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Well a piece of flex track is about 3 feet, and the circumference of a circle is C equals Pi times diameter diameter = 2 (Radius)
C = 3.14 · (d)
Radius= 18" so C= 3.14 (36) = 113.04" 113.04"/36"= 3.028 pieces of flex track
For Atlas sectional track (that's what I used), each 18"R section covers 30 degrees, so 12 pieces.
For Atlas 22"R & 24"R, each section covers 22.5 degrees, so 16 pieces.
Bold added by me. Thank heavens someone who knew what they were talking about answered.
For those calculating lengths for flex track, the numbers shown are going to be short. Remember the radius of a curve is measured from the center of the track. One would really want that outside rail to be long enough so add 1/2 the track gauge to the radius before performing the calculation. For an approximation use 3/8" for HO. Calculate an 18" radius curve using 18 3/8" instead.