Tube Bending Formulas

Tube bending terms

• OD: tube outside diameter. For pipe, use the true OD from the pipe schedule chart, not the nominal size.
• t: wall thickness.
• CLR: centerline radius, the radius of the bend measured to the center of the tube.
• A: bend angle in degrees.
• Tangent point: where the straight ends and the bend begins.
• Intersection point: where the centerlines of two straights would meet if the corner were sharp.

Degree of bend (D of bend)

D = CLR ÷ OD

A 3 in CLR on 1.5 in OD tube is a 2D bend. Below about 2D, bends get difficult. At 1D and below, booster bending is usually needed.

Wall factor

WF = OD ÷ t

The higher the wall factor, the thinner the wall relative to the tube, and the more likely the tube is to wrinkle or flatten. Wall factor and D of bend together decide whether you need a mandrel and wiper die. Our tube bending calculator gives a mandrel and wiper starting point from these two numbers.

Tangent length (setback)

T = CLR × tan(A ÷ 2)

The tangent length, also called setback, is the distance from the tangent point to the intersection point. For a 90° bend it equals the CLR. Use it to convert dimensions measured to intersection points (as on most prints) into straight lengths between bends.

Arc length (bend allowance)

Arc = π × CLR × A ÷ 180

The length of tube in the bend, measured along the centerline. A 90° bend on a 3 in CLR uses 4.712 in of tube.

Bend gain

Gain = 2 × T − Arc = 2 × CLR × tan(A ÷ 2) − π × CLR × A ÷ 180

Because a bend takes a shortcut around the corner, the tube needed is shorter than the sum of the intersection-to-intersection dimensions. Gain is that difference for one bend.

Developed length (cut length)

Cut length = sum of straights between tangent points + sum of arc lengths

or: Cut length = sum of intersection-to-intersection lengths − sum of gains

This is the theoretical length at the centerline. Tube stretches slightly in the bend, so confirm with a test bend and add any clamp or trim allowance. The tube bending calculator works out cut length for multi-bend parts, and the XYZ to YBC converter does it from print coordinates.

Straight length between bends

Straight = intersection-to-intersection length − T(bend 1) − T(bend 2)

If the result is negative or very short, the bends overlap or there is no room for the clamp. As a rule of thumb, a standard smooth clamp needs about 3 × OD of straight; shorter straights call for serrated or compound clamp tooling.

Outside wall stretch

Stretch ≈ OD ÷ (2 × CLR) × 100%

How much the outside wall of the bend lengthens compared with the centerline. A 2D bend stretches the outside wall about 25%.

Approximate wall thinning

Outside wall ≈ t × CLR ÷ (CLR + OD ÷ 2)

Inside wall ≈ t × CLR ÷ (CLR − OD ÷ 2)

A first estimate of wall thickness after bending. Actual results depend on material, tooling and pressure die assist, so check against the wall-thinning limit on your print.

Ovality

Ovality % = (max OD − min OD) ÷ nominal OD × 100

Measured across the bend. Tight specifications usually need a mandrel with more balls and well-fitted tooling. Read more on tube and pipe ovality requirements.

Offset bend formulas

Distance between bends = offset ÷ sin(A)

Shrink = offset × tan(A ÷ 2)

For two equal bends that shift a run sideways by the offset. Common multipliers: 22.5° = 2.613, 30° = 2.0, 45° = 1.414, 60° = 1.155. For a rolling offset, first find the true offset:

True offset = √(rise² + roll²)

Worked example

1.5 in OD × 0.065 in wall tube, 3 in CLR, one 90° bend:

With two 10 in legs measured to the intersection point, the cut length is 10 + 10 − 1.288 = 18.712 in.

Calculators that do the math for you

• Tube bending calculator: D of bend, wall factor, stretch, tooling starting point and cut length, with a PDF report.
• XYZ to YBC converter: bend data and cut length from print coordinates.
• Tube and pipe weight calculator and section modulus calculator.
• Press brake bend allowance and K-factor calculator for sheet metal.

Prefer a spreadsheet? Download the tube bending formulas guide and section modulus calculator.

Frequently Asked Questions

What is the formula for tube bending setback?

Setback (tangent length) = CLR × tan(A ÷ 2). For a 90° bend, the setback equals the centerline radius.

How do you calculate the length of tube needed for a bend?

Add the straight lengths between tangent points and the arc length of each bend (π × CLR × A ÷ 180). Or subtract the gain of each bend from the sum of the intersection-to-intersection dimensions.

What is a good D of bend?

2D and above is generally straightforward. 1.5D to 2D usually needs a mandrel on thin wall. Below 1.5D needs careful tooling, and around 1D or tighter usually calls for booster bending.

Does tube stretch when bent?

Yes. The outside wall stretches and thins and the inside wall compresses and thickens. The centerline stays close to its original length, which is why cut length is calculated at the centerline. Confirm with a test bend.

How do I calculate an offset bend?

The distance between the two bends is the offset divided by the sine of the bend angle (multiplier 2.0 for 30° and 1.414 for 45°). Shrink is the offset times tan(A ÷ 2).