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 a percentage of corresponding to her percentage of missing health. The value increases depending on her level.
 * grants him 35 / 50 / 65 ability power for 25 seconds.
 * aura grants herself and nearby allied champions 8 / 11 / 14 / 17 / 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 1 ability power per 40 bonus health.

Masteries

 * increases your champion's ability power by 0.2 / 0.4 / 0.6 per champion level.
 * increases your champion's ability power and attack speed by 1.33 / 2.66 / 4.00 %.
 * grants +10 ability power while your spell is on cooldown.
 * upgrades your spell to increase nearby allied champions' ability power by 20–70 for 20 seconds.

Runes

 * and runes increase ability power.

Neutral buffs

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