Armor penetration is a champion statistic that allows the champion to ignore some or all of a target's armor. All champions have 0 base armor penetration but can increase it with items, runes, masteries and some champion abilities. This cannot affect enemy armor beyond 0 to deal bonus damage.
Armor reduction is the effect of some items and champion abilities that temporarily reduces the armor of one or more targets. This allows allies to benefit from the reduction of armor. This can reduce armor below 0, resulting in bonus damage (see Armor).

Order of calculations

When attacking, armor penetration and armor reduction are considered in the following order

1. Armor reduction, flat
2. Armor reduction, percentage
3. Armor penetration, percentage
4. Armor penetration, flat

Flat armor reduction

The target's armor is reduced by an amount. Flat armor reduction stacks additively.

Example: 20 armor reduction reduces the target's armor by 20, so a target with 30 armor will be reduced to 10 armor. (30 − 20 = 10)

Flat armor reduction can reduce a target's armor below zero. For example, if an enemy with 10 armor has their armor reduced by 25, the enemy will have −15 armor.

Percentage armor reduction

The target's armor is multiplied by a percentage (100% − the listed reduction). Percentage armor reduction stacks multiplicatively. Percentage armor reduction is ignored if the target's armor is 0 or less.

Example: 20% armor reduction multiplies the target's armor to 80%, so a target with 30 armor will be reduced to 24 armor. (30 × 0.8 = 24)

Percentage armor reduction makes a bigger difference on targets with higher armor. For instance, with 40% armor reduction, a target with 200 armor will lose 80 while a target with only 50 armor will lose 20.

Percentage armor penetration

The target's armor is treated as being multiplied by a percentage for purposes of damage calculation (100% − the listed penetration). Percentage armor penetration stacks multiplicatively. Percentage armor penetration is ignored if the target's armor is less than 0.

Example: 20% armor penetration causes the target to take damage as if its armor was multiplied by 80%, so a target with 30 armor will be treated as though it had 24 for purposes of damage calculation (the target's actual armor value will not change, however).

Because the target's actual armor value does not change, anything else depending on that value also doesn't change (e.g. Rammus's Spiked Shell).
Percentage armor penetration makes a bigger difference on targets with higher armor. For instance, with 40% armor penetration, a target with 200 armor will be considered as having 80 less while a target with only 50 armor will be considered as having 20 less.

Flat armor penetration

The target's armor is treated as being reduced by an amount for purposes of damage calculation, but cannot be reduced below 0. Flat armor penetration stacks additively.

Example: 20 armor penetration causes the target to take damage as if its armor was 20 less, so a target with 30 armor will be treated as though it had 10 for purposes of damage calculation (the target's actual armor value will not change, however).

Because the target's actual armor value does not change, anything else depending on that value also doesn't change (e.g.  Rammus's Spiked Shell).

Given 20 flat armor reduction and 30% armor reduction, and the target is affected by 10 flat armor penetration and 35% armor penetration,

• Target A has 80 armor.
  • The 80 is reduced to 60 by the 20 armor reduction.
  • The 60 is reduced to 42 by the 30% armor reduction.
  • The 42 is considered to be 27.3 by the 35% armor penetration.
  • The 27.3 is considered to be 17.3 by the 10 armor penetration.

Target A takes damage as if it has 17.3 armor.

• Target B has 18 armor.
  • The 18 is reduced to -2 by the 20 armor reduction.
  • The -2 is not affected by any further calculations because it is less than 0.
    • Target B takes damage as if it has -2 armor.

Before Preseason 3 Patch:

• Target A has 80 armor.
  • The 80 is reduced to 60 by the 20 armor reduction.
  • The 60 is reduced to 42 by the 30% armor reduction.
  • The 42 is considered to be 32 by the 10 armor penetration.
  • The 32 is considered to be 20.8 by the 35% armor penetration.

Target A takes damage as if it has 20.8 armor.

• Target B has 18 armor.
  • The 18 is reduced to -2 by the 20 armor reduction.
  • The -2 is not affected by any further calculations because it is less than 0.

Target B takes damage as if it has -2 armor. 

 Notes 

• Armor penetration is a very valuable stat for physical damage dealing champions. There are few sources for it, so Desolation marks and quintessences are very popular runes.
• Armor penetration benefits all sources of physical damage including all champion abilities that deal physical damage.
  • For example, Xin Zhao's Crescent Sweep will benefit from armor penetration as it deals physical damage, however his Audacious Charge will not benefit from armor penetration as it deals magical damage.
  • The items that deal on-hit physical damage: Tiamat, Ravenous Hydra, Sheen, and  Trinity Force, will also benefit from Armor Penetration.