Since no one, including the wiki has yet supplied the accurate penetration depth formulas (though most people here know them from other posts since forever..):
And soon to come in 7.2, the most devastating of all:
So this means a missile warhead of 4 will harm 2 layers. A warhead of 9 - 3 layers, and a 25 warhead is 5 layers. Note that this of course means that you need a 25 warhead to punch through
4 layers of armor (dealing only 1 point of internal damage with that 5th row though).
With lasers for example you have a stretched out, but still essentially square expanding structure, so that is why there is multiplication inside the root. A 3 damage laser pierces through sqrt(3*3)=3 layers as obvious, and a 6 damage laser does 4.{something}, so that is 4. (5 damage would however only be sqrt(15) and not make it)
I find these calculations mostly useful the other way around though, which is planning armor strength. I won't spoiler you, but there are certain attack strengths you can count on out there, and having the exact armor strength that can tank one of those is only sensible planning.
So to figure out what your armor can block, reverse the formulas..
Against lasers that means that x armor layers are at minimum needed to block these y laser powers:
3 blocks 3
4 blocks 5.333, so that is a 15cm with 6
5 blocks 8.333, meaning that a strength 9 laser hit will be enough to pierce 4 armor, so you need 5 from then on.
6 blocks 12, which means up until then 5 armor were enough, so 5 layers also block 20cm laser with strength 10
7 is 16.333, so 6 layers are barely enough to ward against the 25cm~-16 damage laser
8 provides enough against the damage 24 size 30cm lasers
9 is needed against damage 32
11 against 42
22 against 168
88 layers against 2598
More would be vanity, especially considering that shock damage switches into the deal much earlier. With lances coming, up to 51 might also look kind of convincing, depending on how much and how strong use AI make of those.(I dare to predict however: not too much)
///edit: Had to correct wrong armor calculations.