Tube Curve Calculator: Bending Guide & Formula

This tube curve calculator works out the bend allowance and setback for a single 90° bend in a round tube, based on the tube’s outside diameter, the bend radius, and the wall thickness. You enter those three dimensions, and it returns the bend allowance (the length of tube consumed by the bend), the setback (the distance from the end of the tube to the start of the bend), and the length of the straight section needed before the bend. The result is given in millimeters, but the same formulas work with any unit as long as you stay consistent.

Formula

The calculator uses two standard formulas from sheet metal and tube bending practice. For a 90° bend, the bend allowance (BA) is:

BA = (π / 2) × (R − 0.5 × T)

where:

• R = bend radius measured to the centerline of the tube (mm or inches)
• T = wall thickness of the tube (same unit as R)
• π / 2 = 90° expressed in radians (1.5708)

The setback (SB) for a 90° bend is:

SB = R × tan(45°) = R × 1.0 = R

Since tan(45°) = 1, the setback is simply equal to the centerline radius. The straight length before the bend (the distance from the end of the tube to the tangent point where the bend starts) is:

Straight = SB − (R − 0.5 × T)

This subtracts the distance from the centerline to the inside of the bend, giving the length of tube that remains straight before the curved section begins.

Worked Example

Using the default values from the calculator: outside diameter = 25.4 mm, bend radius = 76.2 mm, wall thickness = 3.0 mm.

1. First, compute the bend allowance: BA = (π / 2) × (76.2 − 0.5 × 3.0) = 1.5708 × (76.2 − 1.5) = 1.5708 × 74.7 = 117.34 mm.
2. Second, compute the setback: SB = 76.2 × tan(45°) = 76.2 × 1 = 76.2 mm.
3. Third, compute the straight length: Straight = 76.2 − (76.2 − 1.5) = 76.2 − 74.7 = 1.5 mm.

The calculator shows a bend allowance of 117.34 mm, a setback of 76.2 mm, and a straight length of 1.5 mm. The straight length is exactly half the wall thickness because the bend radius is large relative to the tube.

When to Use a Tube Curve Calculator

This type of calculation is essential for anyone fabricating frames, handrails, roll cages, exhaust pipes, or any structure that requires precise 90° bends in round tube. Without knowing the bend allowance, you will either cut the tube too long (wasting material) or too short (ruining the part). The calculator is most accurate for:

• Single 90° bends with a constant radius
• Round tube with uniform wall thickness
• Bends made on a mandrel bender or a wiper-style bender
• Materials that do not stretch or compress significantly (steel, stainless, aluminum)

It is less accurate for tight radii (less than 1× tube diameter), thin-walled tubing that may kink, or bends that are not exactly 90°.

How to Read the Results

The bend allowance tells you how much tube length is consumed by the curved portion. If you are bending a tube that must have a total length of 500 mm from end to end, you would add the straight sections and the bend allowance to get the starting length. The setback tells you where the bend starts relative to the centerline of the bend. The straight length is the distance from the end of the tube to the point where the bend actually begins (the tangent point). In practice, you mark the tube at the straight length distance from the end, then align that mark with the bend start point on your bender.

Common Mistakes and Limitations

One frequent error is using the outside radius instead of the centerline radius. The formulas here use the centerline radius, which is the radius measured to the middle of the tube wall. If your bender is marked with the outside radius, subtract half the wall thickness to get the centerline radius. Another mistake is mixing units—if you enter the diameter in inches and the radius in millimeters, the result will be nonsense. Always convert to the same unit first.

The formula assumes the neutral axis (the line that neither stretches nor compresses) is at the centerline of the wall. For thin-walled tubes (wall thickness less than about 10% of the diameter), this is a good approximation. For thicker walls, the neutral axis shifts slightly, and you may need a more advanced formula that accounts for the k-factor. Also, the formula does not account for springback, which is the tendency of the tube to relax slightly after bending, especially in aluminum or stainless steel. You may need to over-bend by a degree or two to compensate.

Safety and Practical Tips

When bending tube, always wear safety glasses and gloves. Tube benders can pinch fingers, and the tube can spring back unexpectedly. Measure twice and cut once—it is cheaper to waste a few centimeters than to scrap an entire piece. If you are bending multiple identical parts, test on a scrap piece first to verify your setup. For critical applications like roll cages or structural frames, consult a professional engineer and follow applicable standards.

Frequently Asked Questions

What is the difference between bend allowance and setback?

Bend allowance is the actual length of tube consumed by the curved section. Setback is the distance from the end of the tube to the centerline of the bend, measured along the straight tube. You use the setback to position the bend on the bender, and the bend allowance to calculate the total starting length.

Can I use this for 45° or 60° bends?

No, this calculator is specifically for 90° bends. For other angles, the bend allowance formula changes to BA = (π × angle / 180) × (R − 0.5 × T), and the setback formula becomes R × tan(angle/2). You can adapt the formulas manually, but this calculator only handles 90°.

Does the outside diameter matter in the calculation?

Not directly, but it matters for practical reasons. The bend radius is usually specified relative to the outside diameter (e.g., 3× OD). If you know the bend radius is 3× OD, you would enter the radius as 3 times the OD. The calculation itself only needs the radius and wall thickness.

Why is the straight length sometimes negative?

If the bend radius is very small relative to the wall thickness, the formula can produce a negative straight length. This indicates that the bend starts before the end of the tube, which is physically impossible. In practice, you need a certain minimum straight length (usually at least 1× tube diameter) for the bender to grip the tube. Increase the bend radius or reduce the wall thickness to avoid this.

What is springback and how do I compensate?

Springback is the elastic recovery of the tube after bending, causing the actual bend angle to be slightly less than the tool angle. For steel, springback is often 1–2°; for aluminum, it can be 3–5°. To compensate, over-bend the tube by that amount, or use a bender with angle adjustment. The calculator does not account for springback, so you may need to adjust your process.

Can I use this for square or rectangular tube?

No, this calculator is only for round tube. Square and rectangular tube have different bending characteristics because the walls are not uniform around the cross-section. They also tend to deform more on the inside of the bend. For those shapes, you need a different set of formulas or a specialized calculator.

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in od | Outside diameter | mm | 25.4 | 0
in r | Bend radius (centerline) | mm | 76.2 | 0
in t | Wall thickness | mm | 3.0 | 0
out ba | Bend allowance (90°) | mm | (pi / 2) * (r - 0.5 * t) | 2
out sb | Setback | mm | r * tan(45 * pi / 180) | 2
out straight | Straight length before bend | mm | sb - (r - 0.5 * t) | 2