Armor & Block

Armor reduces the damage you take from physical attacks (except bleeds).

This damage reduction is hard capped at 85%.

$\text{Damage taken after armor}=\text{Damage taken before armor}*(1-\frac{\text{armor}}{\text{armor}+k})$

K is a value that depends on the content you are in.

Example: If I take 10k damage in SoD mythic (k = 3545), and I have 2500 armor. The calculation will be:

$10000*(1-\frac{2500}{2500+3545})=5864.35$

Therefore I would take 5864 damage from that attack after armor.

Each class has its own way of increasing armor further:

Druid

Ironfur increases armor by 1xAgi for 7 seconds and stacks asynchronously (i.e. a new stack does not extend the previous but acts as its own buff)

Demon Hunter

Demon Spikes increases armor by 0.75xAgi for 6 seconds and can stack in duration (i.e. if you use 2 charges of it you will have a buff for 12 seconds)

Death Knight

Bone Shield increases armor by 0.7xStr for 30 seconds or until all charges are consumed. Using Marrowrend will add 3 more stacks and refresh the duration.

Monk

Does not have any rotational abilities which increases their armor. However, Stagger is the cornerpiece of reducing damage taken which will be explained in more detail on the Monk page. The Mighty Pour legendary can increase armor by 50% for 8 seconds when you use Celestial Brew.

Paladin

Shield of the Righteous increases armor by 1.7xStr for 4.5 seconds and can stack in duration (i.e. if you cast it twice you will have a buff for 9 seconds)

Warrior

Does not have any rotational abilities which increases their armor.

Working Though An Example

To further elaborate with a Paladin example. Shield of the Righteous increases armor by 1.7*Str. It may be useful to know how much damage reduction SotR provides, so let's work that out.

$\text{SotR Damage Multiplier}=\frac{\text{Armor Multiplier After SotR}}{\text{Armor Multiplier Before SotR}}$

$=1-\frac{(\text{armor}+1.7*\text{str})⁄(\text{armor}+1.7*\text{str}+k)}{\text{armor}⁄(\text{armor}+k)}$

I'll leave the simplification working as an exercise for the reader, but in short:
$\text{SotR damage multiplier}=1-\frac{1.7*\text{str}}{\text{armor}+1.7*\text{str}+k}$

$\text{SotR damage reduction}=1-\text{damage multiplier}=1-\frac{1.7*\text{str}}{\text{armor}+1.7*\text{str}+k}$

Because there is a relation between the ilvl of the content and K, there is also a relation between a pvp opponent's ilvl and k. As such, trying to calculate armor based off of the tooltip while outside of an instance and targeting a player, yourself or without a target can give unexpected results.