Ability power

Ability power (or AP) is a stat that increases the effectiveness of most champions' abilities. Abilities in League of Legends that are affected by ability power have an ability power ratio. This ratio determines how much a particular ability will benefit from a champion's total ability power, whether through increased damage, healing, and other numerical values. Ability power stacks additively.

Calculations To calculate the bonus to a numerical value in an ability, the formula is
 * Bonus = AP &times; AP ratio.

For example, if a damage spell has an ability power ratio of 0.25, every 4 points of ability power will increase the damage of this ability by 1. Abilities that are affected by ability power are identifiable by a bracketed plus sign with a green font, along with a number that corresponds to the applicable bonus. For example a champion with 50 ability power who has an ability with an ability power ratio of 0.7, it will display "+35" (50 &times; 0.7) next to the corresponding value in the UI.

Classic

 * : On use, grants +20-40 ability power (based on champion level) and +10% cooldown reduction for 4 minutes.
 * : On use, grants +20-40 ability power (based on champion level) and +10% cooldown reduction for 4 minutes.

Champion abilities
Note: Only the ability power buff effect of these abilities is shown here, to read more information on each of these abilities, follow the link on each of them.
 * adds 50% of his total magic resistance to his bonus ability power.
 * increases her ability power by corresponding to her percentage of missing health. The value increases depending on her level.
 * Increases the the Ability power of the target by 20 / 30 / 40 / 50 / 60.
 * grants him 35 / 50 / 65 ability power for 25 seconds.
 * aura grants herself and nearby allied champions 4 / 8 / 12 / 16 / 20 bonus ability power while active.
 * grants him 16 / 24 / 32 / 40 / 48 ability power for 5 seconds upon activation.
 * permanently grants him 1 ability power when the ability kills a unit and passively grants him 1 / 2 / 3 / 4 / 5 ability power when he kills a champion from any damage source.
 * grants him 3 ability power per level.
 * grants him 45 ability power.
 * grants him 1 ability power per 40 bonus health.
 * grants himself 30 / 50 / 70 ability power, and grants nearby allies half of that.

Masteries

 * increases your champion's ability power by 1 per rank. (4 at max rank)
 * increases your champion's ability power by 0.25 per champion level. (1 at max rank)
 * increases your champion's ability power by 1.25% per rank. (5% at max rank)
 * grants +5 ability power while your spell is on cooldown.
 * upgrades your spell to increase ability power gained by 10%.

Runes

 * and runes increase ability power.

Neutral buffs

 * The buff grants +40 ability power (among other bonuses) for 4 minutes.

Trivia
Aside from, who may obtain any amount of ability power due to the passive effect of his Q, , the maximum ability power obtainable by any champion at level 18 is approximately 2,212 AP, obtained by. To reach this amount, she must:
 * have 1 and 5 ; at least one  must be fully-farmed.
 * have a full page of runes.
 * be at less than 30% health.
 * have the mastery, 3 ranks in the  mastery, 4 ranks in the  mastery, 4 ranks in the  mastery, and 4 ranks in the  mastery.
 * possess the buff.
 * have consumed an.
 * have active, and  on cooldown.
 * be affected by a aura.
 * be affected by the auras of nearby and  abilities, and under the effects of.

This combination should result in having 2211.76575, or 2212 AP.

Relevant mathematics:

((0.035)(1320216834.31000(4005))(455)140130418404085.8530203560)1.352211.76575 AP