Can anyone tell me the radius of the turnout on a #6 turnout?
It depends on the manufacturer, but it also depends on your question. Are you asking about the ‘substitution’ radius (meaning whether to insert this ‘non-curved’ turnout into a larger curve so as to interfere as little as possible with the intended path on the larger curve), or the radius of the closure rails and points?
Generally, a #6 turnout has a curve near 43" for the closure rails.
http://www.pcrnmra.org/pcr/clinics/Kolm-TurnoutsWhatYouNeedtoKnow-PCR2008-handout.pdf
Fast Tracks specifies their #6, which is NMRA spec compliant, as having a 45" substitution radius when built to its minimum length.
CG
Since no one has explained, and the way you asked the question, you might want to be sure you understand the geometry of a turnout. The diverging route is not a constant curve, so it does not “fit” into the radius of a curve perfectly.
The points are generally straight, just changing the directon of the train by a few degrees, then the rails curve until they have to cross the straight route, at which point they straighten out again. Then, they may or may not continue to curve after the frog.
The “number” of the turnout refers to the frog angle - #6 = one unit of offset in 6 units of travel.
Maybe someone has a link to a good drawing, or you can read a lot more here:
http://www.nmra.org/index-nmra-standards-and-recommended-practices
Sheldon