Armor

Armor reduces the amount of physical damage a champion receives by a percentage. Every champion starts with a certain amount of armor that increases with level. You can gain additional armor from runes, masteries, some champions' abilities, and items.

At level 18, base armor ranges from 61 to 91 ).

Damage reduction
Incoming physical damage is multiplied by a specific factor based on your armor: \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} $$
 * $$\pagecolor{Black}\color{White}

Example: 25 armor &rarr; $$\pagecolor{Black}\color{White} \text{Damage multiplier} = \frac{100}{100 + 25} = \frac{100}{125} = \underline{0.8}\text{,} $$ so incoming physical damage is reduced by 20 percent.

It is important to note that the amount of health you have is irrelevant to the effectiveness of armor. For example: 25 total armor always reduces damage by 20 percent.

A graph showing the damage multiplier decrease as armor increases above 0.

A graph showing the damage multiplier increase as armor decreases below 0.

Damage reduction from armor and from any other sources stack multiplicatively.

Effective health
You can also view armor as a sort of "extra health," where each point of armor gives your champion 1 percent extra health. For example: if your champion has 100 armor, you could calculate the damage multiplier as being 0.5, or imagine that your champion has 100 percent more health. No matter how you view it, the end result is that physical attacks are half as effective against your champion.

This extra health, combined with your normal health, is called effective health. A champion's effective health can be calculated as:
 * $$\pagecolor{Black}\color{White}

\text{Effective health} = \begin{cases} \frac{health \times (100 + armor)}{100} & \text{if armor} \ge 0\\ 0.5 - \frac{25}{armor - 50} & \text{if armor} \le 0 \end{cases} $$

Example: 500 health and 25 armor &rarr; $$\pagecolor{Black}\color{White} \text{Effective health} = \frac{500 \times (100 + 25)}{100} = \frac{500 \times 125}{100} = 500 \times 1.25 = \underline{625} $$

A graph showing effective health increase as armor increases. (Effective health represented as a multiplier of base health.)

Negative armor
Effects that reduce armor can bring armor into negative values, causing physical damage to be more effective. This is only true for Armor Reduction effects, though, as Armor Penetration cannot reduce armor below 0. Negative armor does not follow the same formula as positive armor, however (see the next section for why). Negative armor &minus;x increases damage by the same percentage that positive armor x reduces damage by.

Example: &minus;15 armor &rarr; $$\pagecolor{Black}\color{White} \text{Damage multiplier} = 2 - \frac{100}{100-(-15)} \approx 2 - 0.87 \approx \underline{1.13}\text{,} $$ so incoming physical damage is increased by ~13 percent.

As a result, the formula for effective health is different as well.

Rationale
If the original damage multiplier formula is followed back into negative numbers, you can see that the multiplier begins to increase dramatically, approaching infinity as armor approaches &minus;100 and being negative when armor is less than that. In order to keep this from happening, a different formula is used that does not have such an asymptote; with this new formula, having &minus;100 armor adds 50% physical damage instead of making it infinite, and the damage increase softly approaches 100%.

Diminishing returns
Contrary to popular belief, armor does not have diminishing returns from an effective health perspective; each point of armor increases the amount of physical damage required to kill the champion by 1 percent of the champion's health. For example: 100 armor initially reduces physical damage by 50 percent, so 100 percent more damage is required to kill the champion.

This table lists damage reduction and effective health bonuses granted by various armor levels. The effective health numbers are based on a champion that has 1000 health. Note that the effective health increase is constant as armor increases; increasing armor from 0 to 10 gives 100 additional effective health, and increasing from 500 to 510 gives the same 100 additional effective health. No matter how much armor is present, the next 10 points provide 100 additional effective health. This can also be seen in the graph linked above (see section: Effective health), showing a straight line that represents the constant increase.

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 cover of smoke for 8 seconds where she gains 10 / 20 / 30 / 40 / 50 armor while in.
 * allows her to enter her egg-state for up to 6 seconds upon reaching 0 health, while on this state, she will receive an armor modifier of.
 * increases her armor by 10/20/30/40/50 for 15 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 each time he kills a unit with a maximum of 25.
 * 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 10/20/30/40/50 for 4 seconds.
 * increases her armor by 30/40/50/60/70 for 3 seconds, deals damage after that time to units around her, and gains another 3 seconds of the buff if she hit any enemy with the blast.
 * increases his armor by 20/25/30/35/40 % for 6 seconds.
 * makes him channel for up to 5 seconds, during this time he increases his armor 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 an allied champion's armor by 10/15/20/25/30 for as long as the ball is attached to it.
 * 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 50/75/100/125/150 for 6 seconds.
 * passively increases her armor by 15/20/25. 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 8/11/14/17/20 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 25/50/75/100/125 for 5 seconds.
 * passively increases his armor by 10/15/20/25/30 and grants himself and nearby allied units' the same bonus again while the ability is not on cooldown.
 * 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
Note that armor penetration and armor reduction are different. See the below article for more information.

List of champions' armor
†The permanent aura of and  and passively increase their armor by 30 and 25 at max ranks. This would put them at 104 armor at Lv 18, topping the rankings at 1st.

‡ however, would let him tie with and  at 90 armor by passively increasing his armor by 22 at rank 5.

The highest possible armor in Summoners Rift is 1871.