K-Factor Calculator (from a Test Bend)
Work out your own K-factor from a test bend: the strip's flat length, the thickness, the inside radius, the angle bent and the two flanges you measured. You get K, the bend allowance and deduction it implies, and how far a measuring error would move it.
The method behind it: How to find your K-factor from a test bend — step by step, with sources.
Dimensions
Results
Preview
The test strip, formed
Drawn to scale with the K found, by the same code as the single-bend tool — which, given this K and these flanges, returns exactly the flat length you entered.
How this tool is verified
- Checked against hand-worked cases, and by a round trip through the single-bend tool over 480 combinations: a K recovered from a strip, fed back with the same flanges, reproduces the blank.
- A second implementation in Python recomputes K, the bend allowance, the deduction and the re-formed blank from the raw measurements on every release.
- Deterministic: the same measurements give the same numbers, and metric and imperial input give the same K.
The method, the reports and the responsibility boundary are on the Verification page.
Built by Ruthen Systems
Free, with no account, and the dimensions you type never leave your browser. If a result looks wrong, or the option your shop needs is missing, say so — reports of a wrong result are dealt with first.
Report a problem or request a toolAssumptions and limits
Read these before you cut anything. They describe exactly what this tool does and does not account for.
- K is the depth of the neutral axis as a fraction of thickness, measured from the inside face of the bend. It is a property of your material, tooling and method together — not of the material alone.
- Measure the angle the strip was actually bent through (90° is a square corner), on the part as it came off the brake, after springback.
- Flanges are measured to the theoretical sharp corner — where the two outside (or inside) faces would meet if extended — not to the start of the radius.
- The inside radius must be the radius the part actually has. In air bending it is set mainly by the die opening, not by the punch nose, so measure it (radius gauge) rather than assume it.
- One test gives one K for that thickness, radius, material and tooling. Bend two or three strips and average; long flanges do not make the result more precise, careful measuring does.
Output is a planning and fabrication aid. You are responsible for verifying dimensions, tolerances and material behaviour before production — full disclaimer.
Worked example
2 mm strip, 100.6 long, bent 90° on a 2 mm inside radius; flanges 52.10 and 51.95 to the outside corner.
- Bend allowance4.550 mm
- K-factor0.448
- ± per 0.1 mm of error0.032
By hand. Outside setback = (R + T) × tan(90°/2) = 4, so the straight legs are 48.10 and 47.95. What the bend took: 100.6 − 48.10 − 47.95 = 4.55. That is the neutral-axis arc, so its radius is 4.55 ÷ (π/2) = 2.897, which is 0.897 into the 2 mm metal from the inside face: K = 0.897 ÷ 2 = 0.448. One measurement off by 0.1 mm changes that by 0.1 ÷ (π/2 × 2) = 0.032.
Method
The relations used
Bend allowance is the arc length of the neutral axis: angle × (inside radius + K × thickness), with the angle in radians — or π × (R + K·T) × A ÷ 180 with A in degrees, the form in the SOLIDWORKS help on the K-factor, where K is likewise measured from the inside face (also BricsCAD's help). The outside setback is tan(angle ÷ 2) × (R + T), and the bend deduction is twice the outside setback less the bend allowance (Steve Benson, “Sheet metal bending calculation basics”, The Fabricator).
Working backwards from a strip
Subtract each flange's setback to get its straight leg; whatever the blank had beyond the two legs went into the bend. That is the bend allowance; divided by the angle it is the neutral-axis radius, and its depth past the inside radius, as a fraction of thickness, is K. Javelin Technologies describes this test-bend procedure (Javelin Technologies, “Calculating bend allowance, bend deduction, and K-factor”; Benson, “Calculating k-factors for the press brake”, The Fabricator, 2023, which also warns that the test material must match production material).
What value to expect
Generic tables put K between about 0.33 and 0.5, rising with the radius-to-thickness ratio and reaching 0.5 once the radius is over about three thicknesses (Benson, “Analyzing the k-factor in sheet metal bending”, after Machinery's Handbook). The FAA's airframe handbook uses a constant 0.0078 × T per degree in its bend-allowance formula, equivalent to K ≈ 0.447 (FAA-H-8083-31B, Ch. 4, p. 4-64). A result well outside 0.3–0.5 is more often a measuring or radius problem than a material property. The tool warns when K comes out at or below 0 or above 0.5, which no real bend gives; between those, check your measurements if the value looks odd.
How this tool is checked
Hand-worked cases; a round trip against this site's single-bend tool over 480 combinations of angle, radius, thickness, K and datum — a K recovered from a strip, fed back, reproduces the blank to a billionth of a millimetre; and a second implementation in Python that recomputes K, the allowance, the deduction and the re-formed blank from the raw measurements on every release.
Questions
What is the K-factor?
Where the neutral axis sits inside a bend — the layer that neither stretches nor compresses — as a fraction of the thickness, measured from the inside face. The bend allowance is the length of that layer through the bend: angle × (inside radius + K × thickness). K = 0.5 is mid-thickness; in practice it lies between about a third and a half.
Why work it out from a test bend instead of using a table?
A published K is a starting value. Your material, temper, grain, tooling and method all move it, and the only way to know your own number is to bend a strip and measure it. Practitioners say the same: reverse-engineering K from test pieces is the reliable route.
How precise does the measuring need to be?
More than people expect. An error in any one length goes straight into the bend allowance, so K moves by that error divided by (angle in radians × thickness). On a 2 mm strip bent 90°, 0.1 mm of error is ±0.03 in K. The tool shows this figure next to the result for your strip. Use a caliper, bend to 90° or more, and average two or three strips.
Which inside radius do I enter?
The radius the part actually has. In air bending the radius is set mainly by the die opening, not by the punch, so a part bent with a sharp punch over a wide die has a larger radius than the punch nose. Measure it with a radius gauge. A K above 0.5 usually means the real radius is larger than the one entered.
Outside or inside flanges?
Either, as long as you say which. Outside: from the edge of the flange to where the two outside faces would meet if extended. Inside: to where the inside faces would meet. Both give the same K for the same strip.
What do I do with the result?
Use it in the bend and profile tools on this site, or make a bend deduction chart with it for that thickness — the link under the result carries the thickness, K and radius across. Re-test when the material, the tooling or the radius changes.
Missing an option?
A different datum, an offset, a shop allowance, another shape altogether — say what this tool does not cover yet. Requests decide what gets built next, and a report of a wrong result is dealt with before anything new.
Rather have the whole part drawn — a shop drawing or a cut file from your sketch? That is paid drafting, quoted per job: drafting for small shops.
Related tools
Cone / Frustum Configurator
Flat pattern with inside/outside dimension basis, plate-roll or press-brake forming, bend angles and out-of-round — plus a clean DXF.
Open the tool →Hopper & Transition Builder
Develop a rectangular hopper or duct transition into four flat panels — centred or offset — with exact developed geometry and a DXF per panel.
Open the tool →Pipe Cut Template Builder
Wrap-around templates for angled pipe ends and pipe-to-pipe saddles, with the export deviation stated rather than assumed.
Open the tool →Segmented (Lobster-Back) Elbow Calculator
Mitred elbows from straight pipe or rolled sheet: cut angle, heel and throat lengths, a cut list for one pipe, and 1:1 templates plus DXF for each piece.
Open the tool →Square / Rectangle to Round Transition
One exact flat pattern for a square-to-round or rectangle-to-round, centred or offset — with true lengths, corner bend lines and a DXF.
Open the tool →Eccentric (Offset) Reducer Flat Pattern
Flat on one side or any offset: one exact flat pattern for an eccentric reducer or oblique cone, a true-length table for hand layout, and a DXF.
Open the tool →Sheet Metal Profile Builder
Build a multi-bend open profile from segments and bends. Live formed section, live flat pattern, and a DXF blank with a directed centreline per bend.
Open the tool →Rolled Cylinder Blank Calculator
Blank length for a rolled cylinder or shell course from the inside, outside or mean diameter and the plate thickness, with a seam gap and a DXF.
Open the tool →Box and Tray Blank Calculator
The flat blank for a sheet metal tray or open box: blank size from the outside dimensions and bend deductions, bend lines, corner notches and a DXF.
Open the tool →Sphere and Dome in Zones
Flat patterns for a sphere or dome built from zones: each band developed as a cone frustum on the chords, a flat crown disc, every pattern radius and angle, and a DXF.
Open the tool →Pipe Offset Calculator (Simple and Rolling)
Travel, run and cut length for simple and rolling pipe offsets at any fitting angle, with the constants and cut-length rule from the US Army pipe-fitting manual.
Open the tool →Metal Weight Calculator (Plate, Tube, Bar)
Weight of plate and sheet, discs and rings, tube and pipe, and round bar — per piece and per quantity — with every density traced to a US government document.
Open the tool →Sheet Metal Gauge Chart and Converter
What a gauge number means in inches and millimetres for steel and aluminium, what a galvanized gauge weighs, both ways — every value traced to a US government source.
Open the tool →Cone in Segments (Multi-Piece Cone)
A cone too big for one plate, split into identical segments: give a count or your plate size, get one segment’s size, angle and chords, and a DXF.
Open the tool →Single Bend Flat Pattern Configurator
Flat length and bend line from your finished flanges — with an explicit datum, a formed section you can check against, and a DXF blank.
Open the tool →Press Brake Tonnage Calculator
An estimate of the force for a 90° air bend from thickness, die opening, bend length and material: kN, metric and US tons, whole bend and per length, with how far to trust it.
Open the tool →Bend Deduction & Allowance Chart
Your own bend deduction, allowance or setback chart for one thickness and K: any radii, any angles, mm or inch, with a CSV download.
Open the tool →Flange / Bolt Circle DXF Generator
Lay out a bolt circle from OD, ID, PCD, hole size and count. Get exact hole coordinates and a DXF with centrelines.
Open the tool →Saved. Need a part drawn from your sketch or photo? A simple flat pattern or DXF of one part is typically C$40–80, with a free quote: drafting for small shops.