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Resistance
Maximum Resistance is capped at 75% by default and cannot be higher than 90%.
Resistance is a form of damage reduction that reduces damage of a particular type by a percentage. Players and enemies all have a resistance stat to each of Fire, Cold, Lightning and Chaos damage, and these are raised or lowered independently. Increases to "Elemental Resistance" are applied to fire, cold and lightning but not chaos.
Resistance has a default value of 0, where it does not affect the damage taken. Maximum resistances are soft capped at 75% by default but can be increased to a hard cap of 90%. Resistance can go into the negatives, which increases damage taken.
Characters receive a -10% penalty to elemental resistance at certain area level thresholds, approximately around the end of each act. By endgame, the cumulative penalty is -60% to all elemental resistances.
Mechanics
Calculation
Final Damage = D * (100-R)/100
Example: being hit by 1000 fire damage, with a fire resistance of 30%, means you would take: 1000 * (100-30)/100 = 1000 * 0.7 = 700 damage
The higher your resistance gets, the more effective an increase in resistance is in reducing damage taken. This makes increases to maximum resistance a particularly valuable stat. For example, increasing resistance by 10 from 0% to 10% will reduce damage taken from 100% to 90%, or 10% less. But increasing by 10 from 60% to 70% would be reducing damage taken from 40% to 30%, reducing damage taken by a quarter.
Resistance Penetration
Having Penetration in a damage type reduces the effective resistance of enemies you damage with that type, thus increasing the damage they take. It only applies against positive resistances; it has no effect once the effective resistance is 0 or negative.
Ignore resistance
Effects which cause damage to ignore enemy resistances will calculate damage as if the enemy had 0% of the ignored resistance, and ignores any further modifications to resistances. It does not affect the actual resistance, and does not interact with stats that care about the specific resistance value.