Flat Pattern Bend Calculator: K-Factor & Deduction

A flat pattern bend calculator works out the flat blank length of sheet metal before bending, using the bend allowance, bend deduction, and K-factor. You enter the material thickness, inside bend radius, bend angle, and K-factor (or a default), and it returns the flat length and bend allowance for a 90° bend or any angle. This is the length you cut before forming, so the part ends up at the right size after the bend.

Formula

The calculator uses the standard bend allowance formula for a single bend:

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

• θ = bend angle in degrees (90° for a right-angle bend)
• R = inside bend radius (same unit as T, usually mm or inches)
• K = K-factor, a dimensionless number between 0 and 1 (typically 0.3 to 0.5)
• T = material thickness (same unit as R)

The flat length for a simple 90° bend with one bend is then the bend allowance plus the two straight legs. For a single bend with equal legs, the flat length = BA + T + R (as shown in the calculator). For multiple bends, you add the bend allowances for each bend plus the straight sections between them.

Worked Example

Using the default values: T = 1.5 mm, R = 2 mm, angle = 90°, K = 0.44.

1. Convert 90° to radians: 90 × (π / 180) = 1.5708 radians
2. Calculate R + K × T = 2 + 0.44 × 1.5 = 2 + 0.66 = 2.66 mm
3. Multiply: 1.5708 × 2.66 = 4.18 mm (bend allowance)
4. Flat length = 4.18 + 1.5 + 2 = 7.68 mm

The calculator gives BA = 4.18 mm and flat length = 7.68 mm (rounded to 2 decimals). That matches the hand calculation.

What Is the K-Factor?

The K-factor is the ratio of the distance from the neutral axis to the inside surface of the bend, divided by the material thickness. During bending, the material on the inside compresses and the outside stretches; the neutral axis is the plane that keeps its original length. The K-factor tells you where that neutral axis sits. For soft materials like aluminum, it’s often around 0.4–0.45; for steel, commonly 0.4–0.5. A higher K-factor means more material is stretched, so the bend allowance is larger. If you don’t have a measured value, 0.44 is a reasonable starting point for many materials.

How to Choose a K-Factor

There is no single universal K-factor; it depends on material, thickness, bend radius, and the bending process. Here are practical guidelines:

• Air bending (most common press brake): K-factor typically 0.4–0.5
• Bottoming or coining: K-factor can be lower, around 0.3–0.4
• Sharp bends (radius less than material thickness): K-factor tends toward 0.3
• Large radii (radius > 5× thickness): K-factor approaches 0.5

For precise work, you should test-bend a sample and measure the actual flat length, then back-calculate the K-factor. Many CAD programs have built-in K-factor tables for common materials.

Common Mistakes and Misconceptions

A frequent error is using the outside radius instead of the inside radius. The formula uses the inside radius. Another mistake is mixing units—if thickness is in mm, radius must also be in mm. Also, the bend allowance formula assumes a constant K-factor, but in reality the neutral axis shifts with the bend angle and radius. For very large bend angles (over 120°), the simple formula becomes less accurate. Another misconception is that the flat length equals the sum of the two outside dimensions; that would ignore the material that stretches or compresses in the bend zone. Always use the bend allowance.

Limitations of the Formula

The formula is a simplification. Real bending involves springback, material thinning, and variations in the bend radius along the bend line. For high-precision work, you need actual test data. The formula also assumes a single bend; for multiple bends, you must add each bend allowance and the straight sections. It does not account for grain direction, which can affect bending across vs. along the grain. For most fabrication work, the formula gives a good starting point, but always verify with a prototype.

Alternatives to K-Factor

Some shops use the bend deduction (BD) instead of the bend allowance. The bend deduction is the amount you subtract from the sum of the outside dimensions to get the flat length. The relationship is: BD = 2 × (T + R) × tan(θ/2) − BA. Others use the Y-factor, which is similar to K-factor but uses a different neutral axis location (typically Y = K × π / 2). Many CAD programs let you input either K-factor or bend deduction. If you have a bend deduction table from your supplier, you can convert it to K-factor using the formula above.

Frequently Asked Questions

What is the default K-factor for mild steel? For air bending mild steel, a K-factor of 0.44 is a common default. For stainless steel, it might be 0.4–0.45; for aluminum, 0.4–0.45. Always verify with a test bend.

Can I use this calculator for 180° bends? The formula works for any angle, but for 180° (hem) bends, the material behavior changes significantly. The simple formula may be off by 10% or more. For hems, use a specialized hem allowance or test data.

How do I measure the K-factor myself? Cut a strip of material, bend it to 90°, measure the flat length and the outside dimensions. Then solve the bend allowance formula for K. Or use the bend deduction to back-calculate K.

What is the difference between bend allowance and bend deduction? Bend allowance is the length of the neutral axis in the bend. Bend deduction is the amount you subtract from the sum of outside dimensions. They are related, but not the same. This calculator gives bend allowance; to get bend deduction, use the formula above.

Does the bend radius affect the K-factor? Yes, the K-factor tends to increase with a larger radius relative to thickness. For a tight radius (R/T < 1), K is lower; for a large radius (R/T > 5), K approaches 0.5.

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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 k | K-factor | - | 0.44 | 0
out ba | Bend allowance | mm | (a * (pi / 180)) * (r + k * t) | 2
out flat | Flat blank length (90° bend) | mm | ba + t + r | 2