# Bend Deduction

Understanding the Bend Deduction and consequently the Bend Allowance of a part is a crucial first step to understanding how sheet metal parts are fabricated.  When the sheet metal is put through the process of bending the metal around the bend is deformed and stretched. As this happens you gain a small amount of total length in your part.  Likewise when you are trying to develop a flat pattern you will have to make a deduction from your desired part size to get the correct flat size.  The Bend Deduction 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.  In our example below a part with flange lengths of 2” and 3” with an inside radius of .250” at 90° will have a total length of 5”.  When we calculate the Bend Deduction we find that it equals .293”.  In order to develop the flat pattern we will subtract .293” from 5” to arrive at 4.707”.  As you can see the Bend Deduction and Bend Allowance are closely related below.

## Bend Deduction Calculator

Below is our simple Bend Deduction Calculator, it works by inputing the Material Thickness, Bend Angle, Inside Radius and K-Factor. It simply processes these variables through the equations we will discuss below. Note that the Bend Angle is the excluded angle, not the included angle.

## Bend Deduction Formula

The Bend Deduction Formula takes into account the geometries of bending and the properties of your metal to determine the Bend Deduction. You will need to know your Material Thickness (MT), the Bend Angle (B<), the Inside Radius (IR), and the K-Factor (K). The Material Thickness will be measured in decimal form, not by the gauge number. For more information on gauges and their decimal equivalents and tolerances view our Gauge Chart page.  The Bend Angle will be something that you determine based on what the complimentary angle of your part is going to be.  It is important to convert from the included angle to the complimentary angle before performing any calculations. The Inside Radius will be the finished radius of the included angle.  For information on how the Inside Radius is determined see our post on the Air Bend Force Chart.  Finally the K-Factor is a property of the material which you are bending.  This property determines how the material is stretched when bending. See our post on the K-Factor for better understanding as well as charts and formulas.

The Formula For Bend Deduction is rather long because it incorporates the Out Side Set Back as well as the Bend Allowance.

$Bend Deduction = {2*(\tan \left( \dfrac{B<}{2}\right) \cdot (IR + MT))-{\dfrac{\pi}{180} \cdot B< \cdot (IR + K \cdot MT)}}$

If you have your Out Side Set Back (OSSB) and Bend Allowance (BA) then the Bend Deduction Formula is shortened considerably.

$Bend Deduction = {2 \cdot OSSB - BA}$

## Bend Deduction Chart

Because Bend Deduction is often confused with Bend Allowance it is important to understand which value you intend on working with.  Once you understand what these values represent you can use them to accurately and quickly develop flat patterns for your sheet metal parts.  Creating a chart with your standard values is a key component of speeding up this process.  Many software packages like Solid Works, Inventor and Solid Edge will let you incorporate a Bend Deduction Chart into its calculations when developing flat patterns.

Unfortunately sheet metal bending is not always going to be the same in every shop. The largest variations come from the materials themselves. Protective coatings, variations in the alloy and thickness as well as many other small factors all add up to give you Bend Deductions unique to your operation.  This chart will get you close enough for most applications and may not require fine tuning on your part, however if you are truly dedicated to precise bending, download the excel sheet and begin plugging in your own values.

The below Microsoft Excel chart is for even numbered gauges 8 through 24 and has a default K-Factor of .33 for each.  The inside radii are based off of a standard Air Bend Force Chart.  You can easily modify the Material Thickness, Inside Radius and K-Factor for each thickness at the top of each column.

Sheet Metal Bend Deduction Chart (PDF)

Sheet Metal Bend Deduction Chart (Excel)

BEND DEDUCTION
8 Gauge10 Gauge12 Gauge14 Gauge16 Gauge18 Gauge20 Gauge22 Gauge24 Gauge
K factor0.33K factor0.33K factor0.33K factor0.33K factor0.33K factor0.33K factor0.33K factor0.33K factor0.33
MTIRMTIRMTIRMTIRMTIRMTIRMTIRMTIRMTIR
0.1630.2100.1350.1640.1050.1180.0750.1050.0600.0920.0480.0660.0360.0200.0300.0200.0240.020
AngleDeductionDeductionDeductionDeductionDeductionDeductionDeductionDeductionDeduction
100.01930.01590.01230.00880.00710.00560.00420.00350.0028
150.02920.02400.01870.01340.01070.00860.00640.00530.0043
200.03960.03250.02530.01810.01450.01160.00860.00720.0057
250.05040.04140.03210.02310.01860.01480.01090.00910.0073
300.06190.05090.03940.02840.02280.01820.01330.01110.0089
350.07420.06090.04720.03410.02750.02180.01580.01320.0106
400.08760.07180.05560.04030.03250.02570.01850.01550.0125
450.10200.08360.06460.04700.03800.03000.02130.01790.0145
500.11790.09650.07450.05440.04410.03480.02430.02050.0166
550.13540.11070.08530.06260.05080.04000.02760.02330.0189
600.15480.12650.09730.07170.05830.04580.03120.02630.0215
650.17630.14390.11060.08190.06670.05220.03510.02970.0243
700.20050.16340.12540.09330.07610.05950.03940.03340.0274
750.22760.18530.14200.10610.08670.06760.04410.03750.0309
800.25810.21000.16060.12050.09870.07680.04930.04200.0347
850.29280.23790.18170.13700.11240.08720.05520.04710.0391
900.33220.26970.20560.15570.12810.09910.06180.05290.0440
950.37740.30600.23290.17720.14600.11280.06920.05940.0496
1000.42930.34770.26440.20200.16680.12850.07760.06680.0560
1050.48950.39610.30070.23080.19090.14670.08730.07530.0633
1100.55980.45250.34300.26430.21910.16800.09850.08520.0718
1150.64250.51880.39270.30390.25230.19310.11160.09670.0818
1200.74070.59750.45160.35090.29180.22290.12690.11030.0937
1250.85870.69210.52240.40750.33940.25880.14530.12650.1078
1301.00260.80740.60860.47650.39750.30250.16750.14620.1250
1351.18090.95020.71540.56210.46960.35680.19480.17050.1462
1401.40671.13090.85040.67050.56100.42550.22930.20120.1731
1451.70031.36581.02580.81160.68000.51480.27390.24090.2079
1502.09571.68221.26201.00170.84040.63520.33380.29420.2546
1552.65402.12871.59521.27011.06690.80520.41810.36930.3205
1603.49732.80302.09831.67571.40941.06210.54500.48250.4199
1654.91063.93312.94132.35571.98361.49270.75720.67180.5864
1707.74866.20204.63363.72123.13692.35751.18271.05150.9203