Attack power

Attack power (AP) is a physical damage attribute derived from strength and/or agility and character level, that serves to increase your base weapon damage by an amount relative to this statistic. There are two forms of attack power: Melee attack power, and Ranged attack power. These can be found on your character sheet in the Melee and Ranged sections, and each form only affects the related type of weapon damage.

By increasing the player's base weapon damage, attack power improves the player's auto-attacks. Many abilities also add some percentage of attack power to the damage they deal (the attack power coefficient).

Although characters of every class will have a listed amount of ranged attack power, the statistic is wholly meaningless to all except Hunters, Rogues and Warriors, as these are the only classes that can use ranged weapons other than wands (wands do not benefit from attack power). Hunters benefit greatly from ranged attack power, while rogues and warriors' benefit is marginal, affecting only a few abilities such as Heroic Throw, Shattering Throw and Deadly Throw.

Likewise, both types of attack power can be considered irrelevant for priests, mages, warlocks, and is generally not acquired by these specs due to gear and talent choices.

Auto-attacks
The base DPS of your auto-attacks (including ranged attacks made using Shoot or Auto-Shot) is increased by 1 for every 14 attack power you have. For example, an AP of 28 will give you 2 DPS. Your DPS is then multiplied by weapon speed to give the real per-attack melee or ranged damage:

Weapon Damage = (Weapon DPS + AP/14) * Weapon Speed

If dual wielding, an off-hand weapon will also receive DPS from AP with the normal damage penalty of 50% by default. Disregarding dual wield specialization talents, the offhand damage is then:

Offhand Damage = [(Weapon DPS + AP/14) * Weapon Speed] / 2.

The bonus from attack power uses the weapon's base speed, not your attack speed (which is often faster because of haste). Thus, attack power and haste will give a greater DPS increase together than separately.

Mob attack power
Mobs have different attack power formulas than players. Damage done per second of mobs is given by:

(DPS_from_AttackPower + Base_DPS) * Multiplier.

For most mobs, attack power is about 30% of total damage; bosses have higher multiplier than trash mobs. That means -attack power debuffs have significant effect on raid mobs. The -AP debuff is capped at -30% total damage effect, as the formula suggests.

Hunter
Before patch 2.0.1, hunters received 2 Ranged AP per agility, whereas now they receive 1 RAP per agility. Some of this loss was made up for in AP increases from items. The reason given for this change was to keep agility from being the be-all and end-all of hunter stats, allowing for flexibility into intellect or stamina without sacrificing a large amount of AP. However, this is slated to be changed back to 2 AP along with the release of Cataclysm.

After Patch 3.0.2, hunters can gain RAP from intellect or/and stamina by Survival and Marksmanship Talent. (See Careful Aim and Hunter vs. Wild)

As of Patch 4.0.6, hunters receive 2 Ranged AP per agility again. Beast Mastery hunters gain a 25% bonus (was 15% with Patch 4.0.1) to their total AP through the summary talent Animal Handler.

Shaman
Before Patch 3.0.2, shamans received 2 AP per strength. This was changed in 3.0.2 in preparation for Wrath of the Lich King. Shamans now received 1 AP from strength and 1 AP from agility.

With Patch 4.0.1, AP calculations changed again; like in Patch 3.0.2, this was in preparation for Cataclysm. Shamans now gain 2 points per level, 1 point per strength, and 2 points per agility.

The Enhancement passive ability Unleashed Rage improves attack power by 10% for all party and raid members within 100 yards.

Druid
Before Patch 3.0.8, many weapons listed feral attack power, making these weapons highly tailored to druids and making other weapons unusable for druids. After the patch, specific feral attack power bonuses were removed. Instead, all weapons with more than 54.8 DPS grant feral attack power equal to [(DPS - 54.8) * 14], rounded down. Only druids see feral attack power in weapon tooltips.

Druids now gain feral attack power from both agility and strength, whether in cat or bear form. This means that agility is always preferred over strength, even for a bear, which is ironic considering that the "of the Bear" suffix denotes strength and stamina. Agility gives dodge which is essential for a bear, given that a bear cannot block or parry.

Cat feral attack power can be increased further with the Heart of the Wild (Classic) talent by 10%. Feral druids gain a 25% bonus to their total Attack Power due to the Aggression talent acquired as part of the Feral Combat specialization.