Sheet Metal Flat Pattern Calculator: Bend Allowance

A sheet metal flat pattern calculator works out the flat blank length you need to cut before bending a part, based on the material thickness, bend angle, inside radius, and the bend allowance or bend deduction method you choose. You enter those dimensions and the calculator returns the flat length, and often the bend allowance and outside setback as well, so you can lay out the part accurately before forming.

Formula

The calculator uses the standard bend allowance formula for a 90-degree bend, which is a simplified version of the K-factor method:

Bend Allowance (BA) = (π / 180) × A × (R + K × T)

Where:

• A = bend angle in degrees (90 for a right-angle bend)
• R = inside bend radius in millimeters (or inches)
• T = material thickness in the same unit as R
• K = K-factor, a constant between 0.3 and 0.5; the calculator uses 0.44 for a typical air bend, which is a common default for mild steel.

The flat length is then:

Flat Length = L1 + L2 – 2 × (R + T) + BA

Here L1 and L2 are the outside leg lengths (measured from the outside of the bend tangent points), and the term 2 × (R + T) subtracts the overlap of the two legs at the bend. This is the standard “outside dimension� method used in most shops.

Worked Example

Using the default values from the calculator (T = 1.5 mm, R = 2 mm, A = 90°, L1 = 50 mm, L2 = 30 mm):

1. Convert the angle to radians: 90 × (π/180) = 1.5708 radians.
2. Calculate the neutral axis radius: R + 0.44 × T = 2 + 0.44 × 1.5 = 2 + 0.66 = 2.66 mm.
3. Bend allowance: 1.5708 × 2.66 = 4.18 mm.
4. Subtract the bend region from the leg sum: 50 + 30 – 2 × (2 + 1.5) = 80 – 7 = 73 mm.
5. Add the bend allowance: 73 + 4.18 = 77.18 mm.

The flat pattern length is 77.18 mm. If you cut a strip that length and bend it 90° with a 2 mm inside radius, the outside legs will measure 50 mm and 30 mm.

Why the Flat Pattern Length Matters

When you bend sheet metal, the material stretches on the outside of the bend and compresses on the inside. The neutral axis—the line that keeps its original length—sits somewhere between the inner and outer surfaces, not at the center. The flat pattern length is the length of that neutral axis along the bend. If you cut the blank to the outside dimensions without accounting for this, the part will come out too long or too short. A flat pattern calculator saves you from trial-and-error scrap, especially when you have many bends or tight tolerances.

For a single 90° bend, the difference between the outside dimension sum and the flat length is called the bend deduction. For the example above, the deduction is (50 + 30) – 77.18 = 2.82 mm. In practice, you often see tables that list bend deductions for specific material thicknesses and radii, but a calculator lets you interpolate for any combination.

How to Use the Calculator Correctly

To get a useful result, you need to measure the inputs the same way the formula expects:

• Leg lengths: Measure from the outside of the bend to the end of the leg, not from the inside. This matches the formula’s assumption.
• Inside radius: Use the radius of the punch (for air bending) or the die radius if you are bottoming. If you do not know it, measure the inside of an existing bend.
• Material thickness: Use the nominal thickness, but for high-accuracy work, measure the actual sheet—mild steel can vary by a few hundredths of a millimeter.
• Bend angle: Enter the included angle of the bend (90° for a right angle, not the complement).

After you get the flat length, add a little extra material (usually 1-2 mm) if you plan to trim the edges later, but for most parts, the calculated length is the cut size.

Common Mistakes and How to Avoid Them

Three mistakes cause most flat pattern errors:

1. Mixing units: If you enter thickness in mm and radius in inches, the result is meaningless. Keep all dimensions in the same unit.
2. Using the wrong K-factor: The 0.44 default works for air bending of mild steel, but for aluminum or stainless, the K-factor can be 0.4 or 0.5. If you have a specific material, look up its K-factor or test a sample.
3. Forgetting the bend deduction for multiple bends: For a part with several bends, you must sum the bend allowances for all bends and subtract the overlaps from the total outside length. The calculator handles one bend; for multiple bends, repeat the calculation for each and add the leg lengths between bends.

Also, the formula assumes a sharp bend with a defined radius. If the inside radius is less than the material thickness (a sharp bend), the material may crack, and the formula becomes less accurate. In that case, use a larger radius or a different method.

Bend Allowance vs. Bend Deduction

Two related terms often confuse beginners. Bend allowance is the length of the neutral axis along the bend arc. Bend deduction is the amount you subtract from the sum of the outside dimensions to get the flat length. They are related by:

Bend Deduction = 2 × (R + T) – BA

For the example, that is 2 × (2 + 1.5) – 4.18 = 7 – 4.18 = 2.82 mm, which matches the difference we saw earlier. Some calculators ask for one or the other; this one uses bend allowance because it is more directly tied to the geometry.

Limitations of the Formula

The K-factor method is an approximation. It assumes the neutral axis shifts linearly with the ratio of inside radius to thickness, but in reality, the shift depends on the material, the bending method (air, bottoming, coining), and the tooling. For most prototyping and low-volume work, the 0.44 default gives parts within a few tenths of a millimeter. For high-precision production, you should calibrate the K-factor by bending a sample, measuring the flat length, and back-calculating the actual K-factor. The formula also does not account for springback, which changes the final angle and requires over-bending.

For very thick materials (T > 6 mm) or very large radii (R > 10 × T), the formula still works but may need a different K-factor. In those cases, consult a bend allowance chart from your material supplier or run a test.

Frequently Asked Questions

What is the difference between bend allowance and bend deduction?

Bend allowance is the arc length of the neutral axis through the bend. Bend deduction is how much you subtract from the sum of the outside leg lengths to get the flat length. They are two ways to express the same correction: flat length = sum of outside dimensions – bend deduction, or flat length = sum of outside dimensions – 2×(R+T) + bend allowance.

How do I find the K-factor for my material?

The K-factor is typically between 0.3 and 0.5. For mild steel with air bending, 0.44 is a common starting point. For aluminum, use 0.4; for stainless steel, 0.5. To get an exact value, bend a sample at 90°, measure the flat length and the outside dimensions, then solve for K using the formula. Many CAD programs have built-in K-factor tables for specific materials.

Can I use this calculator for multiple bends?

Yes, but you must do it step by step. For each bend, calculate the bend allowance using the same formula. Then, add the lengths of the straight sections between bends (measured from tangent point to tangent point) and sum all the bend allowances. The total is the flat length. The calculator handles one bend, so for a part with several bends, repeat the calculation for each and add the results.

What if my bend radius is not specified?

If you do not know the inside radius, you can estimate it as equal to the material thickness for air bending, or use the die opening divided by 6 for a typical 90° bend. For example, a 12 mm die opening gives an inside radius of about 2 mm. If you are using a press brake with a punch, the punch radius is a good approximation.

Does the formula work for aluminum or stainless steel?

Yes, but you may need to adjust the K-factor. Aluminum generally has a lower K-factor (around 0.4) because it stretches less, while stainless steel has a higher one (around 0.5) because it work-hardens and stretches more. If you use the default 0.44, you might be off by a few tenths of a millimeter, which is acceptable for many applications but not for tight tolerances.

Why is my flat pattern length different from what the calculator gives?

This usually happens because the actual inside radius is different from what you entered, or because the material thickness varies. Also, if you measured the leg lengths from the inside of the bend instead of the outside, the result will be off. Finally, the bending method (air vs. bottoming) changes the K-factor. Recheck your measurements and, if necessary, calibrate the K-factor with a test bend.

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in t | Material thickness | mm | 1.5 | 0
in r | Inside bend radius | mm | 2 | 0
in a | Bend angle | deg | 90 | 0
in l1 | Leg length 1 (outside) | mm | 50 | 0
in l2 | Leg length 2 (outside) | mm | 30 | 0
out ba | Bend allowance | mm | (0.017453 * a) * (r + 0.44 * t) | 2
out flat | Flat pattern length | mm | l1 + l2 - 2 * (r + t) + ba | 2