Reading closely again I see that people have commented above on the same thing. I'll leave my somewhat redundant post below since it has a nice picture I stole on the web.

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When you bend something the outside will stretch and the inside will compress.

So the length of the original bar is somewhere in the middle, called the neutral axis.

So the thickness of the material has to be taken into account.

On a large bend radius in relation to the material thickness the neutral line is in the middle.

On tight bends it is closer to the inside of the bend. I found this as a guideline - Basic Diemaking Eugene Ostergaard R<2T C=.33T, R=2T-4T C=.4T, R=>4T C=.5T R=Inside Bend Radius, T=Thickness of material, C=Location of neutral axis.

Anyway, back to the question - 1"X1/4" flat bar that has been rolled and has a diameter of 20".

Since it's a large bend, radius 10" while the thickness of the bar is only 1/4" then neutral line is in the middle.

Is the 20" outside or inside diameter?

**Outside? **
That means the center of the circle is 20"-1/4" = 19.75". Length of the bar is then 62" (length x 3.14).

**Inside? **
That means the center of the circle is 20"+1/4" = 20.25". Length of the bar is then 63.6" (length x 3.14).

If the material thickness in relation to the bend would have been greater, then the formula above would have to be adjusted because the neutral axis would not be in the center anymore.

For instance say taking a 3/8" rod and bending it into a 1" ring.