actual coil the job will run in, wide enough to be stiff and long enough to hold several bends. Measure its length with a caliper, not a tape, and write the number down to four places — this is the single figure the answer is most sensitive to, because the whole calculation is a difference between two lengths that are nearly equal. A tape reading to a sixty-fourth turns a K measurement into a K guess.
Put several identical bends in it, in the tooling the job will run
Same vee, same punch, same material orientation, same operator. Several bends rather than one, because your caliper error is divided by the number of bends: at 16 gauge on a 1/16 in radius, five thousandths of error on the blank moves K by 0.053 with one bend and by 0.013 with four. Nothing else on this page buys accuracy that cheaply, and offcuts are free.
Measure the finished part, including the radius that came out
Outside legs to the corner, angle with a protractor, and the inside radius with radius gauges after the ram has come up. All three have moved from what the tooling suggested: springback opens the angle and the radius together, and in air bending the radius was never the punch nose to begin with. Feeding the tooling's intended geometry instead of the coupon's actual geometry is the commonest way to get a K that is precisely wrong.
Technical specifications
| What it solves | K from six measurements on one coupon: blank length, outside legs, bend count, angle bent through, finished inside radius and material thickness. No table is consulted to produce the answer. |
|---|---|
| Worked example | 0.0598 in sheet, 0.0625 in finished radius, one 90° bend, 4.0000 in blank, outside legs 2.054 and 2.054: K = 0.4091, neutral axis 0.0245 in (0.621 mm) out from the inside face. |
| Sensitivity to the blank measurement | 0.0532 of K per 0.005 in of error at those dimensions, with one bend. The relationship is exactly inverse in bend count, so four bends in the coupon give 0.0133. |
| Coupon bends accepted | One to six identical bends, sharing one angle and one radius. The deduction is averaged over them, which is what divides the measuring error. |
| Refusal band | K outside 0 to 0.50 returns no answer. On this bend the whole physically possible range of K spans only 0.0469 in of deduction — 0.1464 in at K = 0 down to 0.0995 in at the ceiling — so a measurement landing outside it is not a strange material, it is a wrong number. |
| Comparison bands | Four radius-to-thickness bands from under 1t to over 4t, three material classes, twelve ranges. Every one is flagged as varying and none of them is used in the calculation. |
| The inherited constant | 0.4469, shown for context. It is what the old layout formula BA = (0.017453 × R + 0.0078 × t) × θ assumes, recovered by dividing 0.0078 by 0.017453 — one line of arithmetic rather than a figure to take on trust. |
| Where it runs | In this tab. Your coupon measurements, which are effectively a fingerprint of your tooling, are never uploaded, logged or kept. |
Frequently asked questions
Why can I not just take K from a chart and get on with it?
Because the charts disagree with each other by more than the tolerance you are working to. Across the range they publish, K runs from roughly a third to the ceiling of a half, and on 16 gauge steel in a 1/16 in radius that span is 0.0160 in of bend deduction per bend. One bend and it is a rework you can file off; a four-bend box and it is 0.064 in in one direction, which is a panel that binds in its opening. The reason the span is so wide is that K depends on the alloy, the temper, the grain direction, the die opening, the friction at the shoulders and the machine, and a chart cannot know any of those. Twenty minutes with an offcut can.
My measurements give a K above 0.5. What did I get wrong?
One of the six numbers, and the page says which direction to look. K above 0.5 means the calculation found less deduction than the tooling can physically produce, which happens when the blank was measured long, a leg was measured short, or the coupon was bent through a smaller angle than the one entered. The ceiling itself is not a convention that can be argued with: K is the neutral axis position as a fraction of thickness from the inside face, bending compresses the inside more than it stretches the outside, so the axis can only move inward from mid-thickness. A material whose neutral axis sat past the middle would have to get longer on the inside of the bend.
Will the K I measure in air bending hold when we bottom the same part?
No, and that is one of the few things about K that is genuinely predictable. In air bending the sheet spans the die opening and takes a radius from that span, so the effective radius and the strain distribution are set by the vee; bottoming presses the material into the die and the tool radius takes over. The same material bent both ways gives different K, usually higher in air bending because the radius it produces is larger. Coining, which sets the metal into the punch nose, is different again. Measure a coupon per forming method, not just per material, and label the number with the method.
How long should the coupon be, and how many bends do I put in it?
Long enough for the flanges to stay flat and to take four bends comfortably — a strip of a foot or so covers most jobs. Four is the number worth aiming at: the deduction is averaged across the bends, so the caliper error divides by four while the effort only doubles. Keep the flanges at least a die opening and a half long so nothing pivots off the shoulders, keep every bend the same angle and radius, and bend them all in the same direction relative to the rolling direction. If you can only get one bend on the coupon, measure the blank twice and average.
Do I measure the radius before or after springback?
After — on the finished part, with radius gauges, in the same session as the legs. Springback opens both the angle and the radius, so a part released from a die relaxes to a larger inside radius than the tooling implies, and the effect is bigger the stronger the material. Entering the intended radius rather than the achieved one is the reason a lot of measured K values come out too high: the calculation is handed a smaller radius than the metal actually has and pushes the difference into K, which is the only free variable left. Stainless and the high-strength aluminums relax the furthest and are worth measuring most carefully.
Does grain direction change the K-factor?
Slightly, and much less than it changes whether the bend cracks. Bending with the bend line across the rolling direction is the easy direction and along it is the hard one, and the strain distribution differs enough that a carefully measured K moves by a few hundredths between them — real, but small next to the tenth or two that separates the published bands. The reason to care about grain is elsewhere: a bend along the grain in a hardened temper is where the outer fiber cracks. If a part has bends in both directions and the tolerance is tight, measure a coupon in each and use the pair.
I have my number. Where does it live now?
In a shop table indexed by material, thickness, forming method and die opening, because that combination is what it belongs to — a K measured for 16 gauge steel in a 1/2 in vee says nothing about 11 gauge in a 1 in vee. Write down the coupon measurements alongside it so somebody can check the number rather than inherit it, and re-measure when a coil supplier changes. From there it feeds the two layout pages: the bend allowance calculator adds it to flat legs and the bend deduction calculator subtracts it from outside dimensions, and they will agree with each other because they are the same geometry.
About the neutral axis, and why K has to be measured
Bend a beam elastically and the neutral axis sits at the centroid of the section, because the tension above it and the compression below it are symmetric — that is the assumption the beam deflection calculator is built on, and within the elastic range it is a good one. Bend a sheet past yield around a radius of its own order and the symmetry is gone. The inside of the bend is being squeezed into a shorter arc than it wants and thickens; the outside is being pulled into a longer one and thins; and the surface whose length survives the operation slides in toward the inside face. K is the position of that surface, and every number a flat pattern rests on is derived from it. The geometric consequence is a hard ceiling: the axis can move inward from mid-thickness but not outward, so K is always below 0.5 and approaches it only where the radius is generous enough that the two strains nearly balance again.
What K cannot be is looked up, and the reason is that it is not a property of the material. It is a property of the material, the temper, the grain direction, the forming method, the die opening, the friction at the die shoulders and the machine, all at once — which is why published bands span from roughly a third to the ceiling and why two shops bending the same coil get different answers. Fortunately it is easy to measure, because the geometry runs backwards as readily as forwards. Cut a strip, measure it, bend it, measure the outside legs, and the difference between the two lengths is the deduction the bend cost; subtract that from twice the setback and you have the arc, and the arc gives K. Six numbers off one coupon, and the guessing stops. The one thing to be careful of is precision: the whole calculation is a difference between two nearly equal lengths, which is why a five-thousandth caliper error moves K by fifty thousandths at 16 gauge, and why the bend count in the coupon is the most useful control on this page.
What other K-factor pages do is print a number. Sometimes it is 0.33 because a supplier's leaflet said so, sometimes 0.4469 because it fell out of the handbook formula that generations of layout tables were built from — divide its 0.0078 by its 0.017453 and there it is, an assumption rather than a measurement. Both are defensible starting points and neither is your material. The bands lower down this page are here for the case where no coupon has been bent yet, arranged on the one relationship that is not in dispute: K rises with the ratio of inside radius to thickness, and harder material sits higher at a given ratio. Once you have your own figure, it goes to work on the bend allowance calculator for parts dimensioned inside and the bend deduction calculator for parts dimensioned outside. The radius you measured on the coupon has an origin of its own: in air bending it comes from the die opening, which the press brake tonnage calculator selects alongside the force, and the thickness starts as a gauge number that means four different things until its standard is named.
Where your coupon measurements 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.
A measured K is a description of your machine and your supplier's coil, which is competitive information in a job shop. It is computed here in the tab and nothing is sent anywhere, so the only copy that exists is the one you write down.