"The maximum penetration of an AP shell was very roughly equal to its caliber; that is, a 14" shell could penetrate up to 14" of armor at likely battle ranges."USN formula for AP shells against naval armor (naval armor had different chemical compositions compared to other armors for land/air warfare):
T/D = (1728.04)(W/D3)[(V/F)Cos(Ob)]2
T = thickness of the armor
D = diameter of the shell in inches
W = weight in pounds
V = velocity in feet per second
Ob = obliquity in degrees
"The factor F took into account all other effects, including the composition of the armor and deviations from the ideal formula, and the Navy compiled extensive tables of F based on ballistic tests."
I'm looking for these F tables but I haven't found them yet.
"The U.S. Navy anticipated that the Iowas could absorb three torpedo hits with little chance of being sunk (1% chance for one hit, 2% chance for two hits, and 10% chance for three hits.) Thereafter the likelihood of sinking rose rapidly, to 40% for four hits, 70% for five hits, and 90% for six hits. This reflected both the loss of reserve buoyancy and the likelihood of subsequent hits striking close to previous hits, where the underwater protection was already stripped away. The Iowas were considered to have excellent subdivision, suggesting that the odds of survival were significantly less for many other large warships."
Source:
http://pwencycl.kgbudge.com/A/r/Armor.htm