For the Lionheart perk, see Damage Resistance (perk). 
Damage Resistance (DR) is a derived statistic in the SPECIAL character system.
Any damage taken is reduced by a percentage based either completely or in part in this number, depending on the game. Damage Resistance can be increased by wearing armor, or by taking certain chems or perks, depending on the game.
Fallout, Fallout 2, Fallout TacticsEdit
In the original Fallout games, DR (Damage Resistance) is one of three stats by which a character can reduce or avoid damage. The other stats are AC (Armor Class) and DT (Damage Threshold). DR occupies the "final step" for combat and simulates the effect of how armor can help diffuse the energy of a bullet and reduce its lethality (like reallife Kevlar armor).
More specifically, after AC is checked for a successful hit and after DT is checked to reduce the damage, if there is any incoming damage, DR applies:
 $ Final = \text{max}\Bigg(1, Adjusted \times \frac{100\text{min}(DR,\ 90)}{100}\Bigg) $
While DT can completely negate damage done, DR cannot. As the equation suggests, DR is capped at 90%, and any damage that goes past DT has a minimum of 1.
Initial level: 0
 The Damage Resistance Modifier of ammo can preemptively reduce the DR of a target.
 The Toughness perk increases normal DR by 10% per rank.
 The Dermal Impact Armor implants increase normal and explosive DR by 5%.
 The Dermal Impact Assault Enhancement implants increase normal and explosive DR by 10%.
 The Phoenix Armor Implants increase laser, fire, and plasma DR by 5%.
 The Phoenix Assault Enhancement implants increase laser, fire, and plasma DR by 10%.
 The Prizefighter reputation title will increase normal DR by 5%.
Fallout 3Edit
The maximum Damage Resistance is 85%, regardless whether this value is obtained by armor, perks, drugs or a combination of these. This makes the effects of Nerd Rage! and MedX somewhat less useful, as even without chems, the Lone Wanderer can permanently gain up to 94% Damage Resistance through equipment and perks (with The Pitt additional content). The T51b power armor and the Enclave Hellfire power armor plus their respective helmets have a max DR of 60. Combined with the five permanent perks (34%) gives the maximum DR without drugs or having less than 20 percent of your hitpoints. Without the additional content you would still be able to obtain a maximum DR of 91% with power armor. Note that these numbers assume a fully repaired suit of armor, which, when the T51b armor is actually being worn, is only possible if the player boosts Crazy Wolfgang's repair skill to 100 by reverse pickpocketing workman's coveralls from Point Lookout onto him because there is only one copy of this armor and it can only be repaired by nonplayer characters. Enclave Hellfire armor can be found, but it is rare (only obtainable with Broken Steel loaded). For players who prefer nonpower armor, you can still obtain a permanent DR of 82% (79% without The Pitt addon) with ranger battle armor, ghoul mask, the ranger battle helmet and the perks listed below.
All addon CombinationsEdit
 Permanent DR of 73% (temporary of 83%), +5 melee weapons and 148 Action Points with the permanent perks below and Superior Defender, Action Boy/Action Girl, tribal power armor, Ledoux's hockey mask, Almost Perfect and waiting to collect all S.P.E.C.I.A.L. Vault Boy bobbleheads until level 30 has been achieved. This produces perfect SPECIAL stats with the exception of Agility which will be 9 due to the power armor effect. The tribal armor can be repaired with common T45d power armor while the hockey mask is immune to item damage and can be repaired (if found damaged) with regular hockey masks.
The Pitt CombinationsEdit
 Permanent DR of 73%, +1 Strength, +1 Luck, 1 Agility, +5 melee weapons and +65 AP with the permanent perks below and Action Boy/Action Girl, tribal power armor and Ledoux's hockey mask. The tribal armor can be repaired with common T45d power armor while the hockey mask is immune to item damage and can be repaired (if found damaged) with regular hockey masks.
 Replace the hockey mask above with Poplar's hood which has 2 lower DR than the hockey mask but can be worn with the ghoul mask producing 5 DR rather than 4. This combination repairs the Agility damage (+2 small guns, +2 sneak, +2 Action Points), adds +10 sneak, permanent 74% DR, +40 Action Points and feral ghouls will not become hostile. It is a possibility for those who have not yet found the hockey mask, or missed acquiring it altogether. This option, however, excludes obtaining the Barkskin perk which offers 5 DR itself.
Permanently increasing Damage ResistanceEdit
 The Cyborg perk gives +10% damage resistance.
 The Toughness perk gives +10% damage resistance.
 The Barkskin perk gives +5% damage resistance.
 The Survival Expert perk gives up to +6% damage resistance.
 The Superior Defender perk gives +10% damage resistance when standing still.
 The Pitt Fighter perk gives +3% damage resistance.
Temporarily increasing Damage ResistanceEdit
 The Nerd Rage! perk gives +50% Damage resistance, but only if your Health is below 20%.
 The MedX drug gives +25% Damage resistance, and it is possible to double up the effect by wearing the prototype medic power armor and also manually administering the drug.
Fallout: New VegasEdit
In Fallout: New Vegas, DR is mostly replaced by DT (Damage Threshold). MedX and the new consumables Slasher and battle brew provide bonuses to DR, which functions identically to the DR from Fallout 3. If all 3 consumables are taken together, they provide the maximum 85% damage resistance allowed by the game engine.
Damage Resistance is applied before damage threshold, contrary to the original Fallout games. So, for a character with 30 DR and 20 DT (i.e. a NCR Veteran Ranger), an attack that deals 80 damage is first reduced by 30% (leaving 56 damage), then the damage threshold is subtracted from that number, leaving a final damage of 36. As a result of this, a high damage resistance has a very large effect on a character's ability to withstand damage. For full damage formula see Fallout: New Vegas combat.
The only pieces of equipment in the game that raise DR instead of DT are:
 Rebreather from the quest Volare!
 Vault 11 jumpsuits
 the normally nonplayable trenchcoat found on the investigator during the quest Beyond the Beef.
 Scientist outfits
 Regulator duster
In addition, DR can be conferred via the console by entering player.forceAV DamageResist xx where xx is between 0 and 85. Values beyond 85 are ignored by the game; 85 is the maximum DR, a likely holdover in the game engine from Fallout 3.
A rare few nonplayer character characters have perks which grant them DR in addition to the DT from their armor. These include:
 All companions if using Ferocious Loyalty.
 Sunny Smiles (10% DR)
 Ranger Stella (10% DR)
 Legion vexillarius (10% DR)
 Praetorian guards (10% DR)
 Lucius (10% DR)
 Certain Legionary assassins (10% DR)
 Ulysses (10% DR)
 Blister (10% DR)
 Beast (10% DR)
 Bonesaw (10% DR)
 Blade (10% DR)
 Colonel Royez (10% DR)
 Gaius Magnus (10% DR)
 Mean Sonofabitch (20% DR)
 MotorRunner (20% DR)
 Nightkin (30% DR)
 Dog (but not God) (30% DR)
 Certain NCR Rangers (30% DR)
 NCR Veteran Rangers (30% DR)
Fallout 4Edit
Damage resistance returns in Fallout 4. However, the stat is no longer a 11 relationship with actual % damage reduced, as its value can be in excess of 1,000 on certain models of power armor.
Instead, the amount of damage reduction the Sole Survivor gets out of the damage resistance is actually based on how much potential weapon damage is coming in; unlike previous games, net damage reduction is based on a ratio between the potential weapon damage done and the damage resistance, with diminishing returns for high damage resistance.
The amount of damage reduced by damage resistance climbs very quickly until damage resistance is about half of the potential weapon damage, after which diminishing returns means one gets less and less damage reduction per point of damage resistance. If damage resistance is exactly equal to the potential weapon damage done, then exactly half of the damage is negated. In other words, if one has 50 ballistic damage resistance and is shot by an enemy doing 50 ballistic damage, then they will receive 25 damage.
The most important factor is the ratio between damage resistance and potential weapon damage:
Weapon Damage  Resistance  Final Damage  Reduction Percent 

50  0  49.5  1% 
50  10  45  10% 
50  25  32  36% 
50  50  25  50% 
50  100  19  61% 
50  250  14  72% 
50  1000  8  83% 
The upshot is that unlike previous games, it is very hard to get to the point where enemy damage is reduced to the range of ~20% or less. In addition, because the ratio between damage resistance and weapon damage is so important and because damage reduction grows very quickly at first for low values of the ratio, a higher damage resistance pays off mostly because it gives the player character better damage reduction against moredamaging attacks, not necessarily because it gives them better damage reduction against the same, weaker attack as before.
In other words, going from 20 to 40 damage resistance will only further reduce the damage done from a 10damage shot by about ~12% (~61% to ~69% damage reduction), but it will dramatically boost the player character's damage reduction against a 100damage grenade by about 23% (~10% to ~30% damage reduction). However, significant mitigation against such high damage is harder to achieve, since it is harder to get enough damage resistance to generate an appreciably high resistancetodamage ratio. In otherwords, getting a 51 ratio is easy against a 20 damage shot, but very difficult (essentially limited to power armor) against a 100 damage grenade.
Damage Reduction formulaEdit
All final values below are adjusted by difficulty:
Difficulty  Player Damage  Enemy Damage 

Very easy  ×2.0  ×0.5 
Easy  ×1.5  ×0.75 
Normal  ×1.0  ×1.0 
Hard  ×0.75  ×1.5 
Very hard  ×0.5  ×2.0 
Survival^{[1]}  ×.75^{†}  ×4.0 
† Boosted higher depending on adrenaline level. 
This is applied after the ratio and exponent are calculated, so damage resistance is applied on the base potential weapon damage, before difficultybased multipliers are included in. This means that damage resistance is the same level of effectiveness (or ineffectiveness) on every difficulty level.
Companions are unmodified. On all difficulty levels they do 1x damage and take 1x damage from enemies. This means that companions generally become a bit more effective at higher difficulty levels since they will generally be taking less damage and doing more damage than the player character.
Regardless of where one hits an enemy/are hit by an enemy, the total damage resistance of all currently equipped pieces of armor is used for the formula.
The actual damage reduction formula is:
 $ {\it DamageCoeff} = \text{Min}\left(0.99, \left[ \frac{\it Damage}{\it DamageResist}\times 0.15\right]^{0.365} \right) $
 where default game settings are:
 fPhysicalDamageFactor = 0.15
 fPhysicalArmorDmgReductionExp = 0.365
 This is a coefficient (multiplier) for the net damage done, not the actual damage reduction; so lower numbers are better (more damage is negated).
 If one wants the actual % damage reduction simply do $ {\it DamageReduction} = 1  {\it DamageCoeff} $
There are variations on this DamageCoeff calculation based on weapon used:
 Projectile and close combat weapons use PaperDamage (essentially, the number one sees in the PipBoy), RangeMultiplier, and PowerAttackMultiplier for the damage part.
 Energy weapons use WeaponBaseDamage and RangeMultiplier for the damage part (essentially, they are more vulnerable to their respective damage resistance).
 $ {\it PaperDamage} = {\it WeaponBaseDamage} \times {\it Perk}_1 \times {\it Perk}_2 \times \dots \times {\it RangeMulti} $
 WeaponBaseDamage is affected by weapon mods and is e.g. doubled with a 2x charged laser musket
 RangeMulti is 1.0 at 100% WeaponRange or closer, 0.5 at 200% of WeaponRange or farther, and scales from 1.0 to 0.5 as range increases from 100% to 200% of WeaponRange.
For Projectile DamageEdit
 $ {\it DamageCoeff} = \text{Min}\left(0.99, \left[ \frac{\it PaperDamage}{\it DamageResist\times RiflemanMulti}\right]^{0.366} \times 0.5\right) $
 A hunting rifle with 38 BaseDamage and 45.6 PaperDamage (PipBoy value, from 1 rank of Rifleman) does 22.04 damage vs 50 DamageResist at point blank range.
 $ \left(\frac{45.6}{50}\right)^{0.366} \times \frac{45.6}{2} $
 $ \frac{{({1.2} \times {38})}^{1.366}}{{2} \times {50}^{0.366}} $
 The same hunting rifle with 5 ranks of Rifleman, which reduces target damage resistance to 70%, has PaperDamage 76 and does 50.47 damage at the same range against the same target.
 $ \frac{{({2} \times {38})}^{1.366}}{{2} \times ({{50} \times {0.7}})^{0.366}} $
For Poison DamageEdit
Poison deals damage each second, as a distinctly inflicted hit, typically for 10 seconds; for example, if the player character has a poison resistance of 5 and suffers a poison 3 hit, then once per second for 10 seconds, they will suffer a 3 damage hit, resisted with a resistance of 5, which otherwise follows the rules for projectile damage.
For Bleeding DamageEdit
Bleeding works like poison, except that there is no such thing as bleeding resistance. Even robots such as 2nd generation synths and sentry bots will take bleeding damage, as it is a general damage over time effect.
For Energy DamageEdit
 $ {\it DamageCoeff} = \text{Min}\left(0.99, \left[ \frac{\it WeaponBaseDamage\times RangeMulti}{\it DamageResist\times RiflemanMulti}\right]^{0.366} \times 0.5\right) $
 As of version 1.1.30 RiflemanMulti not used in energy resistance reduction (bug report has been filed).
 A laser rifle with 38 BaseDamage and 45.6 PaperDamage from 1 rank of Rifleman does 20.62 damage vs 50 EnergyResist at point blank range.
 (38/50)^{0.366} × 0.5 × 45.6
 $ \frac{{1.2} \times {38}^{1.366}}{{2} \times {50}^{0.366}} $
 The same laser rifle with 5 ranks of Rifleman, which reduces target damage resistance to 70%, has PaperDamage 76 and does 39.16 damage at the same range against the same target.
 $ \frac{{2} \times {38}^{1.366}}{{2} \times ({{50} \times {0.7}})^{0.366}} $
For Radiation DamageEdit
Radiation damage has two subtypes. Almost all of it in the game is poisoning; each point of radiation poisoning from a radiation "hit" is resisted by radiation resistance (as per the energy damage resistance formula), and resolves as a .1% loss of maximum HP for each point that gets through. The only perk that raises radiation poisoning damage inflicted by a weapon is Nuclear Physicist, and radiation immunity makes a target ignore radiation poisoning entirely.
Nonpoisoning radiation damage follows the normal rules for energy damage, including modification by perks; it ignores radiation immunity, and creatures with radiation immunity typically have no radiation resistance.
For Explosive DamageEdit
Explosive modifies other damage types  for example, something can inflict explosive energy damage. Explosive damage uses the same formula as the underlying type, but is affected by additional perks and effects that interact with explosives. Padded and dense armor mods reduce the damage taken by 25% for padded and 50% for dense from explosion base damage. E.g. a dense armor mod reduces the damage taken from a frag grenade by 75 ( 150 * 0.5) in addition to normal physical resistance.
Combined Damage TypesEdit
When something has multiple resistible damage types (ballistic, energy, radiation and poison are the currently resistible types, with any of them capable of being explosive or not, and radiation can be poisoning or not  almost all radiation sources are poisoning), one "hit" resolves as a hit for each damage type applied. Likewise, when something deals both direct and area of effect damage, a target is hit by each one individually. For example, if one removes the Lorenzo's Artifact gun mod from the original gun and attaches it to an Irradiated Gamma gun with an Electric signal carrier antennae, a charged shot from the weapon will inflict 5 distinct "hits": radiation poisoning, radiation damage, explosive radiation poisoning, explosive radiation damage and explosive projectile damage.
For Close Combat DamageEdit
 $ {\it DamageCoeff} = \text{Min}\left(0.99, \left[ \frac{\it PaperDamage \times PowerAttackMulti}{\it DamageResist}\right]^{0.366} \times 0.5\right) $
 PowerAttackMulti = 1.5
Final DamageEdit
 $ \it FinalDamage = PaperDamage \times DamageCoeff \times HeadshotMulti \times SneakAttackMulti $
Damage Reduction formula for VATS Critical AttackEdit
CriticalDamage = [ PaperDamage x CloseCombatMulti ] + [ WeaponBaseDamage x CriticalMulti ]
 CloseCombatMulti = 1.5 for most melee/unarmed weapons
 CriticalMulti = 1 + BobbleheadBonus(0.25) + MagazineBonus(0.05 to 0.5) + WeaponModBonus(2.0)
Projectile / CloseCombatEdit
 $ FinalDamage = \text{Min}\Bigg(0.99, \Bigg[ \frac{CriticalDamage}{DamageResist}\Bigg]^{0.366} \times 0.5\Bigg) \times CriticalDamage \times HeadShotMulti \times SneakMulti $
EnergyEdit
 $ FinalDamage = \text{Min}\Bigg(0.99, \Bigg[ \frac{WeaponBaseDamage}{DamageResist}\Bigg]^{0.366} \times 0.5\Bigg) \times CriticalDamage \times HeadShotMulti \times SneakMulti $
Armor PiercingEdit
 $ {\it Damage Increased With AP} = \frac {\left[ \frac{\it Damage}{\it DamageResist \times 0.6}\right]^{0.366} \times 0.5} {\left[ \frac{\it Damage}{\it DamageResist}\right]^{0.366} \times 0.5} = 1.2056 $
Due to the way the damage formula works, the 40% armor piercing of some weapons mods actually result in a flat +20% effective damage done, on any foe, regardless of the weapon base damage or the DR of the target.
ReferencesEdit
 ↑ Most places cite this as 1.5x and 2.0x, however these numbers are relative to Very Hard difficulty, not Normal. The true, net difficulty modifiers are .75x for the player and 4.0x for enemies. For further discussion see examples such as reddit thread or mod
GalleryEdit
