Centerline Radius Tube Bending: CLR Explained With Real Math

You go to order a die, and the listing says “1.75 × 6 CLR.” A friend tells you to “go 3D.” A rulebook says “three times the tube diameter.” An old drawing just says “6-inch radius.” Are those all the same number? Not quite. Welcome to centerline radius tube bending. CLR is the one number that sets the size, shape and difficulty of every bend you make.

CLR sounds technical, but it isn’t. It’s the radius of the bend, measured to the middle of the tube. The trouble starts when you mix it up with the inside or outside radius. Parts come out the wrong size. Cut lengths drift. Dies get ordered wrong. And on a roll cage, you could end up under a rulebook minimum without knowing it.

This guide clears it all up, the way a friend in the next garage bay would. You’ll learn what CLR is and how it differs from inside and outside radius. You’ll see how to measure it on a die or a bent part, and how to choose the right die CLR for your project. We’ll work real numbers with the math shown, so you can check every step yourself.

Centerline radius tube bending: the plain-English definition

Picture any bend as a slice of a circle. Every circle has a center point. Now picture a line running down the exact middle of the tube, halfway between the walls. That’s the centerline. The centerline radius is the distance from the circle’s center point to that line.

That’s it. The Fabricator’s glossary defines it the same way. It also notes that CLR is often written as a multiple of the tube size. Its example: a “5 × D” bend on 2″ tube has a 10″ CLR. We’ll come back to that “D” idea soon.

The die decides the CLR

On a rotary-draw bender, the die sets the CLR. The tube wraps around the die’s groove, so the bend can only follow that one radius. That’s why dies are sold by two numbers: the tube’s outside diameter (OD) and the CLR. A “1.75 × 6″ die bends 1.75″ OD tube at a 6” centerline radius.

You can’t change the CLR by pulling harder, slower or in smaller steps. Want a bigger or tighter radius? You need a different die. Hand benders for brake line and conduit benders work the same way. Their forming wheel or shoe has a fixed radius built in.

“Bend radius” is a slippery phrase

In tube shops, “bend radius” usually means CLR. But not always. Some drawings, sellers and older references use “bend radius” for the inside curve instead. Stainless Headers’ cut-length calculator sums up the tube-world habit well: bent tubing is normally measured at the centerline, not the inside or outside edge.

CLR vs inside radius vs outside radius

A tube has thickness, so every bend really has three radii. The inside radius is the tight curve on the inside of the bend. The outside radius is the big sweeping curve on the outside. The CLR sits exactly halfway between them.

One quick note on words. Here, “inside radius” means the radius of the tube’s outer surface on the inside of the bend. It’s what you’d touch with a radius gauge. It is not the tube’s bore. Because these numbers are measured on the outside surface, wall thickness doesn’t change them. Only the OD does.

The three formulas

• Inside radius = CLR − (OD ÷ 2)
• Outside radius = CLR + (OD ÷ 2)
• CLR = inside radius + (OD ÷ 2), or outside radius − (OD ÷ 2)

Worked example

Take 1.75″ OD tube on a 6″ CLR die. Half the OD is 1.75 ÷ 2 = 0.875″. The inside radius is 6 − 0.875 = 5.125″. The outside radius is 6 + 0.875 = 6.875″. Swap in 1.5″ tube on a 5.5″ CLR die and you get 4.75″ inside and 6.25″ outside.

Measurement	Measured to	Formula	1.75″ OD on 6″ CLR	1.5″ OD on 5.5″ CLR
Inside radius	Tube surface on the inside of the bend	CLR − OD ÷ 2	5.125″	4.750″
Centerline radius (CLR)	Middle of the tube	Set by the die	6.000″	5.500″
Outside radius	Tube surface on the outside of the bend	CLR + OD ÷ 2	6.875″	6.250″
U-bend leg spacing	Center of one leg to center of the other	2 × CLR	12.000″	11.000″

See how the tube size changes everything? The same inside radius on a different tube gives a different CLR. That’s why a radius with no tube size is only half the story. Whenever you write down a bend, write the OD next to it.

Why the centerline is the number that matters

When tube bends, it doesn’t just curve. The outside wall gets stretched and thins out. The inside wall gets squeezed and thickens. The Fabricator describes the same thing in its tube-bending basics. Somewhere near the middle is a line that’s neither stretched nor squeezed much. For everyday shop math, that line is treated as the tube’s centerline.

That’s why tube lengths are figured at the centerline. Measure on the inside and your number is too short. Measure on the outside and it’s too long.

The numbers, side by side

Let’s bend 1.75″ tube 90° on a 6″ CLR die. First convert the angle to radians: 90° = 1.5708 radians. Arc length is radius × angle in radians.

• Inside arc: 5.125 × 1.5708 = 8.05″
• Centerline arc: 6 × 1.5708 = 9.42″
• Outside arc: 6.875 × 1.5708 = 10.80″

The outside skin is about 2.75″ longer than the inside skin on that one bend. Only the centerline number tells you how much straight tube the bend really uses. That’s the 9.42″ figure.

The JD2 shortcut

JD2’s Model 32 manual writes bend length as CLR × degrees × .0175. That’s the same formula with π ÷ 180 rounded up. The exact value is about 0.017453. On our example, JD2’s shortcut gives 6 × 90 × .0175 = 9.45″. The exact answer is 9.42″. The tiny difference only matters when you add up many bends.

You may also run into sheet-metal “bend allowance” formulas that use a K-factor and the material thickness. Those come from sheet-metal work. For tube on a rotary-draw die, makers and tube calculators use CLR × angle. Our full tube bend length formula guide walks through it with more examples.

Measure bends at the centerline. The inside of the bend is too short, the outside is too long, and the middle is just right.

CLR as a multiple of OD: the “D” number

Fabricators often talk about CLR as a multiple of the tube OD. That ratio is called D of bend. Pro-Tools defines it simply as CLR ÷ OD in its wall factor and D of bend article.

So a 1.75″ tube on a 6″ CLR die is 6 ÷ 1.75 = 3.43D. A “1D” exhaust bend has a CLR equal to its OD. Vibrant, for example, lists a 3″ OD 304 stainless 90° mandrel bend with a 3″ centerline radius. That’s 1D. When someone says “1.5D,” they mean 1.5 × OD, not a 1.5″ radius.

Lower D means a tighter, harder bend

The lower the D number, the tighter the bend and the harder it is on the tube. Pro-Tools puts the practical minimum CLR for bending without a mandrel at about 3 × OD. Baileigh’s basic bending concepts suggests 4 × OD as a starting estimate. Those two aren’t in conflict. One is a floor and the other is a comfortable place to start.

Situation	Typical D (CLR ÷ OD)	On 1.75″ OD tube	Source
Practical non-mandrel minimum	About 3D	About 5.25″ CLR	Pro-Tools
Starting estimate	4D	7″ CLR	Baileigh
Popular off-road dies	1.5″ at about 5.5″ CLR, 1.75″ at about 6.5″ CLR	6.5″ ÷ 1.75 = 3.7D	Baileigh
SCCA Time Trials cage bends	At least 3 × tube diameter, at the centerline	5.25″ CLR or larger	SCCA Time Trials
6061-T6 aluminum	About 3.5–4D; 3D is marginal	About 6.1″–7″ CLR	Rogue Fab
Mandrel-bent exhaust	1D to 1.5D is common	Needs a mandrel bender	Vibrant listings

At the extreme end, BLM Group calls bends with a CLR-to-diameter ratio under 1 “extreme” curvatures that take serious know-how. That’s production machine territory, not garage work.

D of bend is only half the difficulty story. Wall thickness matters just as much. Our guide to wall factor and D of bend shows how the two work together.

How to measure CLR: 4 reliable methods

Sometimes you need to find the CLR yourself. Maybe the die has no markings. Maybe you’re copying a part someone else bent. Here are four methods, from easiest to fiddliest. All of them start with the true OD, so measure it with calipers first. Don’t trust the label.

1. Read the die

Most dies are stamped or listed as OD × CLR. Check the die face, the box, the maker’s die chart or the listing. This is the most reliable number you’ll get. If the maker’s chart and a reseller’s listing disagree, trust the maker and ask.

2. Measure a 180° U-bend

This is the easiest way to measure a bent part. Lay the U-bend flat. Measure from the left edge of one leg to the left edge of the other leg. Same-side edges cancel out the tube size, so this distance is the center-to-center spacing. Divide by 2 to get the CLR.

Or measure the inside gap between the legs, add one OD, then divide by 2. Example: a 10.25″ gap on 1.75″ tube gives (10.25 + 1.75) ÷ 2 = 6″ CLR.

3. Measure a 90° bend with a framing square

Set a framing square against the outside of both legs. Measure the gap from the inside corner of the square to the tube, along the 45° line. Multiply that gap by 2.414 to get the outside radius. Then subtract half the OD.

Example: a 2.85″ gap on 1.75″ tube. 2.85 × 2.414 = 6.88″ outside radius. 6.88 − 0.875 = about 6″ CLR. Be careful, though. Any reading error gets multiplied by 2.4, so measure twice.

4. Measure the die groove

On a die you can measure straight across, find the diameter at the bottom of the groove. That equals 2 × (CLR − OD ÷ 2). So CLR = (groove diameter + OD) ÷ 2. A 10.25″ groove diameter for 1.75″ tube gives (10.25 + 1.75) ÷ 2 = 6″ CLR. This only works on dies wide enough to measure across.

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The tool that makes all of this easier: digital calipers

How to choose a die CLR for your project

For most garage builders, the CLR choice comes down to one die purchase. Dies cost real money, so it pays to think it through once. Work through these questions in order.

1. Do any rules apply?

For roll cages and roll bars, the rulebook comes first. SCCA Time Trials, for example, says cage bends measured at the tube centerline must have a radius of at least three times the tube diameter. Other bodies have their own rules, and they change. Benders Hub is not a tech inspector or an engineer. Read the current rulebook for your class and talk to your inspector before you buy tube or dies. Our roll cage bend radius guide has more.

2. What material are you bending?

Mild steel is the most forgiving. Aluminum is pickier. Rogue Fab says 6061-T6 is more likely to crack on tight radii and recommends about 3.5–4D, calling 3D marginal. If you’ll bend 6061, lean toward a bigger CLR. More in our 6061 aluminum tube guide.

3. What look and space do you need?

A tighter CLR looks sportier and tucks into small spaces. A bigger CLR is gentler on the tube and easier to bend. Off-road builders often land in the middle. Baileigh says the most popular off-road dies are 1.5″ and 1.75″ at about 5.5″ and 6.5″ CLR.

4. Can you buy the die, in your exact OD?

Check that your bender’s maker sells the CLR you want in your tube size. And make sure it’s a tube die, not a pipe die. Pipe is sold by nominal size. A 1-1/2″ pipe measures 1.900″ OD, so a 1.5″ tube die won’t fit it.

Quick recap before you order:

• Rules checked (cages, roll bars, anything sanctioned)
• CLR suits the material, with room to spare
• Die is sold for your bender, in your true OD
• The bend fits the space on your part

How CLR changes your layout and cut length

CLR doesn’t just change how a bend looks. It changes where the bend starts and how much tube it uses. That matters every time you cut a stick to length.

Tangent length grows with CLR

Imagine the two straight legs of a bend extended until they meet in a sharp corner. The distance from where the bend starts to that imaginary corner is the tangent length. It equals CLR × tan(angle ÷ 2). For a 90° bend, tan(45°) = 1, so the tangent length equals the CLR. A 6″ CLR die starts a 90° bend 6″ before the corner. A 7″ die starts it 7″ before.

A quick comparison

Say you need one 90° bend with legs of 24″ and 18″. Both are measured along the centerline to that imaginary corner. The cut length is the two legs, minus two tangent lengths, plus the arc.

• 6″ CLR die: 24 + 18 − (2 × 6) + (6 × 1.5708) = 42 − 12 + 9.42 = 39.42″
• 7″ CLR die: 24 + 18 − (2 × 7) + (7 × 1.5708) = 42 − 14 + 11.00 = 39.00″

Same part, different die, and the cut length changes by about 0.43″. Cut by the wrong number and your legs come out short or long.

Bigger CLRs also eat more straight tube for clamping. Plan for that on parts with bends close together. Our free bend calculator handles tangent, arc and cut length. The geometry visualizer lets you see how a change in CLR moves the bend.

Your bend won’t match the die perfectly

The Fabricator notes that harder tube and a smaller CLR mean more springback and more “radial growth.” In other words, the finished bend can open up a little after you release it. That’s why test bends matter. Our springback guide covers how to measure and correct it.

Real-life lessons about CLR

These are composite stories. The same situations come up again and again in garage-fab forums and build threads. Each one costs someone tube, time or a die order.

Common CLR mistakes (and how to fix them)

Most CLR headaches come from a short list of mix-ups. Here they are, with the fix for each.

Pro tips for working with CLR

These habits make CLR second nature. None of them cost much, and they save tube.

• 💡 Write OD and CLR together, every time. “1.75 × 6” tells the whole story. “6-inch bend” doesn’t.
• 💡 Label your dies. Paint marker or stamps on the die face: OD, CLR and max angle. Future you will be grateful.
• 💡 Keep a U-bend sample from each die. It’s a quick reference for leg spacing, and it lets you check the real CLR any time.
• 💡 Pick a house die. Many builders design most parts around one OD and one CLR. One springback number to learn, and parts that match.
• 💡 Use the centerline in CAD too. Draw tube parts as centerlines with the die CLR at each corner. Your cut lengths then come straight from the drawing.
• 💡 Check D before buying a die. Divide CLR by OD. If it’s under 3 for non-mandrel steel, think twice.
• 💡 Know when you need a mandrel. Tight exhaust bends near 1D–1.5D need mandrel support. Read more in mandrel vs rotary-draw bending.

Frequently asked questions

Your CLR checklist

Run through this list before you order a die or cut tube for a bent part.

CLR is just the radius to the middle of the tube. Get that one number right, write it next to the OD, and the rest of your layout falls into place. Your bends will match your plans, and your plans will match your parts. ✅