Ability power

Ability Power (shortened as AP) is additional Magic Damage the champions' abilities make times their multiplier. Abilities in League of Legends that are affected by ability power have an ability power coefficient. This coefficient determines how much a particular ability will benefit from a champion's total ability power.

Calculation
The concrete Formula to calculate an ability's magic damage is: Damage = Base Damage + AP*APCoefficient. For example, if a damage spell has an ability power coefficient of .25, every 4 points of ability power will increase the damage of this ability by 1. This bonus is added before Magic Resistance. Abilities that are affected by ability power are identifiable by a bracketed plus sign, along with a number that corresponds to the applicable bonus. For example a Champion having 50 ability power who has an ability with an ability power coefficient of .7, it will display +35 ([50*.7=35]) next to the corresponding value in the UI. There is no limit for Ability Power, all bonuses gained work in an additive way.

Items increasing Ability Power

 * +15 AP. +100 Health, +4 Mana Regen per 5 sec. 435 Gold.
 * +20 AP. 435 Gold.
 * +40 AP. 860 Gold.
 * : +80 AP. 1600 Gold.
 * +25 AP. Passive: Gain an additional 5 Gold every 10 seconds. 765 Gold.
 * +40 AP. +10% Spell Vamp. 1200 Gold.
 * +20 AP. UNIQUE Passive: Your champion gains 8 AP per stack, receiving 2 stacks for a kill or 1 stack for an assist. This effect can stack 20 times; you lose a third of your stacks if you die. At 20 stacks, your champion's cooldowns are reduced by 15%. 1235 Gold.
 * +30 AP. +7 Mana Regeneration per 5, UNIQUE Passive: Reduces ability cooldowns by 10%. 1245 Gold.
 * +25 AP. +250 Mana, UNIQUE Passive: 100% chance when an ability is used that your next physical attack deals 100% extra base damage. This effect has a 2 second cooldown. 1260 Gold.
 * +20 AP. +180 Health, UNIQUE Passive: +20 Magic Penetration. 1485 Gold.
 * +25 AP. 50% Attack Speed, UNIQUE: Your physical attacks shred your target doing 20 magic damage and reducing their magic resistance by 6. Magic resistance reduction stacks up to 4 times. 1825 Gold.
 * +45 AP. +35 Attack Damage, Passive: On attack/spellcast, increases your Attack Speed by 4% and Ability Power by 6. Lasts 5 seconds (stacks up to 8 times). 2235 Gold.
 * +70 AP. UNIQUE Passive: Spells penetrate 40% of the defender's magic resist. 2295 Gold.
 * +40 AP. UNIQUE Aura: Gives nearby allied champions +30 AP and 15% Spell Vamp. 2400 Gold.
 * +60 AP. +10 Mana Regen per 5 Sec, UNIQUE Passive: Reduces ability cooldowns by 15%. UNIQUE Active: Deals magic damage to target champion equal to 30% of their current health (+3.5% per 100 Ability Power) with a minimum of 200 damage. 1 minute cooldown. 2610 Gold.
 * +70 AP. +57 Magic Resistance, UNIQUE Aura: Reduces the Magic Resist of nearby enemy champions by 20. 2650 Gold.
 * +45 AP. +400 Mana +25 Mana Regen per 5 sec, Passive: 3% of your Max Mana is converted to Ability Power. UNIQUE Passive: Each time your Champion uses an Ability their Maximum Mana will increase by 4 Mana, up to a maximum of 1000. This effect has a 3 second cooldown. 2840 Gold.
 * +55 AP. +50% Attack Speed, +10 Mana Regeneration per 5, UNIQUE Passive: Reduces ability cooldowns by 25% 2885 Gold.
 * +60 AP. +450 Health, +525 Mana, Passive: Your Champion gains 18 Health, 20 Mana, and 2 AP every 1 min. Bonuses cap at +180 Health, +200 Mana, and +20 Ability Power. 3035 Gold.
 * +80 AP. +550 Health, Passive: Your spell hits slow the target's movement speed by 35% for 2 seconds (15% for multi-target spells). 3105 Gold.
 * +120 AP. UNIQUE Passive: Increases AP by 25%. Activate: Places you in stasis for 2 seconds, making you invulnerable and non-targetable. 3460 Gold.
 * +80 AP. +350 Mana, +30 Magic Resist, +7% Movement Speed, UNIQUE Passive: 100% chance when an ability is used that your next physical attack deals an additional 100% of your Ability Power in damage. This effect has a 2 second cooldown. 3470 Gold.
 * +75 AP. +60 Attack Damage, +15% Life Steal, +13% Spell Vamp, UNIQUE Active: Deals 300 magic damage and slows the target champion by 50% for 3 seconds (700 range). 60 second cooldown. 3625 Gold.
 * +30 AP. +20 Damage, +25% Attack Speed, +12% Crit Chance, +12% Move Speed, +300 Health, +300 Mana, UNIQUE Passive: 25% chance on hit to slow the target by 35% for 2.5 seconds; on cast, increases your base Attack Damage by 150% for one attack. 4070 Gold.
 * +31-65 AP based on champion level and 10% Cooldown Reduction for 4 minutes. 300 Gold.

Other ways increase Ability Power

 * converts 50% of his total magic resistance into ability power.
 * converts 30% of her attack damage to her ability power.
 * grants him 50/80/110 ability power for 8 seconds.
 * grants him 35/50/65 ability power for 25 seconds.
 * grants nearby allied champions 6/8/10/12/14 ability power while active.
 * grants him 16/24/32/40/48 ability power while active.
 * gives him 1 ability power per 25 bonus health.
 * increases your champion's ability power by .2 per level per rank (up to a maximum of .6 per level).
 * increases your champion's ability power by 0.66%, and an increasing amount summing up to an additional 0.66% at level 18 (up to a maximum of 2% on both).
 * increases your champion's ability power by 10 while your spell is on cooldown.
 * upgrades your spell to increase nearby allied units' ability power by 20-70 for 20 seconds.
 * Force and Potency runes may also increase ability power.

Updates
Due to recent updates this article might not be actual. It was last updated during Patch 1.0.0.98. If there is a new version out, please check the data frequently.