Centerline Radius Explained for Tube Bending

Centerline radius (CLR) is the one dimension every tube bending quote needs. What CLR means, how it differs from bend radius, and how to measure it.

Quick answer: Centerline radius, usually shortened to CLR, is the distance from the center of the bend arc to the centerline of the tube. It is the only radius a bending machine and its tooling are built around. It is not the inside or outside radius of the bend. On a Φ50 mm tube, an inside radius of 75 mm is a CLR of 100 mm. CLR is normally written as a multiple of outside diameter, so a 2D bend on Φ50 mm tube means a CLR of 100 mm. No tube bending quotation can be produced without it, because every bend die is ground for one CLR and no other.

Centerline radius, almost always abbreviated to CLR, is the radius of the arc traced by the centerline of a tube as it passes through a bend. In the UK and Australia the same dimension is usually written centreline radius. Every other radius you can name on the same bend, whether inside, outside or die groove, is derived from it.

This article makes CLR unambiguous for anyone working with CLR tube bending specifications. It covers what the dimension is, how it relates to the other radii people quote instead, why a bending machine supplier cannot price a job without it, and how to establish it when nobody wrote it on the drawing. It is written for engineers and buyers specifying industrial tube bending work.

It does not tell you which radius to choose. The smallest radius a given material and wall can take is a separate subject, covered in tube bend radius standards. Here we are only pinning down the number you already have, or finding out that you have the wrong one.

The Three Radii on One Bend and Why Only One Counts

A single tube bend has three radii that all get called the radius in conversation, and mixing them up is the most common cause of a mis-ordered bend die.

• Inside radius (ISR) is the throat of the bend, measured to the inner surface. It is the one a fitter with a tape measure reaches for, because it is the only one you can touch.
• Centerline radius (CLR) is measured to the centerline of the tube. It cannot be touched, only calculated or best fitted, and that is exactly why it is so often reported wrong.
• Outside radius (OSR) is measured to the outer surface of the bend.

The relationships are simple arithmetic. They hold for every round tube regardless of material or wall thickness, because they depend on outside diameter alone.

You have	To get CLR	Example on Φ50 mm tube
Inside radius (ISR)	CLR = ISR + OD ÷ 2	ISR 75 mm gives CLR = 75 + 25 = 100 mm
Outside radius (OSR)	CLR = OSR − OD ÷ 2	OSR 125 mm gives CLR = 125 − 25 = 100 mm
CLR, want ISR	ISR = CLR − OD ÷ 2	CLR 100 mm gives ISR = 75 mm
CLR, want OSR	OSR = CLR + OD ÷ 2	CLR 100 mm gives OSR = 125 mm

Note the size of the error. Order a die on an inside radius of 75 mm believing it to be the CLR and you get tooling 25 mm tighter than the drawing. On Φ50 mm tube that is the difference between a comfortable 2D bend and a marginal 1.5D one. On Φ168 mm pipe the same mistake is 84 mm out.

One point settles most remaining arguments. Wall thickness never enters these formulas. A 2 mm wall and a 6 mm wall on the same Φ115 mm tube share the same CLR for the same die. Wall thickness decides whether the bend can be made, and it has no say in what the radius is.

Why Centerline Radius Is Written as a Multiple of Diameter

You will constantly see CLR written as 1D, 1.5D, 2D or 3D instead of in millimeters, where D is the outside diameter of the tube. The convention exists because the difficulty of a bend scales with that ratio and not with the radius on its own. The arithmetic is trivial. Multiply the outside diameter by the number.

Written as	Meaning	CLR on Φ50 mm tube	CLR on Φ115 mm tube
1D	CLR = 1 × OD	50 mm	115 mm
1.5D	CLR = 1.5 × OD	75 mm	172.5 mm
2D	CLR = 2 × OD	100 mm	230 mm
3D	CLR = 3 × OD	150 mm	345 mm

Engineers think in ratios because the ratio predicts what happens to the material. A CLR of 150 mm is a relaxed 3D bend on Φ50 mm tube and an aggressive 1.3D bend on Φ115 mm pipe. The radius is the same, the job is different, and so is the tooling.

That is also why 1.5D has become a common basis for rating a bender. When a data sheet states a maximum capacity, the figure is quoted against an assumed CLR, and 1.5D is the usual benchmark. The consequence catches people out during machine selection. A headline capacity figure is conditional on CLR. A machine rated for a given tube at 1.5D is not making the same promise at 1D, which demands much more forming force, a tighter mandrel and far better wrinkle control. Comparing two machines on maximum diameter alone, without checking the CLR each rating assumes, compares nothing at all.

Why a Bending Quotation Cannot Be Produced Without CLR

Buyers sometimes read the request for CLR as friction in the sales process. It is not. Four hard reasons stop a machine being specified and tooling being costed until the number is on the table.

A bend die is ground for exactly one radius

A rotary draw bend die is a solid block of hardened steel with a semicircular groove machined at a fixed radius. There is no adjustment. A CNC control can change angle, plane of rotation, feed length and speed at will, but it cannot change the radius, because the radius is a physical property of the tooling. Ask for a different CLR and you are asking for a different die set, meaning bend die, clamp die and pressure die, and usually a mandrel and wiper die with them. Tooling has its own lead time and price, so CLR belongs in the machine order and not in commissioning. The selection logic is set out in tube bending tooling and how to match a die set to the job.

Capacity ratings are conditional on it

Published maximum diameter and wall thickness are quoted against an assumed CLR. Supply a tighter one and the honest answer to the question of whether the machine can do it may change from yes to no on the same tube size. A supplier who quotes without asking is quoting against an assumption and not against your part.

The mandrel decision follows from it

Whether a bend needs internal support, meaning a mandrel running inside the tube through the bend to stop the wall collapsing, is decided largely by two ratios. One is the wall factor, which is OD divided by wall thickness. The other is the ratio of CLR to diameter. Thin-wall tube on a tight CLR needs a mandrel and often a wiper die with it, while heavy-wall tube on a generous radius may not. CLR is one of the two inputs, so the tooling package cannot be assembled without it. The process is described on our mandrel tube bending page.

Several radii in one part change the machine and not just the tooling

If a single part contains bends at two different CLRs, one die cannot make it. The answer is a multi-stack tooling arrangement, with two or more die sets mounted at different heights on the bend head and the machine shifting between levels from one bend to the next. That is a configuration decision with a price attached, and it stays invisible until somebody counts the distinct radii in the part.

The practical rule is that three of the facts a supplier needs describe the part and not the machine. They are the outside diameter, the wall thickness and the CLR, and CLR is the one most often left blank.

How to Measure Centerline Radius on a Part You Already Have

A large share of enquiries arrive as a physical sample or a photograph of one, with no drawing and no radius stated. There are five routes to the number, listed here from most to least reliable.

1. Read it from the drawing, then check what it refers to

This is the fastest route and the one with the hidden trap. A drawing note reading R100 is not self-explanatory. Look for an explicit qualifier such as CLR, centerline, or to center of tube. Piping drawings frequently dimension to the centerline as a matter of course, while sheet-metal and architectural drawings often dimension to the inside surface. If the drawing does not say, ask. One line of clarification costs nothing and guessing costs a die set.

2. Measure the bend die that produced the part

If the part came off known tooling, the die is the authority. Groove radius plus half the groove width gives the CLR, and good tooling is usually stamped with its radius and tube size. This is the only method that gives the intended CLR and not the achieved one, which makes it the right reference when you are diagnosing a part that came out wrong.

3. Chord and rise on the arc

This is the shop floor method when all you have is the bent tube. Lay the part on a surface plate, pick two points on the outer surface of the bend, and measure the straight-line distance between them. That is the chord, c. Then measure the perpendicular height of the arc above the midpoint of the chord. That is the rise, h. The outer surface radius follows from the sagitta relationship.

OSR = h ÷ 2 + c² ÷ (8h), then CLR = OSR − OD ÷ 2

Here is an example on a Φ50 mm tube with a chord of 100 mm and a rise of 10 mm. OSR = 5 + 10,000 ÷ 80 = 130 mm, so CLR = 130 − 25 = 105 mm, which is 2.1D.

That result is almost certainly a 2D bend with a CLR of 100 mm, measured a little imprecisely, because the calculation is very sensitive to the rise. At 10.5 mm instead of 10 mm the answer moves from 130 mm to 124.3 mm. Half a millimeter of reading error costs nearly 6 mm of radius. Use the longest chord the bend will give you, and treat the result as an identification and not a specification.

4. Best fit the centerline with a measuring arm or CMM

A portable measuring arm, a tube inspection system or a CMM takes points around the bend, fits an arc through the reconstructed centerline and reports CLR directly, to roughly a tenth of a millimeter. Use it when the part is a reverse engineering reference, when it will support a production tooling order, or when the CLR is genuinely non-standard.

5. Derive it from the arc length

If a process sheet gives the length of material used in the bend itself along with the included angle, CLR follows from the arc length relationship.

CLR = arc length ÷ (bend angle × π ÷ 180)

An arc length of 157 mm over a 90° bend gives CLR = 157 ÷ 1.5708 = 99.9 mm, which is a CLR of 100 mm. One warning applies. Arc length is not the tangent-to-tangent dimension on the drawing, and it is not the cut length of the blank, because bend deduction and springback intervene. Treating them as interchangeable is the classic source of parts that come out short, and the corrections are worked through in pipe bending calculations.

Whichever route you take, cross-check before ordering anything. Divide your CLR by the outside diameter. If the answer is 1.0, 1.5, 2.0, 2.5 or 3.0, you have almost certainly recovered the intent of the designer. If it is 1.83, you have either an unusual part or a measurement error, and it is worth finding out which before a die is cut.

Five Ways CLR Goes Wrong on a Real Enquiry

These are the recurring failure modes, in rough order of how often they appear.

Nominal pipe size used as though it were outside diameter

This is the most expensive confusion in the list, because it corrupts every calculation that follows. In the NPS system the nominal size of a pipe is a label and not a measurement. A 2 inch NPS pipe has an outside diameter of 60.3 mm, not 50.8 mm. Likewise 1 inch is 33.4 mm, 3 inch is 88.9 mm, 4 inch is 114.3 mm and 6 inch is 168.3 mm. Tube, by contrast, is specified by actual outside diameter. Convert a radius using the nominal figure on 2 inch pipe and you are 9.5 mm out on diameter, 4.75 mm out on CLR and roughly 16% out on the D ratio.

Inside radius reported as CLR

This is still the most frequent single error, because the inside of the bend is the only radius a person can put a rule against. Treat any radius that arrives without a stated reference surface as unverified.

A fitting radius assumed to be a workable machine CLR

This mistake looks reasonable at first sight. Under ASME B16.9 a long radius elbow has a centerline radius of 1.5 times the nominal pipe size, and a short radius elbow has 1.0 times nominal. For 2 inch NPS that is a CLR of 76.2 mm on pipe measuring 60.3 mm across. A fitting described as long radius is therefore only a 1.26D bend in tube bending terms, and a short radius elbow is a mere 0.84D. Both are tighter than the 1.5D at which machine capacities are usually rated.

A forged fitting gets away with it because it was never bent from tube. It was formed and machined with wall thickness placed where the geometry needs it. Specifying the same radius as a long radius elbow for a cold-bent tube quietly asks for one of the harder bends in the process. It is often achievable, but it is not the routine job the phrase implies.

Two or more CLRs in one part, declared as one

A part where three bends sit at a CLR of 100 mm and one at 150 mm is not a single-radius part. Left undeclared, it either forces an operator to break the cycle and change tooling, which destroys the cycle time the quotation assumed, or it needs multi-stack tooling that was never priced. Count the distinct radii and state them all.

CLR taken from a 3D model against the wrong entity

Querying the radius of a swept surface returns the surface radius and not the centerline radius, and probing a filleted solid can return the fillet and not the bend. Interrogate the sweep path or the centerline sketch instead, since that is the CLR by definition. If the model came from imported geometry with no path to query, treat it as a measurement problem and use method 3 or 4.

What the CLR Figure Tells You Before Anything Is Bent

Once CLR is established it predicts a good deal about the bend without a test piece being run. The clearest example is wall thinning on the outside of the bend. The outer fiber has to travel further than the centerline, so it stretches and the wall there gets thinner. Treating the centerline as the neutral axis, the theoretical maximum thinning is (OD ÷ 2) ÷ (CLR + OD ÷ 2), which is a function of the ratio of CLR to diameter alone.

That is a geometric ceiling and not a prediction. Correctly set tooling shifts the neutral axis inward and real thinning falls below these figures, while a badly set pressure die or an undersized mandrel can approach or exceed them. Ovality and springback also worsen as CLR tightens, and both belong to tube bending defects and their causes.

The point for a buyer is narrower. The CLR you specify has already decided roughly how much wall you will lose. If the application needs a minimum remaining wall, that requirement plus the CLR sets the starting wall you must order, and it is far better to find out before the tube is purchased than after the first bend is inspected.

How CLR Drives Machine Selection

Every tube bender has a window of CLR it can handle, and not a single capability. The lower bound is how tight the machine and its tooling can form the tube without collapsing it, and 1.5D is the usual working minimum. The upper bound is physical. The bend die has to fit the bend head and swing inside the envelope of the machine, so beyond a certain radius a larger machine is needed however easy the bend is for the metal.

Treat capacity as a window, not a single number. A large machine is not simply a small machine that takes bigger pipe. It also reaches radii a small machine cannot physically swing. Telhoo’s 168CNC pipe bending machine, built for Φ168 × 15 mm pipe, has a maximum bend radius of 800 mm. A CLR of 600 mm on modest tube is a big machine job because the die is large and not because the bend is hard.

Where CLR interacts with machine choice most sharply is repeatability. Producing one bend at a given CLR is a tooling question, while producing ten thousand within tolerance is a control question. That is the practical dividing line between a NC semi-automatic tube bender and a CNC automatic pipe bending machine. The forming method underneath both is rotary draw bending, and the part types it covers are set out under our tube bending solutions.

The governing documents for the fitting dimensions cited above are ASME B16.9 for buttwelding fittings and ASME B36.10M for nominal pipe size outside diameters.

Getting the Number Right Before You Ask for a Price

CLR is one small dimension that settles a great deal. It decides which die is ground, whether a mandrel is needed, whether the rated capacity of a machine applies to your tube, how much wall you keep on the outside of the bend, and, when a part carries more than one radius, what configuration of machine the job requires. None of it can be settled afterwards.

So before sending an enquiry, confirm three things. They are the actual outside diameter of the tube and not its nominal size, the radius and the surface it was measured to, and how many distinct radii the part contains. With those settled, a supplier can answer the real question, which is whether this machine can make this part repeatably at the rate you need. If the radius is not certain, send the data as you have it. Tell us the tube size, wall thickness, material and the bends you need and we will work the CLR back before proposing a machine.