Sheet Metal Bend Allowance & K-Factor Calculator

What this calculator computes

This tool turns the geometry of a sheet-metal bend into the numbers a fabricator needs to cut the blank right the first time. From the bend angle, inside radius, thickness, and K-factor it computes the bend allowance, the bend deduction, and the outside setback, and it uses them to find the flat-pattern length — the developed length of the flat blank before bending — for one bend or many. It also runs in reverse: give it a measured flat length from a test bend and it solves for the K-factor that matches your material and tooling. It works in metric or imperial units and plots how the K-factor changes with the ratio of radius to thickness.

The reason these calculations matter is that a bend consumes material in a way that is not obvious from the finished dimensions. When a flat sheet is folded, the metal on the outside of the bend stretches and the metal on the inside compresses, so the true length of material used through the bend is neither the inside dimension nor the outside dimension, but the length of the neutral axis somewhere between them. Cut the blank to the wrong length and every bent dimension is off. Bend allowance, deduction, and the K-factor are the tools that account for this consumed material precisely, so the flat blank unfolds to the correct part.

What sets this calculator apart is that it is a complete flat-pattern tool, not a single-formula gadget. It reports the bend allowance and the bend deduction together, computes the flat length by both methods so it matches however your drawing is dimensioned, handles multi-bend parts, and — crucially — solves the K-factor from a measured blank so you can calibrate to your own shop. It carries a K-factor reference table by material, plots K against R/T, and runs entirely in your browser with nothing stored.

How to use this calculator, step by step

Begin by choosing the mode and units. The default mode computes the flat length and the bend values from your geometry; the other mode solves the K-factor from a blank you have already measured. Choose metric millimetres or imperial inches to match your drawing. The input fields change with the mode, so you are only asked for what that mode needs.

Enter the bend geometry: the bend angle in degrees, the inside radius, and the material thickness. In flat-length mode you also enter the K-factor — use a value from the reference table below if you do not have a measured one — the number of bends, and the leg lengths. Enter the sum of the leg lengths measured to the bend lines for the bend-allowance method, and the sum of the outside leg lengths for the bend-deduction method. The calculator opens on a worked example, a single 90° bend in 1 mm material at a 1 mm radius with K = 0.33 and two 30 mm legs, giving a flat length of about 62.09 mm, and every field recomputes live as you type.

Read the result panel, which leads with the flat-pattern length and then lists the bend allowance, bend deduction, outside setback, and the flat length computed by the deduction method for cross-checking. The chart shows how the K-factor typically rises with the R/T ratio, which explains why a single material does not have one fixed K. In solve-for-K mode, enter your measured flat length and the calculator returns the K-factor and the implied bend allowance. You can download or share the result, all locally.

The neutral axis and the K-factor

Everything in bend calculation follows from one physical fact: when sheet metal bends, it does not keep the same length everywhere through the thickness. The material on the outside of the bend is stretched into a longer arc, and the material on the inside is compressed into a shorter one. Between them lies the neutral axis, the one layer whose length is unchanged by the bend. Because it is the layer that neither stretches nor shrinks, the length of the neutral axis through the bend is exactly the amount of flat material the bend consumes — which is why every bend-allowance formula is really a calculation of the neutral axis arc length.

The neutral axis does not sit at the middle of the thickness. Compression and tension in bending are not symmetric: the inner fibres compress more readily than the outer fibres stretch, so the neutral axis shifts toward the inside of the bend. The K-factor is the number that records this shift. Defined as K = t/T, the distance from the inside surface to the neutral axis divided by the total thickness, it would be 0.5 if the neutral axis were centred, but in real bends it is smaller, typically between 0.30 and 0.50. A lower K means the neutral axis is closer to the inside and the bend consumes less material; a higher K means it is nearer the centre and the bend consumes more.

Because the K-factor pins down where the neutral axis lies, it is the one empirical input that makes the geometry match reality. The bend-allowance formula, BA = (π/180)·θ·(R + K·T), is simply the arc length of a circle of radius (R + K·T) — the radius out to the neutral axis — swept through the bend angle θ. Get K right and the formula predicts the real flat length; get it wrong and every calculation inherits the error. This is why K, though only a fraction between zero and a half, is the heart of sheet-metal flat-pattern work.

Bend allowance, bend deduction, and setback

Three related quantities describe what a bend does to the flat length, and knowing how they connect keeps the arithmetic straight. The bend allowance is the length added by the bend — the neutral-axis arc — and it is used with leg lengths measured to the bend lines, the tangent points where each flat leg meets the curved part. The flat length by this method is the sum of those leg lengths plus one bend allowance per bend. This is the most direct method when the part is dimensioned to the bend lines or when you are building the flat from the neutral-axis geometry.

The bend deduction is the length removed from the outside dimensions. Drawings often give the outside dimensions of a bent part — the leg lengths measured to the sharp outside corners where the faces would meet if extended.

Those outside legs overlap at each corner by more than the real material, so a deduction is subtracted: the flat length is the sum of the outside legs minus one bend deduction per bend. The link between the two methods is the outside setback, the distance from the tangent point to the sharp outside corner, given by OSSB = tan(θ/2)·(R + T).

The bend deduction is exactly twice the setback minus the bend allowance, BD = 2·OSSB − BA, because each leg’s outside dimension includes one setback beyond the tangent point.

Both methods give the same flat length; they differ only in which dimensions you start from, and this calculator reports both so you can use whichever matches your drawing and cross-check the two. For a right-angle bend the setback is simply R + T, since tan(45°) is one, and the deduction and allowance are close in value; for sharper or shallower bends the setback and the two quantities diverge, which is why the general formulas, not the right-angle shortcuts, are what the calculator evaluates.

Five worked examples you can follow

Example 1: the default single bend

A 90° bend in 1 mm material at a 1 mm inside radius with K = 0.33 and two 30 mm legs. The bend allowance is (π/180)·90·(1 + 0.33·1) ≈ 2.09 mm, the outside setback is 1·(1 + 1) = 2 mm, and the bend deduction is 2·2 − 2.09 ≈ 1.91 mm. The flat length is 60 + 2.09 ≈ 62.09 mm.

Example 2: the deduction method

The same part dimensioned to its outside corners has two 31 mm outside legs, 62 mm total. Subtracting the 1.91 mm bend deduction gives a flat length of about 60.09 mm — the same blank, reached from the outside dimensions instead of the bend lines.

Example 3: a multi-bend part

A tray with four 90° bends, the same 1 mm material and radius, and 100 mm of legs to the bend lines. The flat length is 100 + 4·2.09 ≈ 108.4 mm. Each bend adds its own allowance, so the number of bends multiplies the correction.

Example 4: solving for K

You bend a test coupon with two 30 mm legs, a 90° bend, 1 mm material, 1 mm radius, and measure the flat blank at 62.089 mm. Switch to solve-for-K mode: the implied bend allowance is 62.089 − 60 = 2.089 mm, and the K-factor that produces it is 0.33 — now calibrated to your material and tooling.

Example 5: a wide-radius bend

A 90° bend in 2 mm material at a 6 mm radius has R/T = 3, a gentle bend, so a higher K near 0.45 is appropriate. The bend allowance is (π/180)·90·(6 + 0.45·2) ≈ 10.8 mm — much larger than the tight-radius case, because the neutral axis sweeps a bigger arc.

Three expert tips for reliable results

The mathematics behind the results

The bend-allowance formula is the arc length of the neutral axis. A circular arc of radius ρ swept through an angle θ in degrees has length (π/180)·θ·ρ. The neutral axis lies a distance K·T out from the inside surface, so its radius from the bend centre is ρ = R + K·T, where R is the inside radius. Substituting gives BA = (π/180)·θ·(R + K·T). Every term has a clear meaning: θ sets how much of the circle the bend covers, R + K·T is the radius out to the layer that does not change length, and the leading factor converts degrees to the radian measure the arc length needs. The calculator evaluates this directly for any angle.

The outside setback comes from the geometry of the sharp corner. Extending the two outside faces until they meet forms a right triangle whose legs run from the tangent point to the apex; the angle at the apex is half the bend angle, and the far side is the outside radius R + T. Trigonometry gives OSSB = tan(θ/2)·(R + T).

The bend deduction then follows from bookkeeping: each outside leg length is its bend-line leg plus one setback, so summing two outside legs double-counts material by two setbacks, while the true flat needs only the bend allowance added; the deduction that reconciles them is BD = 2·OSSB − BA.

The flat-length formulas are then just addition: legs to bend lines plus allowances, or outside legs minus deductions.

The solve-for-K calculation inverts the bend-allowance formula. From a measured flat length and the known leg lengths, the implied bend allowance per bend is (measured flat − sum of legs) ÷ number of bends. Setting that equal to (π/180)·θ·(R + K·T) and solving for K gives K = [BA ÷ ((π/180)·θ) − R] ÷ T.

This is exact given accurate measurements, and it is the most reliable way to obtain K because it captures the real behaviour of your specific material, thickness, tooling, and bending method rather than relying on a table.

The one assumption throughout is that the bend is a clean circular arc of constant inside radius; springback, coining, and very tight bends introduce effects beyond this geometric model, which is why calibrating K to real bends matters for precision work.

Some CAD systems express the same neutral-axis idea through a Y-factor instead of a K-factor, where Y = K × (π/2). The two are interchangeable, and both describe the identical physics — the position of the neutral axis — so a K-factor from this calculator converts directly to a Y-factor by that constant when your software asks for one.

Whichever your CAD uses, the flat-pattern length it produces should agree with the value here for the same geometry, and any disagreement usually points to a different bend-angle convention or a K-factor entered under one definition but interpreted under the other.

Keeping the definitions straight is the last step in making hand calculations and CAD unfolds match.

Where bend calculations are used

Flat-pattern calculation is the foundation of sheet-metal fabrication, the step between a part design and the cut blank.

In design and CAD, every sheet-metal model unfolds to a flat pattern using exactly these formulas, and the K-factor is the setting that makes the CAD flat match the real part; getting it right avoids parts that are consistently a millimetre or two off after bending.

In the shop, the flat pattern drives the cutting operation — the laser, punch, or shear that produces the blank — and an error here wastes material and scraps parts, since a blank cut to the wrong length cannot be corrected after bending. This tool sits at the start of the forming workflow, feeding the blank size that the press brake then bends.

The calculation connects to the other forming and fabrication tools in this silo. The blank it sizes is the workpiece the press and stamping force calculator then evaluates for the tonnage needed to bend it, and the sheet it develops may first be cut to size by shearing or punching, whose force is the same kind of calculation. On the machining side of the silo, the same discipline of accounting for material precisely underlies the cutting calculators, though the physics differs. Return to the Manufacturing Processes hub for the companion tools across machining, forming, and molding.

Beyond the individual part, bend calculations support estimating, nesting, and quality. The flat size feeds material estimates and nesting layouts that decide how many blanks fit on a sheet, and therefore the material cost per part. It underlies quality control, because a part that bends to the wrong dimension usually traces back to a wrong K-factor or flat length rather than to the bending itself. And it informs tooling and process choices, since the achievable inside radius — set by the punch and die — feeds straight back into the R and R/T that drive the K-factor. Accurate flat patterns are what let a sheet-metal shop cut once and bend to size.

K-factor reference by material

When you do not have a measured K-factor, these typical values give a defensible starting point. They assume a moderate bend radius; adjust downward for tight bends and upward for wide-radius bends, because the R/T ratio matters more than the material choice. For any part where the flat size is critical, calibrate K from a test bend using this calculator’s solve-for-K mode rather than relying on the table alone.

Read these values together with the R/T ratio. A tight bend, where the inside radius is smaller than the thickness, pulls the neutral axis inward and lowers the effective K below the table value; a generous radius, several times the thickness, pushes it toward 0.5. The table gives a first estimate for a typical bend; the chart on this page shows the R/T trend; and a measured test bend gives the definitive value for a critical job.

Air bending, bottoming and coining

How a bend is formed on the press brake changes the effective K-factor, which is why the same material can need different values on different machines. In air bending, the most common method, the punch pushes the sheet into a wide V-die without forcing it to the bottom, and the bend radius is set by the die opening and the punch travel rather than by the punch tip. Air bending gives the most springback and the least repeatable radius, so its K-factor varies more and calibration matters most. It is favoured because one tool set bends many angles and thicknesses with low tonnage.

Bottoming presses the sheet firmly against the die, so the inside radius is set by the die and springback is reduced; the K-factor is more consistent than in air bending and closer to the material’s nominal value.

Coining goes further still, forcing the punch into the material under very high tonnage so the metal yields through its full thickness, which nearly eliminates springback and produces a tight, precise radius — at the cost of much higher force. Because coining strains the whole section, its neutral-axis behaviour differs from the light-bending model, and its K-factor tends toward higher values.

Whichever method your shop uses, the reliable path is to calibrate the K-factor from a test bend made the same way as the production part, so the geometric model is anchored to the real process.

Springback and why calibration matters

Springback is the elastic recovery that occurs when the bending force is released: the metal relaxes slightly and the bend opens up, so the part springs back to a larger angle and a larger radius than the tooling formed. It happens because only part of the bending strain is permanent; the elastic part reverses when the load comes off. Springback grows with material strength and with the bend radius, and it is the reason press-brake operators over-bend — forming to a tighter angle than the target so the part relaxes to the right one. It affects the flat pattern indirectly: the final radius after springback, not the radius in the tool, is the R that governs the true bend allowance.

This is the deepest reason to calibrate the K-factor rather than trust a table. A measured K from a test bend captures not just where the neutral axis sits but the net effect of springback, the real formed radius, the tooling, and the bending method, all rolled into one number that makes the flat pattern come out right.

The geometric model in this calculator assumes a clean circular arc at a definite inside radius; springback, coining, and very tight bends push reality away from that ideal.

Calibrating K absorbs the difference, which is why a shop that measures its own K-factors for its own materials and tooling gets flat patterns that unfold to size, while one relying on generic values chases dimensional errors bend after bend.

From flat pattern to material cost

The flat-pattern length is not only a cutting dimension; it is the basis of the material cost of a sheet-metal part. Once the flat blank is known, its area and the way multiple blanks nest on a standard sheet determine how many parts come from each sheet, and therefore the material cost per part and the scrap rate.

An accurate flat pattern lets a nesting layout pack blanks tightly and predict yield; an inaccurate one either wastes material through excess margins or, worse, produces blanks that bend to the wrong size and become scrap.

The few millimetres that a correct bend allowance adds or removes, multiplied across every blank on a sheet and every sheet in a job, move the material cost and the yield measurably.

The flat pattern also drives the cutting operation that produces the blank, whether laser, plasma, waterjet, punch, or shear, and the cut length and pierce count that set that operation’s time and cost come from the flat outline. In this way the bend calculation feeds both the material estimate and the cutting estimate that together make up much of a fabricated part’s cost, before the forming and finishing operations are added. Getting the flat pattern right at the design stage is therefore not just a matter of dimensional correctness but of costing accuracy, which is why sheet-metal estimating begins with an accurate unfold.

Common mistakes to avoid

A few errors recur in flat-pattern calculations. Watch for them.

• Guessing the K-factor for critical parts. A table value can be off enough to spoil a tight tolerance. Calibrate K from a test bend when the flat size matters.
• Mixing the two methods. Bend allowance uses legs to the bend lines; bend deduction uses outside legs. Adding a deduction to bend-line legs, or an allowance to outside legs, doubles or drops a correction.
• Confusing bend angle with included angle. The formulas use the angle the sheet is bent through (90° for a right angle). If the drawing gives the included angle between faces, convert with bend angle = 180° − included angle.
• Ignoring R/T. Using one fixed K for every bend ignores that tight and wide bends have very different neutral-axis positions. Let R/T adjust the K-factor.
• Forgetting to multiply by the number of bends. Each bend consumes its own allowance or deduction. A four-bend part needs four corrections, not one.
• Overlooking springback and coining. The geometric model assumes a clean arc; heavy coining or springback shifts the result, which is another reason to calibrate K to your actual process.

Input format and quick reference

Choose a mode and units, then enter the bend angle, inside radius, thickness, K-factor, number of bends, and leg lengths; in solve-for-K mode enter the measured flat length instead. The reference below explains each output.

Frequently asked questions

Sources, disclaimer and editorial transparency

This calculator uses the standard sheet-metal relations: bend allowance BA = (π/180)·θ·(R + K·T); outside setback OSSB = tan(θ/2)·(R + T); bend deduction BD = 2·OSSB − BA; and flat length as legs + n·BA or outside legs − n·BD, consistent with standard sheet-metal design practice and references such as DIN 6935. The typical K-factor values by material are published ranges for general guidance. This calculator and guide are created and reviewed by the OpsCalculators team; see our Editorial Policy for how each tool is researched, built, and tested.

Results are accurate estimates for design, estimating, and education, not a substitute for a calibrated K-factor from your own test bends. Springback, coining, tooling, and very tight radii shift real results beyond the geometric model. See our full Disclaimer. OpsCalculators.com is operated by MAFHH INTERNATIONAL LTD. Your data is processed in your browser and never stored; see our Privacy Policy.