Theoretically the ballistic coefficient can be calculated if you know the mass M (lbs), diameter D (in), drag coefficent c and drag coefficent of the so-called G1 model bullet (0.52 roughly), so (theoretically) the question is the same as asking what is the drag coefficient.
A ballpark figure for the drag coefficient of any given bullet is 0.3 (probably not a boattail), so a 223 caliber (.224" diameter) 62 grain bullet would have a BC of
BC = M/c/d/d*G1 = 62/7000 lbs /.3/.224/.224*0.519 = .306, possibly within 5%
Edited to say, looking through the manuals just now it looks like the 0.3 drag coefficient assumption probably applies to only to pointed bullets, since the stated BC's for round noses & hollow points appear to depart radically from theory (the BC is much lower) :-/