K Factor Calculation: Formula & How to Use It

This calculator works out the K factor for sheet metal bending: the ratio of the neutral axis position to the material thickness. You enter the inner bend radius, the material thickness, and the bend angle, and you get the K factor, along with the neutral axis offset and the bend allowance for a 90° bend. The K factor is a dimensionless number between 0 and 1 that lets you predict how much material stretches during bending, which is essential for accurate flat pattern development.

Formula

The K factor is defined as the distance from the inner surface of the bend to the neutral axis, divided by the material thickness. In symbols:

K = t_neutral / t

Where:

• t = material thickness (mm or inches)
• t_neutral = distance from the inner bend surface to the neutral axis (same unit as t)

The neutral axis is the imaginary plane inside the material that does not stretch or compress during bending. For a sharp bend (r/t small), the neutral axis sits closer to the inner surface, so K is small. For a gentle bend (r/t large), the neutral axis moves toward the center of the material, so K approaches 0.5. The calculator above uses a common empirical approximation:

K = 0.65 + 0.35 × log�₀(r / t)

This formula works reasonably for r/t ratios between 0.5 and 4. For r/t below 0.5, the logarithm becomes negative and the K factor can drop below 0.3, which matches real behavior for very tight bends. For r/t above 4, K approaches 0.5 asymptotically.

Worked Example

Using the default values: thickness t = 1.5 mm, inner radius r = 2.0 mm, bend angle a = 90°.

1. Compute r/t = 2.0 / 1.5 = 1.3333
2. Take log�₀(1.3333) = 0.1249
3. Multiply by 0.35 → 0.0437
4. Add 0.65 → K = 0.6937, which rounds to 0.694
5. Bend allowance for 90°: BA = (r + K × t) × (π/2) = (2.0 + 0.694 × 1.5) × 1.5708 = (2.0 + 1.041) × 1.5708 = 3.041 × 1.5708 = 4.78 mm

The calculator shows K = 0.694 and bend allowance = 4.78 mm for a 90° bend.

Why the K Factor Matters

When you bend a sheet metal part, the outer surface stretches and the inner surface compresses. Somewhere in between, there is a plane that keeps its original length — that is the neutral axis. The K factor tells you where that plane sits. If you know the K factor, you can calculate the bend allowance (the length of the neutral axis through the bend), which is exactly the amount of material you need to account for in the flat pattern. Without it, your finished part will be either too short or too long.

For example, a 90° bend with a 2 mm inner radius in 1.5 mm steel has a bend allowance of about 4.78 mm. If you ignored the bend allowance and just added the two leg lengths, you would end up with a part that is roughly 5 mm too short after bending. That is why press brake operators and CAD users rely on K factors for every bend.

How to Choose the Right K Factor

There is no single universal K factor — it depends on the material, the tooling, and the bend geometry. Here are the practical ranges:

• Sharp bends (r/t < 0.5): K often falls between 0.25 and 0.35. The neutral axis moves inward because the material thins significantly.
• Standard air bending (r/t between 0.5 and 2): K typically ranges from 0.33 to 0.45. Most general-purpose fabrication uses K ≈ 0.44 for mild steel.
• Large radius bends (r/t > 2): K approaches 0.5. For r/t > 5, many engineers simply use 0.5 because the neutral axis is essentially at the center.
• Aluminum: Often uses a slightly lower K (0.4 to 0.45) because it work-hardens differently.
• Stainless steel: Often uses a slightly higher K (0.45 to 0.5) because it has a higher yield strength.

If you have access to a physical sample, the most accurate way is to bend a test piece, measure the outside dimensions, and back-calculate the K factor from the bend allowance. Many CAD programs let you set the K factor per material and thickness, and they store tables from the material supplier or from your own shop trials.

Common Mistakes and Misconceptions

One frequent error is using the K factor as a fixed number for all bends. In reality, K changes with the r/t ratio — a 90° bend with a small radius has a different K than a 135° bend with a large radius. Another mistake is mixing units: if you enter the radius in inches and the thickness in millimeters, the ratio r/t is wrong by a factor of 25.4, which completely changes the K factor. Always use the same unit for both.

Another misconception is that the K factor is the same as the bend allowance. They are related but different: the K factor is a dimensionless ratio, while the bend allowance is a length. The bend allowance is calculated from the K factor, the radius, and the angle, as shown above. Also, the K factor does not account for springback — that is a separate phenomenon where the metal springs back slightly after bending, so the final angle is larger than the tool angle. Springback depends on the material’s yield strength and is not part of the K factor calculation.

Limitations of the Formula

The empirical formula used here (logarithmic) is a good approximation for air bending of common metals, but it is not universal. For bottoming or coining, where the punch forces the material into the die, the K factor can be different because the material is squeezed more. For very thin materials (under 0.5 mm) or very thick plates (over 25 mm), the formula may deviate from measured values. Also, the formula assumes a constant K across the bend, but in reality the neutral axis shifts slightly along the bend arc, especially for large angles.

For critical aerospace or medical parts, you should always use a K factor derived from actual test bends of the exact material and thickness you are using. The formula gives you a starting point, not a guarantee.

K Factor vs. Bend Deduction

In sheet metal shops, you will also hear about the bend deduction (BD). While the bend allowance is the length of the neutral axis through the bend, the bend deduction is the amount you subtract from the sum of the outside dimensions to get the flat length. They are related by:

BD = 2 × (r + t) × tan(a/2) − BA

Where a is the bend angle in degrees. The bend deduction is often easier for operators because they measure the outside of the part. If you know the K factor, you can compute the bend allowance and then the bend deduction. Many CAD systems let you input either K factor or bend deduction, and they convert internally. The K factor is the more fundamental property because it is dimensionless and transferable between different bend angles, while the bend deduction depends on the specific angle and radius.

Frequently Asked Questions

What is a typical K factor for mild steel?

For mild steel air bending with a standard V-die, a common K factor is 0.44 for r/t ratios around 1. For tighter bends (r/t = 0.5), K drops to about 0.33. For larger radii (r/t = 3), K rises to about 0.46. Always check with your material supplier if you need high accuracy.

How do I measure the K factor from a test bend?

Bend a sample at a known angle and inner radius, then measure the outside dimensions (leg lengths). Calculate the flat length you would need if there were no bend allowance, subtract the measured flat length, and that gives you the bend allowance. Then rearrange the bend allowance formula to solve for K: K = (BA / (π/180 × a) − r) / t.

Does the K factor change with bend angle?

Yes, slightly. The neutral axis shifts a little as the bend angle increases, but many formulas ignore this for simplicity. For angles between 30° and 120°, the change is usually less than 0.02 in K, which is acceptable for most fabrication. For very acute or obtuse angles, you may need to adjust.

What is the difference between K factor and Y factor?

The Y factor is an older term used in some CAD systems, defined as Y = K × π/2. So Y is approximately 1.57 times the K factor. Both serve the same purpose, but K is more common now. If you see a Y factor of 0.5, that corresponds to K = 0.318.

Can I use the K factor for tube bending?

No, the K factor is specifically for flat sheet metal bending. Tube and pipe bending uses a different set of parameters, such as the neutral axis shift and the wall factor, because the cross-section is not rectangular and the material behaves differently.

Why does my CAD software ask for a K factor when I use a bend table?

CAD software uses the K factor to calculate the flat pattern automatically for any bend angle and radius. A bend table is just a precomputed set of K factors for different materials and thicknesses. If you have your own bend table, you can enter those values directly, but the K factor is the underlying variable that makes the calculation work.

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in t | Material thickness | mm | 1.5 | 0
in r | Inner bend radius | mm | 2.0 | 0
in a | Bend angle | degrees | 90 | 0
out k | K factor | - | (0.65 + 0.35 * log10(max(r / t, 0.01))) / 1.0 | 3
out ba | Bend allowance (90°) | mm | (r + k * t) * (90 * pi / 180) | 2