Flat Pattern Calculator: Bend Allowance & K-Factor

A flat pattern calculator works out the size of a sheet metal blank before it is bent, using the bend allowance and K-factor. You enter the material thickness, inside bend radius, bend angle, and K-factor, and it returns the flat length of the part (the length of the neutral axis) plus the bend allowance for each bend.

Formula

The bend allowance (BA) is the arc length of the neutral axis—the imaginary line inside the material that does not stretch or compress during bending. The standard formula is:

BA = θ × (π / 180) × (r + K × t)

• BA = bend allowance (mm or in)
• θ = bend angle in degrees (90° for a right-angle bend)
• r = inside bend radius (same unit as t)
• K = K-factor (dimensionless, typically 0.3–0.5)
• t = material thickness (same unit as r)

The flat length is the sum of the straight sections plus the bend allowance for each bend. For a single bend with no straight flanges, the flat length equals the bend allowance plus the two straight leg lengths (if any). The calculator above gives the bend allowance and the flat length per bend (the arc length contribution).

Worked Example

Using the defaults: t = 2 mm, r = 3 mm, θ = 90°, K = 0.44.

1. Convert the angle to radians: 90 × (π / 180) = 1.5708 rad
2. Compute the neutral axis radius: r + K × t = 3 + 0.44 × 2 = 3.88 mm
3. Multiply: 1.5708 × 3.88 = 6.0947 mm
4. Round to 2 decimals: bend allowance = 6.09 mm

The flat length per bend is the same value in this case because there are no straight legs. If the part has two 20 mm flanges, the total flat length would be 20 + 6.09 + 20 = 46.09 mm.

What Is the K-Factor and Why Does It Matter?

The K-factor is the ratio of the distance from the inside face of the bend to the neutral axis, divided by the thickness. A K-factor of 0.5 means the neutral axis is exactly in the middle of the material—that happens only with very large bend radii. For typical air bending, the K-factor is between 0.3 and 0.5, with 0.44 being a common default for mild steel.

The K-factor depends on the material, the bend method (air bending, bottoming, coining), and the ratio of bend radius to thickness. A smaller K-factor means more material is stretched, so the bend allowance is smaller. If you use the wrong K-factor, your flat pattern will be off by a noticeable amount—often 0.1–0.3 mm per bend, which accumulates over multiple bends.

Most CAD sheet metal tools let you set a K-factor table based on material and thickness. If you do not have a table, start with 0.44 for air bending of steel, 0.35 for aluminum, and 0.5 for a sharp bend (radius much smaller than thickness).

How to Use the Flat Pattern Calculator

To get an accurate flat pattern, follow these steps:

1. Measure the material thickness with calipers—do not rely on nominal gauge.
2. Measure the inside bend radius of the finished part (or use the punch radius for air bending).
3. Determine the bend angle (90° for a right angle, but acute and obtuse angles are common).
4. Choose a K-factor from a reliable table or from your shop’s experience.
5. Enter these values into the calculator to get the bend allowance.
6. Add the bend allowance to the sum of the straight flange lengths (measured to the tangent points, not to the mold line).

For a part with multiple bends, calculate the bend allowance for each bend separately—they may have different radii or angles—then sum all straight lengths and all bend allowances.

Common Mistakes and How to Avoid Them

One frequent error is using the outside radius instead of the inside radius. The formula uses the inside radius because the neutral axis is measured from the inside surface. If you only know the outside radius, subtract the thickness to get the inside radius.

Another mistake is mixing units. The formula requires consistent units—if thickness is in mm, radius must be in mm, and the result will be in mm. If you mix inches and mm, the answer will be off by a factor of 25.4.

Rounding too early is also a problem. Keep at least four decimal places during intermediate steps, then round the final answer to two decimals (or one decimal for larger parts). The calculator above rounds outputs to two decimals, which is fine for most fabrication work.

Finally, remember that the K-factor is not a constant for a material—it changes with the bend radius. Using a fixed K-factor for all bends can cause inaccuracies, especially for tight radii (r/t < 1) or very large radii (r/t > 5). In those cases, consult a bend allowance table or use a more advanced model.

Limitations of the Formula

The bend allowance formula is an approximation based on the neutral axis concept. It works well for air bending of ductile metals like steel, aluminum, and stainless steel, but it does not account for:

• Springback—the material’s tendency to relax after bending, which changes the final angle.
• Material thinning at the bend—especially with hard materials or tight radii.
• Grain direction—bending parallel to the grain can cause cracking, but this does not affect the flat length.
• Tooling variations—different punch and die radii produce different actual bend radii.

For high-precision work, you may need to run test bends and adjust the K-factor empirically. The formula gives a starting point that is usually within 0.2 mm for a single bend.

When to Use a Flat Pattern Calculator vs. CAD Software

If you are working in a CAD package with sheet metal tools, the software will compute the flat pattern automatically using its own bend allowance tables. The calculator is useful when you are working without CAD, need a quick sanity check, or want to understand the math behind the software.

For a single bend or a simple bracket, the calculator is faster than setting up a CAD model. For complex parts with many bends, CAD is more reliable because it handles the geometry of flanges, reliefs, and corner treatments. However, even CAD users benefit from knowing the bend allowance to verify that the software’s K-factor matches their shop’s reality.

Frequently Asked Questions

What is the difference between bend allowance and bend deduction?
Bend allowance is the arc length of the neutral axis, which you add to the straight lengths to get the flat length. Bend deduction is the amount you subtract from the sum of the outside dimensions (the mold line dimensions) to get the flat length. They are two ways of expressing the same correction. The relationship is: bend deduction = 2 × (r + t) × tan(θ/2) − bend allowance.

How do I find the K-factor for my material?
You can use a published table from a sheet metal handbook, or you can determine it experimentally: bend a sample, measure the flat length, and solve the formula for K. Many shops use a default of 0.44 for mild steel air bending, but this varies with thickness and radius. Some CAD software includes K-factor tables based on material and thickness.

Does the bend allowance formula work for aluminum?
Yes, the formula is material-agnostic—it works for any ductile metal. The K-factor differs for aluminum (typically 0.35–0.45) because aluminum has a different yield strength and elongation. Use a K-factor appropriate for your specific alloy and temper.

What if my bend radius is very small, like 0.5 mm on 2 mm steel?
With a radius-to-thickness ratio below 1, the neutral axis shifts, and the K-factor becomes lower (around 0.3–0.35). The formula still works, but the accuracy decreases. For sharp bends, you may need to use a bend allowance table specific to tight radii.

Can I use this calculator for a 180° hem?
Yes, but the bend angle is 180°, and the formula gives the bend allowance for a full fold. However, a hem typically involves two bends (a 90° bend then a flattening), so you would calculate each step separately. The K-factor for a hem is often lower because the material is compressed.

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in t | Material thickness | mm | 2 | 0
in r | Inside bend radius | mm | 3 | 0
in a | Bend angle | degrees | 90 | 0
in k | K-factor | - | 0.44 | 0
out ba | Bend allowance | mm | (a * (pi / 180)) * (r + (k * t)) | 2
out flat | Flat length (per bend) | mm | (r + t) * (a * (pi / 180)) + ba | 2