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There are six types of damage:
Fire
Cold
Lightning
Poison
Physical
Magical

Fire, cold, lightning, and poison resistances are displayed on the Character Screen. Your physical and magical resistances are hidden.

There are many items with "Damage Reduced by x", but one only item with real physical resistance: Rockfleece Field Plate, +10%. Two Necromancer curses reduce physical resistance: Amplify Damage by -100%; and Decrepify by -50%.

There are no items with magical resistance, which is why the Necromancer's Bone Spirit and the Paladin's Blessed Hammer are such deadly skills to other players.

Minimum Resistance
Your base resistance levels for Fire, Cold, Lightning, and Poison are determined by the game's difficulty:

Normal Difficulty: 0
Nightmare Difficulty: -20
Hell Difficulty: -50

The absolute minimum resistance is -100. Resistance can never be lowered to below that value.

Your base Physical and Magical resistances are 0 in all three difficulties.

Maximum Resistance
Each character has a default maximum resistance of 75%, although certain items can raise that number as high as 95%. You can never become totally immune to elemental attacks with Resistances alone.

The only items that increase maximum resistances:
    Iratha's Finery: Using the entire set gives +10% to all max resists.
    Hotspur Boots: +10% to max fire resist.
    Hawkmail Scale Mail: +10% to max cold resist.
    The Jade Tan Do Kris: +20% to max poison resist.
    Venom Ward Breast Plate: +15% to max poison resist.
    Thawing potions give +50% to cold resist and +10% to max cold resist for 30 seconds*.
    Antidote potions give +50% to poison resist and +10% to max poison resist for 30 seconds*.

*The time length stacks: Use two potions and get a minute of +50/+10max resist.

The Paladin skill Resist Fire gives the aura wearers +x% to max resist, where x is equal to the number of hard skill points in Resist Fire. When not active, the paladin receives +(x/2)% to max fire resist, where [again] x is the number of hard skill points in Resist Fire.
The same holds true for Resist Cold and Resist Lightning.

Mercenaries also have a max resist of 75%.
Minions have no max resist. If they reach or exceed 100% resist (via Resist Fire, Cold, Lightning or Salvation), they become immune to that specific element(s).

Cold Resistance
The magical ability "Half Freeze Duration" halves chill length, but this reduction is only applied once: Multiple items with this ability do not lower chill length further. "Cannot be Frozen" provides the protection against chill by setting the duration to 0. This should not be mistaken with Holy Freeze. The Holy Freeze aura will slow Animation speed directly while still showing the same blue overlay as when you're chilled.

Damage modifications are calculated in this order:
Energy Shield
Bone Armor and Cyclone Armor
Damage Reduction and Magic Damage Reduction
Resistances
Direct Absorb