# Bend Allowance Calculator

Created by Luciano Mino
Reviewed by Steven Wooding
Last updated: Oct 14, 2022

With this bend allowance calculator, you will learn how to calculate the length of a sheet metal bend so you can optimally create metal bendings without a bend allowance chart. It works as a bend deduction calculator too!

This tool calculates bend allowance/deduction based on material thickness, bend angle, inside radius, and k-factor, as you will learn from the bend allowance equation. Just input your parameters and start working!

## Bend allowance and bend allowance charts

Sheet metal is one of the most commonly used materials in many industries, such as aircraft parts, construction, and automotive, to name a few. So, in order to work accurately with this material, we need to know how it behaves in different scenarios.

Whenever sheet metal is bent, we will define two surfaces in relation to the bend angle $\theta$; the inner and outer surfaces. These surfaces are deformed in opposite ways. The inner surface is compressed while the outer surface is stretched.

💡 See how the lateral and axial strain relate to each other with our Poisson's ratio calculator.

The bend allowance is an approximation of this bend's total length (our arc length calculator is the perfect tool to calculate the length of a curved line segment).

Usually, your supplier will have a bend allowance chart for each type of bend and material, such as a 90-degree bend deduction chart (we will cover bend deduction later on in the text).

We need to know where to measure this bend in the sheet metal bending calculation. Should we measure it at the inner surface? Outer? Or where? The answer is somewhere in the middle determined by the neutral axis, which is the portion in the metal that maintains its length during the bending.

### K-factor

The neutral axis's position is determined experimentally and is presented via the K-factor, $K$:

$\quad K = \frac{t}{T}$

Here $t$ is the distance from the inner surface to the neutral axis, and $T$ is the thickness of the material.

This factor doesn't take into account the forming stresses of the material.

What is stress in mechanics? Check our stress calculator to learn more!

💡 Remember to check with your supplier for the K-factor values. These values will vary depending on the bend method, inside radius, and several other factors. That's why they need to be determined experimentally beforehand.

So, summarizing, the bend allowance is the length of the neutral axis in a bend and, if we know the K-factor beforehand, we can account for it so that our metal sheet is cut with the correct length.

## Bend allowance formula

Here is the bend allowance equation:

$\quad BA = \frac{\theta \cdot \pi}{180} \cdot (r + K\cdot T)$

where:

• $BA$ – Bend allowance;
• $\theta$ – Bend angle in radians or degrees (you can convert between angles with our angle conversion tool too);
• $r$ – Inside radius;
• $K$ – K-factor; and
• $T$ – Material thickness.

As you can see, the bend allowance formula is straightforward, and you only need four parameters to begin using our bend allowance calculator.

🙋 If you need more accurate results, you should ask your supplier for a bend allowance chart since this is an estimation.

## Bend deduction calculator

This calculator works as a bend deduction calculator as well! Below you will find its definition and formula.

### Bend deduction definition

Another similar concept used when working with sheet metal is the bend deduction. When measuring the length of the flanges, as seen in the picture above, we see that the sum of both will result in a length greater than the total length of the cut. The bend deduction is the amount of material we need to take from the metal sheet to achieve the correct length.

### Bend deduction formula

The formula uses the same parameters as the bend allowance equation:

$\quad\footnotesize{BD = 2\cdot (r + T)\cdot \tan\left(\frac{\theta}{2}\right)-BA}$

🙋 While we don't need a 90-degree bend deduction chart to estimate the bend deduction for that type of bend, it is always advisable to ask your supplier for such information.

## Sheet metal bending calculation using the bend allowance calculator

Using the two formulas we have explained, the sheet metal bending calculation is simple. So far, in this text, we've covered:

• Bend allowance definition;
• Bend allowance formula;
• Bend deduction definition; and
• Equation for the bend deduction for sheet metal.

Let's see how we can use both equations in some practical examples.

### Bend allowance example:

Say we need to create a bend on a metal sheet with the following properties:

• Bend angle, $\theta = 45°$; and
• Inside radius, $r = 2\ \text{mm}$.

And the metal sheet has a thickness $T = 5\ \text{mm}$ and K-factor $K = 0.35$.

How much material will be needed to create said bend?

We already have all the information we need to calculate it from the bend allowance formula. Using the data as input in our bend allowance calculator, we obtain:

• $BA = 2.945\ \text{mm}$

### Bend deduction example:

Now let's see how to obtain the length we will need to subtract from a metal sheet to keep its length after bending it in $\theta = 30°$ with $r = 5\ \text{mm}$.

This metal has a k-factor $k = 0.43$ and thickness $T = 15\ \text{mm}$.

So, using this tool as a bend deduction calculator, we obtain the bend deduction for this metal sheet:

• $BD = 4.723\ \text{mm}$

## FAQ

### How do I calculate bend allowance?

To calculate bend allowance:

1. Obtain the properties of the bend (bend radius, angle, and method used).
2. Obtain the characteristics of your material (thickness and K-factor for this specific bend).
3. Input everything into the bend allowance formula: BA = angle × (π/180) × (radius + K-factor × thickness).

### What is the K-factor value?

The K-factor value is generally between 0.3 and 0.5. It's calculated by dividing the neutral axis position (from the inner bend surface) by the material's total thickness.

### What determines K-factor?

The K-factor is determined by the properties of the material and the bend itself. Therefore, a single material will have different K-factors for each bending method, radius, angle, and so forth.

### Why is bend allowance important?

Bend allowance is important because it gives us the information to cut sheet metal to produce a bent metal piece accurately. Precise measures reduce the amount of trial and error, which in turn reduce the cost of producing bent metal pieces.

Luciano Mino
Bend angle (θ)
deg
in
Material thickness (T)
in
K-factor
Bend allowance (BA)
in
Bend deduction (BD)
in
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