Everything you need to know about the K-factor

If we want to bend a flat metal sheet, the dimension of the bent part does not always match the flat blank exactly. Why is that? The K-factor. This little number has a huge influence over the precision of your actual 3D design. 

We answer the following questions here:

1. What is the K-factor?
2. Why is the K-factor so important?
3. How do you calculate the K-factor?
4. The K-factor and Sophia®
5. Ordering a flat blank only

1. What is the K-factor?

When we bend a metal sheet, the outside of the radius gets stretched, and the inside gets compressed. Somewhere in between these two layers is a neutral line or ‘axis’: a zone that neither stretches nor shrinks, but remains unchanged.

The K-factor gives the ratio between (i) the distance from the neutral axis to the inner radius of the bend and (ii) the sheet thickness.

In formula form:

K-factor = the distance from the neutral axis to the inner radius / sheet thickness

The drawing below illustrates this. 

The sheet thickness is 3 mm and the distance from the neutral axis to the inner radius is 1.25 mm. So in this case, the K-factor is 1.25/3 = 0.42.

With a K-factor of 0.5, the neutral axis is exactly at the centre of the sheet (halfway point). But during bending, this line shifts inwards. So in practice, the K-factor typically varies from 0.3 to 0.5, depending on factors such as the material and the bend radius.

2. Why is the K-factor important?

Bending always starts with a flat sheet. But when we bend a sheet, the length of each flange gets a bit longer. This is because the radii stretch. This lengthening is also known as the bend allowance. To achieve a specific final dimension, benders must know the bend allowance.

So where does the K-factor come in?

We need the K-factor to calculate the bend allowance. Let’s have a look at the formula for the bend allowance:

BA = θ × (R + K × t)

Where:

• BA = Bend allowance (in mm)
• θ = Bend angle in radians ((bend angle in degrees × π) / 180)
• R = Inner radius of the bend (in mm)
• K = K-factor (ratio between neutral axis and thickness)
• t = Sheet thickness (in mm)

For further details on this formula, please see our blog on flat blanks.

An incorrect K-factor will result in an incorrect bend allowance, and thus also deviations in your parts. 

So the K-factor is critical to ensure the correct dimensions of your bent piece. That’s why it’s so important.

3. How do you calculate the K-factor?

A theoretical calculation of the K-factor is practically impossible. There’s simply too much going on at the same time, such as:

• The material stretches. How much it stretches depends on the ultimate tensile strength, hardness and yield strength ratio.
• The neutral axis shifts. How far it shifts depends on the radius, sheet thickness and bending method.
• The use of the machine, where the specific tools, settings and the spring return may vary.

Every metal type responds differently to bending. Thin sheets bend differently from thick sheets. A small radius causes more deformation than a large radius. No two tools are the same. Etc.

All of these factors have an influence and make it difficult to calculate the K-factor or give a standard value.

There’s a good reason why manufacturers and engineers use guide values. For instance, they perform test bends to determine the right K-factor for their material and process. They record these so they can select the most accurate value possible for future bending parts.

So it is not possible in practice to calculate the K-factor in advance, and we advise against this.

But you can in fact determine the K-factor afterwards if you have a bending test or CAD result. You can do this with the formula:

K = ((BA / θ) – R) / t

Where:

• K = K-factor (ratio between neutral axis and thickness)
• BA = Bend allowance (in mm)
• θ = Bend angle in radians ((bend angle in degrees × π) / 180)
• R = Inner radius of the bend (in mm)
• t = Sheet thickness (in mm)

4. The K-factor and Sophia®

In our online software, Sophia®, 247TailorSteel also uses guide values from our own database. We have collected these from years of bending work and testing.

If you order bent parts from us using Sophia®, it will calculate all of the necessary values for our benders. As the customer, you don’t have to do anything. Easy, right?

5. What if you only order a flat blank?

Sophia® offers the option to upload a STEP file and export it as a DXF (and re-upload it). 

This function generates the flat blank for the bent part you designed. If you are ordering this flat blank, you don’t need to laser-cut it yourself, but you can perform the bending yourself. This is handy if you have your own bending machines.

Please note here that flat blanks are calculated based on our practical values. In particular, our machine settings and tools may differ from yours. This poses a risk of deviations in the dimensions. So always conduct the necessary testing yourself to ensure that you get the right dimensions for your machines.

Questions about the K-factor?

If you have further questions on this topic, please feel free to contact us.