Armour

Armour is a form of defence that mitigates incoming physical damage from hits. Armour rating can be increased by wearing equipment, taking certain passive skills, using skills (e.g. ), and drinking flasks (e.g. ).

Mechanics
Along with evasion and energy shield, armour is one of the three defence types that can implicitly appear on equipment. Unlike resistance, armour has diminishing returns as its effectiveness is based on the magnitude of incoming physical damage (multiplied by 10). As a result, armour is most effective in mitigating small hits (i.e. 50% and better reduction for initial damage less than a tenth of the armour value) and least effective in mitigating very large hits (where its absolute reduction can at most be one tenth of the armour value).

Supposedly the most armour monsters have in the game is about 983.

Physical damage reduction from armour only mitigates physical damage from hits. It falls under the modifier. Physical Damage Reduction is capped at %.

Armour does not mitigate damage over time, as armour will only mitigate damage from hits. Bleed is a damage over time debuff that is based on the initial physical hit, armour would reduce the initial hit but not the damage over time. However both the initial hit and the damage over time can be mitigated with other sources for example or endurance charges because they don't only apply to hits.

Armour will only mitigate physical damage hits, not for elemental or chaos damage. If the Transcendence keystone is taken, armour mitigates elemental damage hits, but not physical.

Rule of thumb

 * To prevent one third of damage, you need armour 5 times the damage (e.g. 500 armour for 100 damage)
 * To prevent half of damage, you need armour 10 times the damage (e.g. 1000 armour for 100 damage)
 * To prevent two thirds of damage, you need armour 20 times the damage (e.g. 2000 armour for 100 damage)
 * To prevent three quarters of damage, you need armour 30 times the damage (e.g. 3000 armour for 100 damage)
 * To prevent 90% of damage, you need armour 90 times the damage (e.g. 9000 armour for 100 damage)
 * armour will never prevent more damage than its value divided by 10 (e.g. 1000 armour will never prevent more than 100 damage)

Formulas
The amount of physical damage reduction is a function of armour rating and the physical damage taken.

Relative Physical Damage Reduction (Base Formula)
This is the base formula all other formulas are based upon. It is used to calculate the factor, i.e. the percentage by which the physical damage is mitigated.

$DR(A, D_{raw}) = {A \over A + 10 * D_{raw} }$

where A is the defender's armour rating and Draw is the raw physical damage.

Required Armour Rating
To calculate the armour rating you need to mitigate a given amount of Physical Damage at specific ratio, you can use this formula:

$A(D_{raw}, DR) = {DR * 10 * D_{raw} \over 1 - DR}$

Reverse Physical Damage
You can also calculate the raw physical damage that would have resulted for a given Physical Damage Reduction and Armour rating:

$D_{raw}(A, DR) = {A \over 10 * DR} - {A \over 10}$

Resulting Physical Damage
To calculate the net physical damage (i.e. the damage after damage reduction, the following formula can be used:

$D_{net}(A, D_{raw}) = {10 * {D_{raw} }^2 \over A + 10 * D_{raw} }$

Absolute Physical Damage Reduction
Another way of looking at it is in terms of absolute physical damage reduction:

$DR_{abs}(A, D_{raw}) = {A * {D_{raw} } \over A + 10 * D_{raw} }$

Defense factor
$DF(A, D_{raw}) = {A \over 10 * D_{raw} } + 1$

Examples
The plots below displays how much damage reduction occurs at different armour ratings and raw physical damage. From the plot below we can further conclude:
 * If raw damage is much less than Armour / 10, raw damage has a near-quadratic effect on net damage. Equivalently, in this regime raw damage has a near-linear effect on net DPS if the raw DPS is held constant.
 * If raw damage is much greater than Armour / 10, raw damage has a near-linear effect on net damage. Equivalently, in this regime raw damage has little effect on net DPS if the raw DPS is held constant.
 * Against attacks of a fixed raw damage, armour has a linear effect on the number of attacks it takes to deplete a certain amount of hit points.



Mechanics Scaled by Armour Rating
The following items provide some bonuses that scale with Armour rating.

Notable Armour Rating
Unique items that can potentially grant upwards of 1,000 Armour rating.

Global Armour increases
Unique items that grant increased global Armour rating.

Global flat Armour
Unique items that grant a flat bonus to global Armour rating.

Passive skills
There are passive skills that grant armour bonuses.

Base passives
These passive skills grant increased armour rating or additional base armour rating. The Iron Reflexes keystone is special in that it converts evasion rating to armour rating.

Cluster jewel passives
The following cluster jewel-only passives are related to armour: