Accurately calculate Bend Allowance (BA) and Bend Deduction (BD) for your sheet metal projects.
Sheet Metal Bend Calculator
The thickness of the sheet metal.
The inside radius of the bend.
The angle of the bend in degrees.
0.33 (Common for soft materials like aluminum, brass)
0.40 (General purpose)
0.45 (Common for stainless steel, harder materials)
0.50 (For sharp bends, often theoretical)
Custom
Represents the location of the neutral axis.
Calculation Results
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Formula Used:
Bend Allowance (BA) = [ (2 * π * (R + K*T)) * (A / 360) ] – (2 * BD)
Bend Deduction (BD) = 2 * (R – (K*T))
(Note: Some formulas simplify BA by directly using the bend radius and K-factor, or use different methods for BD. This calculator uses a common approach.)
Bend Deduction (BD) —
Outside Setback (OSSB) —
Outside Bend Radius (OBR) —
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Bend Allowance vs. Bend Angle
Bend Allowance and Deduction Table
Bend Angle (A)
Bend Allowance (BA)
Bend Deduction (BD)
Outside Setback (OSSB)
Outside Bend Radius (OBR)
Sheet Metal Bending Calculation: Mastering Bend Allowance and Deduction
What is Sheet Metal Bending Calculation?
Sheet metal bending calculation refers to the process of determining the precise amount of material needed for a bend in a sheet metal part. This involves calculating two critical values: Bend Allowance (BA) and Bend Deduction (BD). Bend Allowance is the length of the neutral axis of the material that will be formed during the bend. Bend Deduction is the amount of material that is "lost" or reduced from the flat pattern due to the bending process. Accurate sheet metal bending calculations are fundamental in sheet metal fabrication, ensuring that flat patterns (or "blanks") can be cut correctly to produce finished parts that meet exact dimensions after bending.
Who should use it: This calculation is essential for anyone involved in designing, engineering, or manufacturing sheet metal components. This includes mechanical designers, CAD technicians, sheet metal fabricators, machinists, workshop managers, and even hobbyists working with sheet metal. Precise calculations prevent costly errors, material waste, and rework.
Common misconceptions: A frequent misconception is that the flat pattern length is simply the sum of the straight leg lengths. This ignores the material deformation that occurs during bending. Another is that the bend radius is always measured to the outside; it's crucial to distinguish between inside and outside radii and how they affect calculations. The K-factor is also often misunderstood; it's not a fixed material property but depends on tooling, material, and bend type.
Sheet Metal Bending Calculation Formula and Mathematical Explanation
The core of sheet metal bending calculation lies in understanding the geometry of the bend and how the material behaves. The neutral axis is an imaginary line within the material that neither stretches nor compresses during bending. Its location is influenced by the material's properties and the tooling used, and it's represented by the K-factor.
Bend Allowance (BA)
Bend Allowance is the length along the neutral axis that forms the arc of the bend. The formula is derived from the circumference of a circle segment:
BA = (2 * π * (R + K*T)) * (A / 360)
Where:
π (Pi) is approximately 3.14159.
R is the inside bend radius.
K is the K-factor, representing the ratio of the neutral axis distance from the outer surface to the material thickness.
T is the material thickness.
A is the bend angle in degrees.
The term (R + K*T) represents the radius to the neutral axis. Multiplying this by 2 * π gives the circumference of a full circle at the neutral axis. The fraction (A / 360) scales this circumference to the specific angle of the bend.
Bend Deduction (BD)
Bend Deduction is the total amount of material removed from the flat pattern legs due to the bend. It's calculated by subtracting the Bend Allowance from the sum of the two outside setbacks:
BD = Outside Setback (OSSB) * 2 - BA
A more direct calculation for Bend Deduction, often used, relates to the difference between the outside mold line and the neutral axis:
BD = 2 * (R - (K*T))
This formula calculates the difference between the radius to the outside mold line (R) and the radius to the neutral axis (K*T), then doubles it.
Outside Setback (OSSB)
Outside Setback is the distance from the mold line intersection (the theoretical sharp corner) to the point where the bend begins on the outside surface. It's calculated as:
OSSB = Outside Bend Radius (OBR) - Bend Radius (R)
Or, more commonly derived from the geometry:
OSSB = (R + T) - (R + K*T) = T - K*T = T * (1 - K)
However, the most practical definition for flat pattern layout is often derived from the outside mold line:
OSSB = OBR - R where OBR = R + T. This leads to OSSB = T. This is a simplification. A more accurate geometric calculation relates to the tangent points.
A widely used formula for Outside Setback is:
OSSB = tan(A/2) * (R + T) - R (This is complex). A simpler, common approach relates to the difference between the outside mold line length and the leg length:
OSSB = (R + T) - (R / tan(A/2)) (This is also complex). The most practical definition for layout is often derived from the relationship between BA and BD:
OSSB = (BA + BD) / 2
Outside Bend Radius (OBR)
This is the radius measured from the center of the bend to the outermost surface of the bent material.
OBR = R + T
Variable Table
Here's a breakdown of the variables used in sheet metal bending calculations:
Variable
Meaning
Unit
Typical Range
T (Material Thickness)
Thickness of the sheet metal being bent.
Length (e.g., mm, inches)
0.1 – 25+ (depends on application)
R (Inside Bend Radius)
The radius of the bend measured on the inside surface.
Length (e.g., mm, inches)
Often 0.5*T to 5*T, or specified by design. Cannot be 0 unless specified as a sharp bend.
A (Bend Angle)
The angle of the bend, typically measured between the two legs.
Degrees
0° to 180° (most common 30° to 150°)
K (K-Factor)
Ratio determining the location of the neutral axis. K = Distance from outer surface to neutral axis / T.
Unitless
0.33 to 0.50 (common values)
BA (Bend Allowance)
Length of the neutral axis arc.
Length (e.g., mm, inches)
Varies based on inputs
BD (Bend Deduction)
Total material reduction from flat pattern legs.
Length (e.g., mm, inches)
Varies based on inputs
OSSB (Outside Setback)
Distance from the mold line intersection to the start of the bend on the outside.
Length (e.g., mm, inches)
Varies based on inputs
OBR (Outside Bend Radius)
Radius measured to the outside surface of the bend.
Length (e.g., mm, inches)
R + T
Practical Examples (Real-World Use Cases)
Example 1: Simple L-Bracket
A designer needs to create a simple L-bracket from 2mm thick aluminum (T=2mm). The bend will be 90 degrees (A=90°), and they want a conservative inside bend radius of 3mm (R=3mm). For aluminum, a K-factor of 0.33 is suitable (K=0.33).
Inputs:
Material Thickness (T): 2 mm
Bend Radius (R): 3 mm
Bend Angle (A): 90°
K-Factor (K): 0.33
Calculation using the calculator:
Bend Allowance (BA): Approximately 5.76 mm
Bend Deduction (BD): Approximately 2.62 mm
Outside Setback (OSSB): Approximately 1.31 mm
Outside Bend Radius (OBR): 5 mm
Interpretation: To create this L-bracket, the flat pattern will need to account for these values. If the two legs were intended to be 50mm each *after* bending, the flat pattern length would be calculated as: Leg1 + Leg2 + BA = 50mm + 50mm + 5.76mm = 105.76mm. However, if the dimensions refer to the outside mold lines, the calculation changes. A common layout method uses the outside mold line dimensions minus the setback: (50mm – OSSB) + (50mm – OSSB) + BA = (50 – 1.31) + (50 – 1.31) + 5.76 = 48.69 + 48.69 + 5.76 = 103.14mm. This highlights the importance of defining dimensions clearly.
Example 2: U-Channel from Stainless Steel
A fabricator is making a U-channel from 1.5mm thick stainless steel (T=1.5mm). The bend angle is 120 degrees (A=120°), and the desired inside bend radius is 2mm (R=2mm). Stainless steel typically requires a K-factor of 0.45 (K=0.45).
Inputs:
Material Thickness (T): 1.5 mm
Bend Radius (R): 2 mm
Bend Angle (A): 120°
K-Factor (K): 0.45
Calculation using the calculator:
Bend Allowance (BA): Approximately 4.44 mm
Bend Deduction (BD): Approximately 1.58 mm
Outside Setback (OSSB): Approximately 0.79 mm
Outside Bend Radius (OBR): 3.5 mm
Interpretation: For a U-channel with two 120° bends, the flat pattern length calculation is critical. If the channel's inner dimensions are specified, the calculation involves subtracting the bend deduction from the leg lengths and adding the bend allowance. For instance, if the two outer faces of the channel legs were meant to be 40mm each, the flat pattern length would be: (40mm – OSSB) + (40mm – OSSB) + BA = (40 – 0.79) + (40 – 0.79) + 4.44 = 39.21 + 39.21 + 4.44 = 82.86mm. This ensures the final U-channel has the correct dimensions after forming.
How to Use This Sheet Metal Bending Calculator
Our Sheet Metal Bend Calculator simplifies the complex geometry involved in bending sheet metal. Follow these steps for accurate results:
Enter Material Thickness (T): Input the thickness of the sheet metal you are working with. Ensure units are consistent (e.g., mm or inches).
Enter Bend Radius (R): Specify the desired inside radius of the bend. This is a critical parameter affecting the bend's geometry and material stress.
Enter Bend Angle (A): Input the angle of the bend in degrees. Common angles include 90°, 45°, and 135°.
Select K-Factor (K): Choose a K-factor from the dropdown that best represents your material and tooling. Common values are provided (0.33 for softer metals, 0.45 for harder metals). If you have a specific K-factor, select 'Custom' and enter it.
Click 'Calculate': The calculator will instantly display the primary result: Bend Allowance (BA).
Review Intermediate Values: Examine the calculated Bend Deduction (BD), Outside Setback (OSSB), and Outside Bend Radius (OBR) for a complete understanding of the bend geometry.
Understand the Formula: Read the brief explanation of the formulas used to see how the results were derived.
Use the Table and Chart: The generated table and chart provide visual and tabular data for different bend angles, helping you compare scenarios or verify calculations.
Copy Results: Use the 'Copy Results' button to easily transfer the key values for use in your CAD software or documentation.
Reset: Click 'Reset' to clear all fields and return to default values for a new calculation.
How to read results: The primary result, Bend Allowance (BA), is the length needed along the neutral axis. Bend Deduction (BD) tells you how much material is effectively "lost" from the flat legs. Outside Setback (OSSB) helps determine the flat pattern length when using outside mold line dimensions. Outside Bend Radius (OBR) is the radius to the outermost surface.
Decision-making guidance: Use these results to accurately dimension your flat patterns. If your design specifies dimensions to the outside mold lines, you'll subtract the OSSB from each leg length and add the BA. If dimensions are to the inside mold lines, you'll use the inside leg lengths directly and add the BA. Always verify with your specific tooling and material properties.
Key Factors That Affect Sheet Metal Bending Calculation Results
Several factors significantly influence the accuracy of sheet metal bending calculations. Understanding these is crucial for precise fabrication:
Material Type and Temper: Different metals (e.g., aluminum, mild steel, stainless steel) and their tempers (hardness/strength) affect how they deform. Softer materials tend to have a larger bend radius and may require different K-factors than harder materials. This directly impacts the neutral axis location and thus BA and BD.
Bend Radius (R): A smaller bend radius causes more material stretching and compression, leading to different BA and BD values compared to a larger radius. The relationship is non-linear.
Material Thickness (T): Thicker materials generally require larger bend radii to avoid cracking and exhibit different deformation characteristics. Thickness is a direct input into the BA and BD formulas.
Bend Angle (A): The angle directly scales the arc length calculation for Bend Allowance. A 180° bend requires twice the BA of a 90° bend (all else being equal).
Tooling (Die Width, Punch Radius): The width of the die opening and the radius of the punch significantly influence the resulting bend radius and the K-factor. Wider dies generally allow for larger inside bend radii and affect material flow.
K-Factor (K): As discussed, this factor is critical. It's not a fixed material property but a representation of the neutral axis location, influenced by tooling, material, and bend type. Using an inappropriate K-factor is a common source of error.
Grain Direction: For some materials, especially certain alloys or when bending to very small radii, the direction of the material's grain can affect the likelihood of cracking. Bending across the grain is generally less desirable.
Springback: After the bending force is removed, the material tends to slightly spring back to its original shape. This phenomenon must often be compensated for by over-bending the part slightly, which affects the final angle and can indirectly influence the required flat pattern dimensions.
Frequently Asked Questions (FAQ)
What is the difference between Bend Allowance and Bend Deduction?
Bend Allowance (BA) is the length of the material along the neutral axis that forms the curved portion of the bend. Bend Deduction (BD) is the total amount subtracted from the flat pattern legs to account for the material deformation during bending. BD is typically calculated as 2 * OSSB – BA, or derived from the geometry.
How do I determine the correct K-Factor?
The K-factor is empirical and depends on the material, tooling (die width, punch radius), and bend angle. Common values range from 0.33 to 0.50. For soft materials like aluminum, 0.33 is often used. For harder materials like stainless steel, 0.45 is common. It's best to consult tooling manufacturers' charts, perform test bends, or use established industry standards.
What is Outside Setback (OSSB)?
Outside Setback is the distance from the theoretical sharp corner (mold line intersection) to the point where the bend begins on the outside surface of the material. It's crucial for calculating flat pattern lengths when dimensions are referenced to the outside mold lines.
Can I bend sheet metal with a 0mm bend radius?
A 0mm bend radius implies a sharp bend, which is often not physically possible without significantly deforming or potentially cracking the material, especially with thicker stock or harder metals. A minimum bend radius is usually specified based on material type and thickness.
How does springback affect my calculations?
Springback is the tendency of the material to return to its original shape after the bending force is removed. It causes the final bend angle to be slightly less than the angle formed by the tooling. Accurate flat pattern development may require calculating the amount of springback and adjusting the bend angle or tooling accordingly. This calculator does not directly account for springback compensation.
What are mold lines?
Mold lines (or mold lines) are imaginary lines representing the surfaces of the bending tool (punch and die). They are used as reference lines for dimensioning flat patterns. Outside Mold Line (OML) dimensions refer to the length along the outer surface, while Inside Mold Line (IML) dimensions refer to the length along the inner surface.
Does the calculator handle different units (mm vs. inches)?
This calculator assumes consistent units for all inputs (e.g., all in millimeters or all in inches). Ensure you use the same unit system for thickness, radius, and any resulting lengths. The output units will match the input units.
Why is my calculated flat pattern length different from my CAD software?
Different CAD software and fabrication shops may use slightly different algorithms or default K-factors for their bend deduction calculations. Always verify the calculation method and K-factor used in your specific software or by your fabrication partner to ensure consistency.