This document serves as a resource for calculating the damage numbers for all 4 of the Vault Hunters inside of Borderlands 3! These general-use formulas were put together with the help and information from quite a few stand-out individuals who tested and confirmed how all of these separate characters and items work! If you have any questions about the formulas below or how to use them please contact SSpyR#7851 or Prismatic#9001 in the Official Borderlands Discord. Make sure to check out the resources and users that allowed this to happen!

Document Maintained by SSpyR#7851 from the Official Borderlands Discord
Help from Prismatic#9001 and Ratore

Thank you to DrStrangeLove on the GBXForums for the Critical Hit Calculations and Sticky Formulas
Thank you to Skwuruhl on the GBXForums for the Amara Damage Explanation
Thank you to Demonite on Youtube for the FL4K Numbers Explanation
Thank you to jafortune on the GBXForums for the Math Behind Fade Away
Thank you to Prismatic on the GBXForums for the Moze Damage Explanation
Thank you to PlayMyTrapCard from the Official BL Discord for the Moze Ammo Equation
Thank you to Melting_NT from the Official BL Discord for the Playing Dirty Equation
Thank you to HurdyGurdy on the GBXForums for the Splash Damage and Splash Anointment List

Primer to Borderlands Math by Prismatic

[forums.gearboxsoftware.com]

Demonite Video Explaining This (Using FL4K)

ThiccFilA Video Explaining Beginner Introductions to BL Math

Link to BL3 Damage Calculator Program[github.com]

The * 2 and onwards with each VH’s formula is Crit Damage, remove that portion if you want to calculate without Crit Damage. (If you want exact numbers, keep the Guardian Rank Gun Damage and C-C-Combo Bonus Portion of the Formula)

If not testing for any specific gun, then set Gun Card Damage = 1

V1 and V2 are different Versions/Variants of Flat Damage Increases (“+30% Damage” for example), Whether something is V1 or V2 can change based on source to source but generally V1 is something that relies on you (Power Inside, using AS and being above 50% health for more Damage) while V2 is something that relies on an enemy (Ice Breaker, doing more Damage against Frozen Targets)

%BonusElement is the percentage of your Base Damage on the gun equal to that of the source of the Bonus Element (a 526 Maggie with 50% Bonus Element would use 263 as its %BonusElement for the Bonus Element formula)

The initial 2% of C-C-Combo Bonus is still applied even if only 1 shot is fired, make sure to account for this

If working with a weapon that contains more than one pellet (or when accounting for a possible extra pellet), only enter the base number not multiplied by number of pellets into the Base Damage section. To account for extra pellets, multiply your final result by however many pellets are present.

Manufacturer Gun Damage is Additive with Gun Damage

The While Sliding and While Airborne Anointments may or may not be additive with each other but since you cannot have them both at the same time I just put them both in the same section.

What Tediore Toss Scales By: Weapon Damage (General), Manufacturer Specific Weapon Damage, Grenade Damage, AoE Damage, Splash Damage, Elemental Boost, Mag Size

Tediore Equation (Thanks to Prismatic):
Damage = Base Damage * Gun Damage * Grenade Damage * Splash * Bullets in Mag * Elemental

If it states +/- Weapon Damage or Gun Damage, it goes into the Gun Damage category of the formula

Torgue Sticky Impact Formula: NormalDamage * 0.07

Torgue Sticky Explosion Formula: NormalDamage * 0.70 * (1 + Sticky Bonus * (N-1))
N Being Number of Projectiles
NormalDamage would be the VH Formula

It’s P*ss, Execute, and Eruption’s Debuff Effects are all counted as V1

Amp Damage is in its Own Category, Multiply it in at the End

Life Steal from Moxxi and Life Steal Anoint (Thanks to Prismatic)
= [Life Steal %] x [Base Damage] x [Gun Damage] x [Zane’s Barrier Amp (If Applicable)] x [Airborne/Sliding Anointment] x [Regular Amp]

Multiple Zane Barriers are Multiplicative with Each Other, so all separate categories

CDR Formula: [Original Cooldown Time / (1 + Cooldown Rate Bonuses)]

Crit Damage Explained[forums.gearboxsoftware.com]
Torgue Sticky Damage Explained[forums.gearboxsoftware.com]
Amara Damage Explained[forums.gearboxsoftware.com]
FL4K Numbers Explained
Math of Fade Away Explained[forums.gearboxsoftware.com]
Moze Damage Explained[forums.gearboxsoftware.com]

Overkill Explained[forums.gearboxsoftware.com]
Damage Reduction/Resistance Math[forums.gearboxsoftware.com]
Moze Mindsweeper Math[forums.gearboxsoftware.com]
In-Depth on Personal Space for Amara[forums.gearboxsoftware.com]
Prismatic’s Gearology and Math[forums.gearboxsoftware.com]
List of All Splash Weapons[forums.gearboxsoftware.com]
DrStrangeLove’s Melee Deep Dive[docs.google.com]
Prismatic’s Moze Math Compendium[docs.google.com]

[(Gun Card Damage) * (1 + Wrath + Dread + Samsara + Driver Base + Driver Scaled + Jab Cross + Phazeserker + Com Generic Wep Boost + GunDmgAnoint) * (1 + C-C-Combo Bonus + Victory Rush) * (1 + Laid Bare) * (1 + Personal Space + Com Type Boost + Artifact Type Boost) * (1 + Arms Deal + Class Mod Splash Damage + Artifact AOE Damage + Splash Damage Anointment) * (1 + While-Sliding Damage Anoint + While-Airborne Damage Anoint) * (1 Tempest + Tempest Shock + Artifact Elemental)] * 2 * [(1 + SniperBonus) * (1 + WeaponCritBonus) * (1 + ManufacturerBonus) * (1 + Transcend + ClassMod + GuardRank + Anointment)] * [(1 + Guardian Rank Gun Damage)]

[(%BonusElement) * (1 + Wrath + Dread + Samsara + Driver Base + Driver Scaled + Jab Cross + Phazeserker + Com Generic Wep Boost + GunDmgAnoint) * (1 + C-C-Combo Bonus + Victory Rush) * (1 + Laid Bare) * (1 + Personal Space) * (1 + While-Sliding Damage Anoint + While-Airborne Damage Anoint) * (1 Tempest + Tempest Shock + Artifact Elemental)] * 2 * [(1 + SniperBonus) * (1 + WeaponCritBonus) * (1 + ManufacturerBonus) * (1 + Transcend + ClassMod + GuardRank + Anointment)] * [(1 + Guardian Rank Gun Damage)]

Driver Base is 20% at Normal Speed

Driver Scaling is 0.60 for 1, 2, 3 and 4 points in Mindfulness.
Driver Scaling is 0.72 for 5 points in Mindfulness
Driver Scaling is 0.80 for 6 points in Mindfulness

Scaling means for every 1.0% of Movement Speed Amara gets
She gets that % in Gun Damage (0.60)

This Damage is Applied on Shot

However, for stickies when you are reloading to proc, slide beforehand

[(Gun Card Damage) * (1 + Furious Attack + Turn Tail + Furryous + Persistence Hunter + Horned Skag Gun Damage + Dangerous Game + Grim Harvest + Com Generic Wep Boost + St4ckB0t + GunDmgAnoint) * (1 + Frenzy + Empathic Rage + Pack Tactics + Skag Damage + Interplanetary + Power Inside + C-C-Combo Bonus + Victory Rush) * (1 + Hidden Machine + Hunter's Eye + DE4DEYE Mod + Rakk Anoint + Com Type Boost + Artifact Type Boost) * (1 + Class Mod Splash Damage + Artifact AOE Damage + Splash Damage Anointment) * (1 + While-Sliding Damage Anoint + While-Airborne Damage Anoint) * (1 + Artifact Elemental + Scorcher) * [(Fade Away/Guerillas in the Mist + Unblinking Eye) + (Hunter's Eye Human) + 2 * [(1 + SniperBonus) * (1 + WeaponCritBonus) * (1 + ManufacturerBonus) * (1 + Ambush Predator + Dangerous Game + Galactic Shadow + Gunslinger Jabber + ClassMod + GuardRank + Anointment)] * [(1 + Guardian Rank Gun Damage)]

[(%BonusElement) * (1 + Furious Attack + Turn Tail + Furryous + Persistence Hunter + Horned Skag Gun Damage + Dangerous Game + Grim Harvest + Com Generic Wep Boost + St4ckB0t + GunDmgAnoint) * (1 + Frenzy + Empathic Rage + Pack Tactics + Skag Damage + Interplanetary + Power Inside + C-C-Combo Bonus + Victory Rush) * (1 + Hidden Machine + Hunter's Eye + DE4DEYE Mod + Rakk Anoint) * (1 + While-Sliding Damage Anoint + While-Airborne Damage Anoint) * (1 + Artifact Elemental + Scorcher) * [(Fade Away/Guerillas in the Mist + Unblinking Eye) + (Hunter's Eye Human) + 2 * [(1 + SniperBonus) * (1 + WeaponCritBonus) * (1 + ManufacturerBonus) * (1 + Ambush Predator + Dangerous Game + Galactic Shadow + Gunslinger Jabber + ClassMod + GuardRank + Anointment)] * [(1 + Guardian Rank Gun Damage)]

[(Gun Card Damage) * (1 + Furious Attack + Turn Tail + Furryous + Persistence Hunter + Horned Skag Gun Damage + Dangerous Game + Grim Harvest + Com Generic Wep Boost + St4ckB0t + GunDmgAnoint) * (1 + Frenzy + Empathic Rage + Pack Tactics + Skag Damage + Interplanetary + Power Inside + C-C-Combo Bonus + Victory Rush) * (1 + Hidden Machine + Hunter's Eye + DE4DEYE Mod + Rakk Anoint + Com Type Boost + Artifact Type Boost) * (1 + Class Mod Splash Damage + Artifact AOE Damage + Splash Damage Anointment) * (1 + While-Sliding Damage Anoint + While-Airborne Damage Anoint) * (1 + Artifact Elemental + Scorcher) * [(1 + Fade Away/Guerillas in the Mist + Unblinking Eye)] * [(1 + Guardian Rank Gun Damage)]

{[(Gun Card Damage) * (1 + Armored Infantry + Drowning in Brass + Desperate Measures + Phalanx Doctrine + Tenacious Defense + Click, Click + Com Generic Wep Boost + GunDmgAnoint) * (1 + C-C-Combo Bonus + Victory Rush) * (1 + Target Softening) * (1 + Com Type Boost + Artifact Type Boost) * (1 + Class Mod Splash Damage + Artifact AOE Damage + Splash Damage Anointment + Blastmaster Mod) * (1 + While-Sliding Damage Anoint + While-Airborne Damage Anoint) * (1 + Stoke the Embers + Artifact Elemental)] * 2 * [(1 + SniperBonus) * (1 + WeaponCritBonus) * (1 + ManufacturerBonus) * (1 + Scorching RPM's + ClassMod + GuardRank + Anointment)] * [(1 + Guardian Rank Gun Damage)]}

+ {{[(%BonusElement) * (1 + Armored Infantry + Drowning in Brass + Desperate Measures + Phalanx Doctrine + Tenacious Defense + Click, Click + Com Generic Wep Boost + GunDmgAnoint) * (1 + C-C-Combo Bonus + Victory Rush) * (1 + Target Softening) * (1 + Com Type Boost + Artifact Type Boost) * (1 + While-Sliding Damage Anoint + While-Airborne Damage Anoint)] * 2 * [(1 + SniperBonus) * (1 + WeaponCritBonus) * (1 + ManufacturerBonus) * (1 + Scorching RPM's + ClassMod + GuardRank + Anointment)] * [(1 + Guardian Rank Gun Damage)]]} * [((Selfless Vengeance + Experimental Munitions + Cloud of Lead + %BonusIncendiaryAnoint) + ((Base Damage * Gun Damage) * (Fire in The Skag Den) * (1 + Scorching RPM’s Iron Bear Damage + Stainless Steel Bear’s Iron Bear Damage)) * (1 + Stoke the Embers + Artifact Incendiary)]}

+ {[(Regular Formula)] * [(ShortFuseDMG%) * (1 + Class Mod Splash Damage + Artifact AOE Damage + Splash Damage Anointment + Blastmaster Mod)] * [1 + Scorching RPM’s Iron Bear Damage + Stainless Steel Bear’s Iron Bear Damage] * [1 + C-C-Combo Bonus + Victory Rush]} + {[(ShortFuseDMG%)] * [(Regular Formula)] * [(Fire in the Skag Den)] * [(1 + Stoke the Embers + Artifact Incendiary)]}

(Gun Mag Size) * (1 + Mag Size Modifiers) * (Redis/Forge %) - (Gun Fire Rate * (1 + Fire Rate%) * (1 - Cloud of Lead Chance) * (# of Ammo Consumed))

example with:
kyb's worth with 44 mag size, 40% mag from relic, 2 redis = 10% regen, 7.88 fire rate, 5/5 cloud of lead
(44)*(1+.4)*(.1) - (7.88*(1-1/4)) = 6.16 - 5.91 = .25 ammo/second regen while firing

[(Gun Card Damage) * (1 + Confident Competence + Violent Momentum Base + Violent Momentum Scaled + Donnybrook + Synchronicity + Double Barrel + Infiltrator Mod + Antifreeze Mod + Retaliation + Com Generic Wep Boost + GunDmgAnoint) * (1 + C-C-Combo Bonus + Victory Rush) * (1 + Barrier Amp) * (1 + Icebreaker + Artifact Type Boost + COM Type Boost) * (1 + Class Mod Splash Damage + Artifact AOE Damage + Splash Damage Anointment * (1 + While-Sliding Damage Anoint + While-Airborne Damage Anoint) * (1 + Artifact Elemental)] * 2 * [(1 + SniperBonus) * (1 + WeaponCritBonus) * (1 + ManufacturerBonus) * (1 + Executor Mod + ClassMod + GuardRank + Anointment)] * [(1 + Guardian Rank Gun Damage)]

[(%BonusElement) * (1 + Confident Competence + Violent Momentum Base + Violent Momentum Scaled + Donnybrook + Synchronicity + Double Barrel + Infiltrator Mod + Antifreeze Mod + Retaliation + Com Generic Wep Boost + GunDmgAnoint) * (1 + C-C-Combo Bonus + Victory Rush) * (1 + Barrier Amp) * (1 + Icebreaker) * (1 + While-Sliding Damage Anoint + While-Airborne Damage Anoint) * (1 + Artifact Elemental)] * 2 * [(1 + SniperBonus) * (1 + WeaponCritBonus) * (1 + ManufacturerBonus) * (1 + Executor Mod + ClassMod + GuardRank + Anointment)] * [(1 + Guardian Rank Gun Damage)]

VM Scaling at 5/5 Baseline: 0.8
VM Scaling at 5/5 with DFC: 1.0
VM Scaling at 5/5 with DFC and with Seein’ Dead: 1.20

Scaling means for every 1.0% of Movement Speed Zane gets
He gets that % in Gun Damage (0.8 at 5/5 Baseline)

This Damage is Applied on Shot

However, for stickies when you are reloading to proc, slide beforehand

Reproc Chance: (PD Chance)*(1-((1-0.04)^(5 (Pellet Count +1))))

Effective damage up: (1/Pellet Count)

This equation works for guns that are consistent with hits and pellets across the board[/i]