Armor

Armor is a stat shared by all units, including minions, monsters, and buildings. Increasing armor reduces the physical damage the unit takes. Each champion begins with some armor which increases with level ( being the only exception). You can gain additional armor from abilities, items, masteries, and runes. Armor stacks additively.

Excluding whose base armor does not scale with levels, base armor ranges from 65.5  to 96.7 ( and ) at level 18.

Damage reduction
Incoming physical damage is multiplied by a factor based on the unit's armor:

$${\rm Damage\ multiplier}=\begin{cases} {100 \over 100+{\it Armor}}, & {\rm if\ }{\it Armor} \geq 0\\ 2 - {100 \over 100 - {\it Armor}}, & {\rm otherwise} \end{cases}$$

Examples:
 * 25 armor &rarr; &times; incoming physical damage (20% reduction, +25% effective health).
 * 100 armor &rarr; &times; incoming physical damage (50% reduction, +100% effective health).
 * &minus;25 armor &rarr; &times; incoming physical damage (20% increase, effective health).

Stacking armor
Every point of armor requires a unit to take 1% more of its maximum health in physical damage to be killed. This is called effective health.
 * Example: A unit with 60 armor has 60% more of its maximum health in effective health, so if the unit has 1000 maximum health, it will take 1600 physical damage to kill it.

What this means: by definition, armor does not have diminishing returns in regard of effective hitpoints, because each point increases the unit's effective health against physical damage by 1% of its current actual health whether the unit has 10 armor or 1000 armor.


 * Note: Unlike health, increasing armor also makes healing more effective because it takes more effort to remove the unit's health than it does to restore it.

For a more detailed explanation, see this video.

When a unit's armor is negative because of armor reduction or debuffs, armor has increasing returns, because negative armor cannot reduce effective health to less than 50% of actual health. A unit with −100 has (gains ) of its maximum health as effective health.

Armor as Scaling
These use the champion's armor to increase the magnitude of the ability. It could involve total or bonus armor. By building armor items, you can receive more benefit and power from these abilities.

Champions

 * grants armor equal to of his bonus armor to himself and the target ally (in addition to a base amount) for 3 seconds.
 * grants armor to himself equal to 20% of his bonus armor.
 * grants armor to herself equal to 20% of her bonus armor (in addition to a base amount) for 3 seconds.
 * grants armor to himself equal to of his armor.
 * deals magic damage equal to 30% of his armor (in addition to a base amount).
 * deals magic damage equal to 10% of his armor (in addition to a base amount).
 * grants attack damage to himself equal to 25% of his armor.
 * grants his next basic attack bonus magic damage equal to 20% of his armor after using an ability.
 * grants bonus armor to himself and nearby allied champions equal to 12% of his armor.
 * active deals magic damage equal to 20% of his armor (in addition to a base amount) and reduces nearby enemy armor by 5% of his armor (in addition to a base amount) for 4 seconds.
 * steals 20% of the target's armor. He continues to drain an additional 20% the target's armor over 4 second before decaying 4 seconds after the drain completes.

Items

 * active increases its slow duration by a base amount plus of the wearer's total armor.

Champion abilities
Note: Only the armor buff effect of these abilities is shown here, to read more information on each of these abilities, follow the link on each of them.
 * allows her to enter an egg-state for up to 6 seconds upon reaching 0 health. While in this state, she will receive an armor modifier of.
 * increases her armor by for 5 seconds.
 * increases armor by to himself and the target ally for 3 seconds.
 * increases an allied champion's armor by for 4 seconds.
 * increases his armor by 2level when transform into.
 * increases his armor by 20% of his bonus armor.
 * increases his armor by every second he remains in combat. This bonus stacks up to 10 times. Graves is considered in combat if he has dealt or received damage in the last 3 seconds.
 * increases his armor by.
 * increases his armor by for 4 seconds.
 * increases her armor by  for 3 seconds, deals damage after that time to units around her, and retains the defensive buff for an additional 3 seconds if any enemy is struck by the blast.
 * increases his armor by for 6 seconds.
 * increases an allied unit's armor by for 6 seconds.
 * passively increases his armor by.
 * increases an allied champion's armor by for as long as the ball is attached to them.
 * increases her armor by for 5 seconds upon attacking or being hit by an enemy, stacks up to 10 times. She can also activate this ability to gain max stacks.
 * increases his armor by for 6 seconds.
 * Rengar lets out a battle roar, damaging enemies increases his armor by for 4 seconds. Rengar gains additional 50% armor for each enemy champion or large monster hit.
 * grants her bonus armor each times she damages an enemy with an ability or attack for 2 seconds. Subsequent damage will increase the duration by 2 seconds up to a cap of 8 seconds, after where damage will refresh the duration.
 * passively increases her armor by . This bonus is doubled while she is in Dragon Form.
 * increases his armor by for 25 seconds.
 * passively increases his armor by while the ability is not on cooldown and grants himself and nearby allied units' 12% of his armor.
 * passively generates souls for him to collect, with each soul collected granting armor permanently.
 * takes 40% of the target's armor and gains an equal amount of armor. Over 4 seconds, the bonus armor is doubled. The armor bonus lasts for another 4 seconds after the drain completes.
 * increases his armor by for 5 seconds upon activation.
 * passively grants him armor for each nearby enemy champion.
 * increases his armor by for each enemy champion hit for 8 seconds.

Masteries

 * increases bonus armor and magic resistance by.
 * increases your champion's armor by.
 * grants your champion armor and  magic resistance for each nearby enemy champion

Ways to reduce armor
See armor penetration. Note that armor penetration and armor reduction are different.

Armor vs. Health
Note: The following information also applies to Magic Resist.

It can be helpful to understand the equilibrium between maximum HP and Armor, which is represented in the graph on the right. The equilibrium line represents the point at which your champion will have the highest Effective Health against that damage type, while the smaller lines represent the baseline progression for each kind of champion from level 1-18 without items. The most important point to keep in mind when studying this graph is the fact that HP is much easier to come by in a full item build, therefore you should not worry about trying to hit the exact equilibrium. You can also see that for a somewhat brief period in the early game HP is the most gold efficient purchase.

There are many other factors which can effect whether you should buy more Armor or HP, such as these key examples:
 * Whether or not the enemy is capable of delivering true damage or percent health damage, thus reducing the value of HP stacking.
 * The presence of resist or HP steroids built into your champion's kit, such as in Garen's or Cho'Gath's.
 * Against sustained damage Life steal and healing abilities can be considered as contributing to your maximum HP (while being mostly irrelevant against burst damage).
 * The need to prioritize specific items mainly for their other qualities (regardless of whether or not they contribute towards the ideal balance between HP and resists).

Trivia
[Last updated 4/6/2015 on patch 5.10] One of the biggest amount of armor any champion can obtain, aside from, is (which reduces physical damage by ), being a level 18  with:
 * All armor runes and masteries
 * 9 Marks of Armor
 * 9 Scaling Seals of Armor
 * 9 Glyphs of Armor
 * 3 Scaling Quintessences of Armor
 * 3 points in
 * 2 points in
 * 4 points in
 * 6
 * cast by a.
 * cast by an.
 * cast by a with the maximum amount of armor.
 * cast by.


 * Relevant mathematics:


 * Armor(())
 * Armor((()))

Having an enemy with the same setup use  on  will yield a total of  armor. This is the highest possible finite amount of armor (without using metagame effects—see below), and reduces physical damage by.

Relevant mathematics:


 * Armor
 * Armor((()))

It is still possible to go higher through metagame functions. If a summoner disconnects from the server and is in the fountain, his champion will gain 1000 armor. With the same setup as above, a disconnected  with a disconnected  will have approximately 2779 armor. cannot exceed this. This reduces physical damage by.

If disconnecting grants armor quickly enough that  remains active, can reach 3143 armor. This reduces physical damage by.

, with his effectively infinite stacking, can obtain a maximum of  armor off his passive alone. With the same set-up as above, he can obtain a total of about armor, reducing physical damage by. If he disconnects, he can obtain up to armor, reducing it by