Max armor penetration?

Armor reduction (which is provided in percentiles and usually stacks on hit) is vastly different than penetration. What makes reduction unique is that it is required for penetration to truly have a noticeable effect. You apply X% of armor reduction before applying X-Value of armor penetration. The math can be a bit confusing for some people to figure out because it's exponential. Honestly the exponential part doesn't matter, what matters is that it IS exponential which means there is a chance for multiplicities, there in armor penetration and reduction are dependent on each other to see a vast difference from seeing them at work separately. Also keep in mind, any damage over the enemies armor (obtained through the mix of penetration and reduction, which together is known as peeling) is true damage. Some people mistake what true damage is. Some think that true damage can only happen when using an item or an active that says true damage specifically. All that true damage means is that the specified damage is ignoring all resistances, unless prevented. (I.E. Barrier/Regenerative Healing/Block/Dodge etc. Now that I have explained what true damage is typically associated with, I will explain the correlation between armor pen, reduction, and true damage. Reduction enables armor penetration to multiply itself and eventually with enough reduction to "pierce" through armor. So the equation is basically this. Reduction + Armor Penetration = X -Armor Value + X True Damage, the True damage is obviously Attackers Damage - Defenders Remaining HP. This may seem op, and it can be in the right team comp because it allows for the strongest initiation possible in a team fight, however, it can be countered by building items that negate attacks, slows attacks, reflects damage, or creates a barrier. This may not seem like much of a counter because all it takes is time for the attacker to break though, however it provides a window for burst and dps to melt the glass cannon. To be able to counter this you would need your tanks to avoid damage until after the enemy is burst down and come in for the clean up before the enemy can peel and finish off the tank/fighter/bruiser. I personally have had no problems steamrolling with an armor penetration and reduction focused build,but it does make you a glass cannon, similar to an ap carry that only builds offensive items.

I know I rambled some, but there are distinct differences between the two features and also a huge difference when not using them along side each other. if you're not building reduction, don't bother building armor pen because it will be negated by stacking armor.

Champions that I have found work well with armor pen include: Vi/Darius/Xin/Renekton/Talon/Sivir (plus several other adc's ofc)/Noct/Olaf....Many others as well but I don't feel like going through a list. lol You can figure it out after playing around with it a little. Vi/Darius are top pics because of their natural peeling abilities, Talon not too far behind but less opportunistic than Vi and Darius because of thelowe rchances of aplifying the peeling effect. He is however a great burst/peel combo. :)

Definams answer is wrong because the max flat armor Pen is 59.2 and flat armor pen is getting applied after the % armor pen and if you also have 5 cleaver stacks the way you calculate is:

a = Armor
p = Flat Pen
b = Black Cleaver
i = Ignored Armor (% armor Pen)

We search for X = Armor after all pen

[a * (100% - b) * (100% - i)] - p = x

For example with these stats:

a = 200    p = 40    b = 25%    i = 35%

we'd have:

(200 * 75% * 65%) - 40 = 97.5

97.5-40 = 47.5

If I now take the maximum Armor Penetration possible

a = 200     p = 59.2    b = 25%    i = 48.6%

the actual armor of the target would be:

(200 * 75% * 51.4%) - 59.2 = 77.1

77.1-59.2 = 17.9

So with maximum Armor Pen on Darius you do nearly True DMG to Enemies with 200 Armor since they technically only have 17.9 armor left. And Enemies with under 154 armor recieve True dmg.

Armor Pen doesn't stack, it's being multiplied so the maximum amount you can have there is

0.35*1.06*1.25 = 0.486