# 0° – 180° Bend Deduction: Formulas, Calculators & Charts

## 1. What Is Bend Deduction?

Bend deduction is commonly referred to as the “back-off amount”. It is a straightforward algorithm used to explain the process of sheet metal bending.

The bend deduction method states that the flattened length (L) of a part is equal to the sum of the lengths of the two flat parts extending to the “cusp” (the point where the two flat parts intersect virtually) minus the bend deduction (BD).

## 2. Factors Affect Bend Deduction

There are several factors that affect Bend Deduction, including the Neutral Axis, Bend Angle, Bend Radius, K-Factor, and Inside Radius.

Neutral Axis

The Neutral Axis is an imaginary line that runs through the center of the material being bent. It is the line where the material experiences neither compression nor tension during bending. The position of the Neutral Axis depends on several factors, including the material properties and the bend radius.

Bend Angle

The Bend Angle is the angle formed by the two legs of the bend. It is important to note that this angle is measured on the inside of the bend. The Bend Angle affects the amount of material that must be removed in order to achieve the desired flat pattern.

The Bend Radius is the radius of the arc formed by the bend. It is measured on the inside of the bend. The Bend Radius affects both the position of the Neutral Axis and the amount of material that must be removed in order to achieve the desired flat pattern.

K-Factor

The K-Factor is a property of the material being bent. It determines how much the material will stretch when it is bent. The K-Factor is used to calculate both the position of the Neutral Axis and the amount of material that must be removed in order to achieve the desired flat pattern.

The Inside Radius is the radius of curvature on the inside surface of a bend. It is determined by both the Bend Radius and material thickness. The Inside Radius affects both the position of the Neutral Axis and how much material must be removed in order to achieve a desired flat pattern.

## 3. Bend Deduction Formula

How to calculate the bending deduction coefficient in sheet metal fabrication?

The bending deduction in sheet metal fabrication is a term used in the setting parameters of Solidworks and is also a formula used for many years in sheet metal fabrication workshops. Let’s take a look at the calculation formula in Solidworks.

Lt = A + B – BD

Where:

• Lt is the total unfolded length
• A and B are as shown in the figure
• BD is the bending deduction value.

The bending deduction in Solidworks is only used for the calculation of 90-degree bends in sheet metal.

However, it can also be used for the calculation of non-90-degree sheet metal unfolding, but the bending deduction value for non-90-degree bending needs to be used according to the bending coefficient table.

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Each manufacturer has a different table, and there may be errors. Some sheet metal factories may not use non-90-degree bending often.

Today, I will mainly share the calculation method of the bending deduction for 90-degree bending that I am familiar with.

Today, I will share the calculation method for the bending deduction of 90-degree bending that I am familiar with.

There are roughly three algorithms for calculating bending deductions:

1. 1.7 times the thickness of the material.

Sheet metal factories generally use 1.7 times the thickness of the material as the bending deduction, which is the simplest calculation method for sheet metal unfolding.

However, it is not very accurate. If the precision requirement is not high in sheet metal processing, it can be directly used.

Different materials may also have different values; aluminum plates can be calculated based on 1.6 times the thickness of the material, while stainless steel plates can be calculated based on 1.8 times the thickness of the material.

1. Bending deduction = 2 times the thickness of the material + 1/3 the thickness of the material.

This bending deduction calculation formula has been summarized by the sheet metal manufacturing industry for a long time and is also a rough calculation method.

The theoretical explanation of this calculation formula is: Sheet metal unfolding = Length A + Length B – 2 times the thickness of the material + 1/3 the thickness of the material’s elongation coefficient.

The calculation starts by adding up the lengths of the shortest straight line and the elongation factor. It is believed that the sheet metal will elongate during the bending process.

1. Bending deduction = 2 times the thickness of the material – (0.72t-0.075V-0.01).

This formula is derived from a journal article online. Its feature is that it considers the influence of the width of the lower die on the bending deduction.

The test data is derived from experiments on carbon steel plates, and the accuracy of usage for other materials is unknown. I used this formula for the unfolded calculation of a one-time aluminum plate bent with a slot width of 4 times the thickness of the material, and the resulting numerical value was relatively accurate. This formula is very accurate for unfolded calculation of carbon steel plates.

Explanation: t is the actual thickness of the sheet metal, and nominal thickness should not be used for calculation. The above two methods have rough calculations and are not strict in thickness requirements. This formula needs to be calculated based on the actual thickness measured by calipers.

V is the width of the slot in the lower die during bending. Generally, 6-8 times the thickness of the material is taken as the slot width. The actual amount used is calculated according to the actual usage, for example: using 10 lower die bending for 1.5.

There are many methods for calculating bending deductions, including formulas based on the neutral layer theory. This formula is not conducive to actual sheet metal processing, so it is not mentioned here.

The above three methods are the most practical and simplest sheet metal bending deductions or unfolding calculation methods suitable for sheet metal factories.

## 4. Bend Deduction Calculator

Other related calculators:

## 5. Bending Dimensional Accuracy

The dimensional accuracy of bent workpieces is related to the positional precision of the press brake’s back gauge and the precision of the sheet metal cutting machine. Utilizing reliable machines for both cutting and bending processes can address these issues.

A critical factor affecting the dimensional accuracy of bent workpieces is the accuracy of the sheet metal’s flat pattern development. When a flat sheet is bent into a workpiece with a specific angle, measuring the dimensions of the bent workpiece reveals that they do not equal the dimensions of the flat sheet, as shown in the illustration.

This discrepancy is known as the bending deduction.

If the bending deduction is inaccurate, the flat pattern size will be imprecise, and regardless of the precision of subsequent operations, the final workpiece will not meet the required dimensional accuracy.

The bending deduction is complex, and a rudimentary method is to simply use twice the material thickness.

However, this approach is quite crude. A more refined method is to apply the neutral axis theory from the DIN 6935 standard, which involves calculating a factor ‘k’ and combining it with the thickness and angle of the sheet to be bent.

This formula yields a more precise bending deduction. Yet, even the bending deductions calculated according to the neutral axis theory from DIN 6935 may not be precise enough, as the actual deductions also depend on the characteristics of the material, the thickness, the bending angle, and the tooling used.

Different materials, thicknesses, and calculation methods yield varying bending deductions, as shown in Table below.

Table Deduction value for bending dimensions corresponding to different materials, thicknesses, and methods

For example, for a 4mm thick S235JRG2 plate using a V30 lower die, the bending deduction varies by method: twice the material thickness results in 8mm, the DIN 6935 formula yields 7.57mm, and the database empirical value gives 7.26mm.

There are discrepancies between the methods, which become even more significant when workpieces require multiple bends, leading to larger cumulative deviations. The empirical values from the database are derived from extensive practical testing and are stored in the database, providing the utmost precision.

## 6. Bend Deduction Chart

### (1) Sheet Metal Material Bending Deduction Table

Explanation:

• T: Material thickness;
V: Lower die groove width;
W: Lower die width;
α: Internal angle after bending;
H: Minimum distance from the bending center of the die to the edge of the material;
Z: Minimum size of Z-bend.
• Unfold formula: L = A + B – K; (A, B: Outer dimensions of the part; K: Material bending coefficient);
• Expanded size of flattened steel plate: L = A + B – 0.45T;
• Expanded size of pressed steps: L = A + B – 0.3T;
• Minimum size of Z-shaped bend: Z = W/2 + 2T + 1;
• The deduction coefficients for cold-rolled steel plate, aluminum-zinc coated plate, stainless steel plate, electrolytic plate, and aluminum plate are the same;
• According to the current upper die conditions of the company, the bending coefficient of upper die R1 is suitable for cold-rolled steel plate, aluminum-zinc coated plate, and stainless steel plate; The bending coefficient of upper die R2 is suitable for aluminum plate, copper plate, electrolytic plate, etc.

### (4) Bend Deduction Chart for Cold Rolled Steel Plates at Various Angles

1. The following table shows the deduction factor for each 5-degree angle increment from 90 degrees outward: (180°-n°)÷90°×(deduction factor at 90°).
2. The inside bending radius is uniformly set to R0.2, and the gap distance is set to G0.2.

### (5) 0°-180° sheet metal bending deduction table

1) The bending deduction table is applicable for sheet metal bending processes where no pressing plate is used and the sheet width is more than three times the thickness (t).
2) When bending on the bending machine, calculations can be made according to this table.
3) According to the dimensions indicated in the diagram, the calculation formula for the unfolded size of the bent workpiece is as follows:

L=a+b-y

Where:

• L – Unfolded size of the bent workpiece;
• a, b – Indicated lengths from the straight edge to the vertex of the bent workpiece in the diagram;
• y – Bending deduction value of the bent workpiece (correction value for the R part);

4) Due to the numerous factors influencing sheet metal bending, this sheet metal bending deduction value table is provided for reference only.

## 6. Determining Flange Lengths and Total Length

You can use our sheet metal bending calculator for free to quickly calculate important parameters in sheet metal bending, including the K-factor, Y-factor, bend allowance, bend deduction, arc length, and unfolding flat size.

## 7. FAQs

1. What is Bend Deduction?

Bend Deduction is a value used to explain the process of sheet metal bending. It is defined as the material you will have to remove from the total length of your flanges in order to arrive at the flat pattern. The flange lengths are always measured to the apex of the bend.

2. How is Bend Deduction Calculated?

Bend Deduction is calculated using a formula that takes into account several factors, including material thickness, bend angle, inside radius, and k-factor. The formula for Bend Deduction incorporates both the Outside Setback and Bend Allowance.

3. What is the difference between Bend Allowance and Bend Deduction?

Bend Allowance is an approximation of the bend’s total length. It is measured along the neutral axis of the material. By definition, the bend deduction is the difference between the bend allowance and twice the outside setback.

4. What is a Bend Deduction Calculator?

A Bend Deduction Calculator is a tool that helps you calculate the correct values for your sheet metal bending projects, ensuring accurate results and minimal waste.

5. How does a Bend Deduction Calculator work?

A Bend Deduction Calculator calculates bend allowance/deduction based on material thickness, bend angle, inside radius, and k-factor. You input your parameters and the calculator processes these variables through the equations to determine the Bend Deduction.

### 4 thoughts on “0° – 180° Bend Deduction: Formulas, Calculators & Charts”

1. XAI

Hello,

I have been struggling to find the bending duction formula
Is it possible to supply the bending duction formula given above?

1. Shane

Hope our online tool can be helpful for you.

2. Satish Walimbe

Is your “BEND DEDUCTION CALCULATOR” valid for M.S. Cold Rolled Sheet, and S.S.-304 Sheet too?

1. Shane

Yes

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