Damage reduction
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Armor damage reduction
Armor reduces physical damage done against you by a certain proportion against all attackers. It depends entirely on the level of the monster (or player) hitting you and your own armor. Your level doesn't matter. By hovering your mouse over Armor on your Character screen, you can see the percentage value of this reduction for damage done by enemies that are at your current level. This percent reduction will actually fall as soon as you gain a level if you're still wearing the same armor. You haven't lost anything, it's merely showing you that your armor isn't as effective against monsters one level higher than you used to be.
The most important thing to remember about armor is: An X% increase in armor means an X% increase in armor's contribution to the amount of damage you can take.
The formula for the base armor value is:^{[citation needed]}
Base Armor = 2 * Agility + gear armor + magic armor 
Gear armor is the armor value from the gear you are wearing. Magic armor is the extra armor from buffs such as scrolls, mage armor, armor kits etc.
Note that talents which give a percentage bonus to armor (like druid bear form) do not include magic armor in their boost to the armor rating. This is especially important for druids since bonuses received from armor kits, sets and green effects in general are not affected by Bear, Moonkin, or Tree Form or armorincreasing talents.
For enemies from level 1 to 59, the reduction to physical damage, as a percentage, is given by the following formula:
%Reduction = (Armor / ([85 * Enemy_Level] + Armor + 400)) * 100 
For enemies from level 60 and up, the reduction to physical damage, as a percentage, is given by the following formula:
%Reduction = (Armor / ([467.5 * Enemy_Level] + Armor  22167.5)) * 100 
For level 80 and raid bosses, this simplifies to:
%Reduction for 80 = (Armor / (Armor + 15232.5)) * 100 
%Reduction for 83 = (Armor / (Armor + 16635)) * 100 
Note that the maximum damage reduction is capped at 75%. The 15232.5 and 16635 numbers in the denominator are often confused. The constant is based on the attacker's level, not the target's level. Use 15232.5 for your attacks (outgoing) and 16635 for damage received.
For level 83 bosses, as described below, armor caps at 49905. The Diminishing Returns on armor as you approach the cap are rather harsh; both functions are graphed below.
Armor required to get X% damage reduction
To calculate the amount of armor needed for maximum mitigation against a lvl 59 or below enemy, one can use the following formula:
Armor = 1200 + 255 * Enemy_Level 
Thus a lvl 59 character who wants to achieve 75% reduction vs. lvl 59 mobs would need 16245 AC. Note that this changes beyond lvl 59, as the formula to calculate damage reduction for levels 60 and up requires much more armor to get the same mitigation. Despite the much higher armor values required for 75% reduction at levels 70 and higher, it is currently possible for a wellgeared druid to reach this point (see this page).
Or a more general formula. The amount of armor needed for a specific reduction is:
Armor = %Reduction * (400 + 85 * Enemy_Level) / (100  %Reduction) 
Against a level 59 and less:
Armor = (400 + 85 * Enemy Level ) / ( 100 / %Reduction  1) 
Against a level 60 and up:
Armor = (467.5 * Enemy Level  22167.5 ) / ( 100 / %Reduction  1) 
Armor required to get 50%, 60%, 70% and 75% damage reduction against lvl 60, 63, 70 and 73 mobs.
Damage reduction  

Enemy lvl  50%  60%  70%  75% 
60  5883  8824  13726  17648 
63  7285  10928  16999  21855 
70  10558  15837  24635  31673 
73  11960  17940  27907  35880 
80  15233  22849  35543  45698 
83  16635  24953  38815  49905 
%Reduction Formula
%Reduction = 100 / ( (467.5 * EnemyLevel  22167.5) / Armor + 1 ) 
That EXTRA armour that I need  General formulae
This article or section may need to be wikified to meet WoWWiki's quality standards.

This section is written to answer the question "What's the amount of extra armour that I should add in order to gain extra 5% or 7.3% or 27.4% or whatever EXTRA percentage that I wish to gain in damage reduction?".
The most straightforward/obvious solution is to use the "armourdamagereduction" formulae given in the section above. However, there is an exact general formula to find the answer for each case  either against a level 59 or lower mob or against a level 60 or higher mob. The formulae are given below the example of straightforward solution.
Example of straightforward solution: (you may skip this part)
If your current total amount of armour provides you with 35% in damage reduction and you wish to add extra 10% to get a total of 45%, what is the amount of extra armour that you should add?
Against a mob with level no higher than 59, you could do the following subtraction:
Extra armour = new armour  current armour
"Current armour" is the total amount of armour that you currently possess. "New armour" is the new total amount of armour that you want to have in order to gain that extra percentage in damage reduction.
From the previous section, "new armour" = (400 + 85 * Enemy Level ) / ( 100 / 45  1) and obviously you get the value "current armour" by summing the amount of your equipments armour. Then, by doing the subtraction you get the amount of "extra armour" you need in order to gain extra 10% in damage reduction.
Note though, that you need to calculate your current percentage in damage reduction by solving the armour formula with your current armour value.
The general formulae
Before looking at the formulae, please note the following representations:
A = current amount of armour
= extra amount of armour that you need to add to your current amount of armour to get certain extra percentage in damage reduction
R = current percentage in damage reduction provided by your equipments, buffs, etc
= extra percentage in damage reduction that you wish to add to your current percentage in damage reduction
L = enemy's level
Please also note that these formulae are derived based on the equations given in the previous section which are still lacking in citation.
Against a level 59 or lower mob: Against a level 60 or higher mob:These formulae are in fact more general than the formulae given in the section above. In addition to using these general formulae to calculate difference, if you take R to be 0, these general formulae are in fact the same as the formulae given in the previous section.
Example:
From the table in the previous section we have the following figures:
Damage reduction  

Enemy lvl  50%  60%  70%  75% 
63  7285  10928  16999  21855 
If your current armour provides 50% in damage reduction against a level 63 mob, you have 7285 armour. However, if you want to add another 25% on top of your 50% to get 75%, you'll need 21855 armour. So the EXTRA amount of armour that you need to add is 21855  7285 = 14570.
Let's see if we can get the same extra amount of armour (14570) by using the formula given above (note: please punch the numbers into your calculator carefully or use wolfram alpha). For level 60 or higher mob, we have:
A = 7285
R = 50
= 25
L = 63
Proofs
Warning: college level calculus is required.
proof: against lvl 59 and lower
proof: against lvl 60 and higher
There are only two steps in each of the proofs.
1. Differential
2. Integrate both sides with the following limits:
a) The limits for the first term on the right are L and L. This is because while your character is fighting against one enemy, you don't expect the enemy to level up or down.
b) The limits for the second term on the right implies if you add armour you also add extra percentage in damage reduction.
Resilience damage reduction
 Main article: Resilience
Resilience is an defensive attribute that provides damage reduction, but only against enemy players and their pets during PvP. Each point of resilience provides about 0.01% damage reduction against all damage done by players and their pets or minions.
Damage soak
Although the character sheet tooltip gives the amount of damage that the armor absorbs, it is more useful to think of how much more damage the player can take.
In general, the armor reduction formula can be written as
Reduction = Armor / (Armor + X) 
If the enemy is lower than level 60, X = 85 * Enemy_Level + 400. If the enemy is level 60 or higher, X = 467.5 * Enemy_Level  22167.5 Therefore, the amount of damage that the player takes after their armor's damage reduction is applied is:
Damage_Taken = Damage_Dealt * ( 1  ( Armor / (Armor + X) ) ) 
or 
Damage_Taken = Damage_Dealt * ( X / (Armor + X) ) 
So the ratio of damage dealt to damage taken is:
Damage_Dealt / Damage_Taken 
or 
(Armor + X) / X 
or 
1 + (Armor / X) 
Therefore, the increase in the amount of damage the player can take compared to having no armor at all, as a percentage, is:
(Armor / X) * 100 
Therefore, an X increase in armor (compared to 0 armor) means an 100% increase in the amount of damage the player can take. e.g. For a level 70 enemy, X = 10557.5. So a player with 10557.5 armor attacking a level 70 enemy would be able to take 100% more damage. A player with 31672.5 armor would be able to take 300% more damage than a player with 0 armor (which is the maximum).