Find Your Radius

Published: February 15, 2021
by Charles Busada
A flared tubing section that has seen years of use.

How to identify the radius of a bend for a bend less than 180 Degrees.
Imagine if you got a picture like this in your email and your customer said, “make us one just like this.” On top of that, they insist that this is a bend on a 24″ radius. They can’t ship you the old bend because they are still using it. Your gut feeling is that if you replace this with a 24″ radius bend, your customer will not be happy about the result.

The customer was not careful to measure the true arc of the bend, and thus, estimated a much larger circle. Pictured here, is our result and the radius of 9″ is quite different!

So, with a few principles, we can get a close approximation of the bend radius even from the photograph.

What we need to do is estimate the circle that the inside curve of the bend makes. From that, we can estimate the radius (the inside radius) and then knowing the Outer Diameter of the bend, we can estimate the CLR (Center-Line-Radius).

A radius of a circle is the length of a line from the center of a circle to its perimeter. When measuring a curved bend you can measure from the inside of the bend or outside to yield the inside or outside radius respectively. From that, you can deduce your true center-line radius.

1) First, simply draw the arc of your mystery bend (either inside or outside). Tape a pencil on the end of a yardstick to do this easily.

2) Create two chords.

A chord is a straight line connecting two points on a curve. Draw two chords as pictured (the longer the better) and using a measuring tape, measure the distance between the two end of the chord. This measurement will be the chord length. The longer the chord you create, the better your radius calculations will turn out.

3) Create midpoints:
The midpoint is the middle point of a line segment. To find the midpoint on your chords simply divide your chords in two. Mark the midpoint and draw lines at 90 Degree angles as in your picture.

Draw intersecting lines. Measure the lines from the intersections to the chord.

Final step. If you drew your arc from the inside of your bend, add 1/2 the tube outer diameter to get your true center-line radius.

If you drew your arc from the outside (top) of your bend, subtract 1/2 of the tube outer diameter to get your true center-line radius.


For a check you could add a third chord, and you should get the same intersection point.

If you really want to check again you can . . .
Measure the distance 90 degrees off the midpoint of one of the chords that you drew. This is called the “mid-ordinate rise” or simply the “rise.” The more accurate you are in creating this right angle with your measuring tape and string, the more accurate your radius calculations will be.

To calculate the radius of the curved surface, just follow the formula below.

Other Helpful Resources

Share This