Armor

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

At level 18, base armor ranges from 61 to 90 ( and ).

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

Damage reduction when armor greater than or equal to 0 is formulated by 100 / (100 + armor value)

$$\pagecolor{Black}\color{White} \text{Damage multiplier} = \begin{cases} \frac{100}{100 + armor} & \text{if armor} \ge 0\\ 2 - \frac{100}{100 - armor} & \text{if armor} \le 0 \end{cases} $$

Examples:
 * 25 armor &rarr; &times;0.8 incoming physical damage (20% reduction).
 * 100 armor &rarr; &times;0.5 incoming physical damage (50% reduction).
 * &minus;25 armor &rarr; &times;1.2 incoming physical damage (20% increase).

Damage Reduction % values displayed in game are calculated as:

( armor / ( 100 + armor ) ) or ( 1 - ( 100 / ( 100 + armor) ) ) 

Stacking armor
the more armor you have, the less efficient buying more armor becomes
 * Example: A unit with 60 armor has 37% physical damage reduction(so if the enemy has an auto attack of 100, it would only do 63 damage, or an auto attack of 200, only 126) However If a unit has 120 armor, they only recieve 54% Physical damage reduction, not 74%. this is becuase if a unit got 100% physical damage reduction, they would be immune to ALL physical damage(assuming there enemy has no armor pen.)

What this means: by definition, armor has diminishing returns.
 * 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.

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.
 * lays down a cloud of smoke for 8 seconds. While inside of the cloud, she gains 10 / 20 / 30 / 40 / 50 armor.
 * 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 20/30/40/50/60 for 8 seconds.
 * increases an allied champion's armor by 30/45/60/75/90 for 4 seconds.
 * allows him to increase his armor by 0.5 permanently (max. 25) each time he kills a unit.
 * 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.
 * passively increases his armor by 10/13/16/19/22. When activated it throws a flag to a target location that grants the passive benefit to nearby allies and to himself again.
 * increases his armor by 25 / 35 / 45 (+0.3 per bonus attack damage) for 8 seconds.
 * increases his armor by 10/20/30/40/50 for 4 seconds.
 * increases his armor by 10/15/20/25/30 for 5 seconds.
 * increases her armor by 30/40/50/60/70 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 20/25/30/35/40 % for 6 seconds.
 * causes him to channel for up to 5 seconds. While channeling his armor is increased by 100/150/200/250/300.
 * increases an allied unit's armor by 10/15/20/25/30 for 6 seconds.
 * increases her armor by 10/20/30 while active.
 * increases his armor by 30/45/60 for 6 seconds.
 * increases an allied champion's armor by 10/15/20/25/30 for as long as the ball is attached to them.
 * increases her armor by 1.5/2/2.5/3/3.5 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 40/60/80/100/120 for 6 seconds.
 * passively increases her armor by 10/15/20. This bonus is doubled while she is in Dragon Form.
 * increases his armor by 35/50/65 for 25 seconds.
 * Aura: increases nearby allied champions' armor by 3/6/9/12/15 while active and persists for two seconds after deactivation.
 * Activation: increases hers and one nearby allied champion's armor by an extra 8/11/14/17/20 for 3 seconds.
 * increases an allied unit's armor by 25/45/65/85/105 for 5 seconds.
 * passively increases his armor by 10/15/20/25/30 while the ability is not on cooldown and grants himself and nearby allied units' the same bonus again as a permanent aura.
 * targets an enemy to steal their armor by 15/20/25 %. This amount is doubled over the next 6 seconds. Trundle increases his own armor by the same flat amount as the armor they enemey lost.
 * increases his armor by 80 / 105 / 130 for 5 seconds upon activation.
 * passively grants him armor for each nearby enemy champion.
 * passively grants 15% of his ability power as bonus armor.
 * increases his armor by 25 (+7/10/13 for each enemy champion hit) for 8 seconds.
 * increases his armor by 25 (+7/10/13 for each enemy champion hit) for 8 seconds.

Masteries

 * increases your champion's armor by 2/4/6.

Runes

 * and runes also increase armor.

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

Trivia
A level 18 with 6, 3 points in , , , , ,  aura, Marks and Glyphs of , Seals and Quintessences of , and  enabled will give a total of approximately 1461 armor. Switching for  and having an enemy  with the same setup use  on  and the allied  use  on the enemy, will yield a total of approximately 1864 armor. This is the highest possible amount of armor.