Welcome! This is a breakdown of FL4K’s Damage Formula, from Weapons to Action Skills, Pets and other interactions!
Recommended Resources
Critical Hit Calculation by @DocStrangelove
The Math of Fade Away by @jafortune
FL4K’s Universal Multiplicative Damage Boosts video by @DemoniteBL
BL3 Math Basics video by @flightx3aa
Prismatic’s Gearology and Math to better understand how specific gear or weapons work.
FL4K Pet Compendium by @boombumr
Fl4k Skills, Augments and Pets  Rating and Analysis by @darreltan2004
Thank you to the creators of all those!
Special thanks to @Prismatic for their work in general in regards to BL3 Math, and the assistance with formatting.
Special thanks to @plenipotence for all of their testing and assistance. A lot of what you see here has them involved.
Thank you to @boombumr for their perseverance in dealing with pets and all the stuff they’ve figured out for them.
Table of Contents
 Base Formula
 General Formula
 Action Skill Damage
 Pet Damage Formula
 Hunt Power and Skill Values
 Barbaric Yawp and Pet Bonuses
 Final Notes
BASE FORMULA
No Guardian Rank, no anointments, no class mod/shield/artifact stat boosts. Basically skills and class mod special effects only.
Final Damage Output = Base Damage x Gun Damage x V1 x V2 x Elemental Multiplier x Crit
 V1 and V2 are just made up naming schemes originally used in Demonite’s FL4K video. Skill tree wise, V1 is quite unique to FL4K compared to other Vault Hunters, and a general boost that increases all damage dealt from any source. V2 has both general boosts and specific boosts (like weapon type boosts).
Base Damage = Original weapon hit damage, which may or may not match weapon card damage, depending on the weapon’s effects. Can be basically any number depending on what you intend to test.
Gun Damage = (1+ FuriousAttack + TurnTail + FastFurryous + PersistenceHunter + HornedSkagGunDmg + DangerousGame + GrimHarvest + St4ckbot)
V1 = (1 + Frenzy + EmpathicRage + PackTactics + SkagDmg + Interplanetary + PowerInside)
V2 = (1 + HiddenMachine + HuntersEyeArmor + DE4DEYE)
Elemental Multiplier = [ElementalDamageMultiplier x (1 + ArtifactElementalDmg + IntStalkerCorrosive + ScorcherAnt)]
Crit = [2 x [(1 + SniperBonus) x (1 + WeaponCardBonus) x (1 + ManufacturerBonus) x (1 + AmbushPredator + DangerousGame + GalacticShadow + GunslingerJabber)] + (Fade/Guerillas + UnblinkingEye) + (HuntersEyeHuman)]
 Crit has what are called “Post Add” bonuses. These are additive bonuses to the main Critical hit formula, and on this base formula they appear in the form of Fade Away and Hunter’s Eye Human Crit Bonus.
GENERAL FORMULA
Includes Guardian Rank, anointments and other boosts.
Final Damage Output = Base Damage x Gun Damage x V1 x V2 x Pearl Stacks x Splash x Slide/Airborne Damage Anoints x Elemental Multiplier x Crit x Guardian Rank Gun Damage x Amp Shield x Harmageddon

It’s unknown if Slide/Airborne Damage anointments are additive to each other, but since they can’t be used together anyway (as of now at least), they’ll be displayed like that for ease of use.

The “Rakk Attack 100%” Anointment is referred to as “Rakk Slag” in this.

The “300% vs. above 90% HP” Anointment is referred to as “High Health Breaker” in this.

Pearl Of Ineffable Knowledge appears in both Gun Damage and on its own section. The Gun Damage from it is the final 90% Boost that you get by achieving maximum stacks. The stacks are their own Pearl Stacks section and currently act as purely multiplicative, as far as testing went.
Base Damage = Original weapon hit damage, which may or may not match weapon card damage, depending on the weapon’s effects. Can be basically any number depending on what you intend to test.
Gun Damage = [color=steelblue](1 + FuriousAttack + TurnTail + FastFurryous + PersistenceHunter + HornedSkagGunDmg + DangerousGame + GrimHarvest + ComWeapDmg + St4ckbot + GunDmgAnoint + PearlFinalBoost)
 PearlFinalBoost is the 90% boost you get at max Pearl Stacks. This boost, while implied otherwise in its description, is Gun Damage.
V1 = (1 + Frenzy + EmpathicRage + PackTactics + SkagDmg + Interplanetary + PowerInside + VictoryRush + CCCombo)
V2 = (1 + HiddenMachine + HuntersEyeArmor + DE4DEYE + RakkSlag + ComTypeBoost + ArtifactTypeBoost + IceBreaker + GrenadeThrowAnoint + HighHealthBreaker)
Pearl Stacks = (1.01^Stacks)
 Pearl Stacks are multiplicative to each other, and end up as 1.01^15 = 1.1609 (16.09%).
Splash = (1 + ClassModSplashDmg + ArtifactAreaDmg + SplashAnoint)
Slide/Airborne Damage Anoints = (1 + WhileSliding/AirborneDmgAnoint)
Elemental Multiplier = [ElementalDamageMultiplier x (1 + ArtifactElementalDmg + IntStalkerCorrosive + ScorcherAnt + GRank Elemental + OldGod)]
Crit = [2 x [(1 + SniperBonus) x (1 + WeaponCardBonus) x (1 + ManufacturerBonus) x (1 + AmbushPredator + DangerousGame + GalacticShadow + GunslingerJabber + ClassMod + GRankCrit + GenericCritAnoint) x (AirborneCritAnoint)] + (Fade/Guerillas + UnblinkingEye) + (HuntersEyeHuman) + (RakkCritAnoint)]
 Crit has what are called “Post Add” bonuses. These are additive bonuses to the main crit formula, and on this general formula they appear in the form of Fade Away’s Crit Damage, Hunter’s Eye Human Crit Bonus and Rakk Attack Crit Anointment.
Guardian Rank Gun Damage = [(1 + GRankGunDamage)]
Amp Shield = [(1+ AmpShield)]
Harmageddon = [(1 + 0.05)], up to [(1 + 0.20)]
Each unique status instance is an additional + 0.05, which goes up to 0.20 for a x1.20 multiplier.
CRITICAL HIT
The Crit section has some specific values that are not known at a glance, alongside some other things like the already mentioned Post Add boosts. Here’s a quick breakdown of the general formula:
Crit = [2 x [(1 + SniperBonus) x (1 + WeaponCardBonus) x (1 + ManufacturerBonus) x (1 + AmbushPredator + DangerousGame + GalacticShadow + GunslingerJabber + ClassMod + GRankCrit + GenericCritAnoint) x (AirborneCritAnoint)] + (Fade/Guerillas + UnblinkingEye) + (HuntersEyeHuman) + (RakkCritAnoint)]

SniperBonus = 20% for all Sniper Rifles of any manufacturer.

WeaponCardBonus = The critical hit bonus listed on a weapon’s card.

ManufacturerBonus = Hidden manufacturer specific boost. 5% for Hyperion, 10% for Jakobs (any of their weapons).

Hunter’s Eye is actually 6% Post Add crit per point up to 30%, unlike the 15% the card states.
This is because the card tries to represent its effective formula value as a “real” crit on the section that has Skills and other boosts:
 Damage x [2 x [(RestOfCritFormula) x (1 + 0.15 + CritBoosts)] = 2.30
But the reality is:
 Damage x [2 x [(RestOfCritFormula)] + 0.30] = 2.30
Post Add crit bonuses are referred to like that because of how they behave in regards to the formula. Quoting @DocStrangelove’s explanation in their Critical Hit Calculation thread,
FADE AWAY, BODYSHOTS AND CRITS
Fade Away hits are considered a crit for practical effects, like skills and weapons that depend or have features related to crit. Damagewise, though, they are closer to a “fake” or pseudocrit, not an “automatic true crit”. This means you still get more damage by hitting the enemy’s weak points. Here’s how Fade Away behaves on Bodyshots and weak point hits:
 The Base/General Formula is simplified as “Damage” and “RestOfCritFormula” here.
Fade Away Nonweak point hit = Damage x (1 + Fade/Guerrillas + UnblinkingEye)
Fade Away Weak point Hit = Damage x [2 x (RestOfCritFormula) + (Fade/Guerrillas + UnblinkingEye)]
Fade Away Bodyshots simply get the Fade Bonus on top of the Damage, without receiving any other form of crit boost.
A Weak point Hit gives you the “true” crit damage alongside Fade Away damage. This also means Megavore can proc on Fade Away bodyshots. The Fade Away boost has a varying degree of diminishing returns with the crit formula, due to its high value and how it is applied as a Post Add bonus.
Another way to represent a Fade Away Weak point hit is:
Fade Away Weak point Hit = Damage x [2 x (RestOfCritFormula)] + [Damage x (Fade/Guerrillas + UnblinkingEye)]
This basically represents Fade Away adding a % of bodyshot damage as damage to your overall shot.
CRIT AND BASE CALCULATION EXAMPLE
Let’s assume we have a Kinetic Jakobs Sniper with the following stats:
 1000 Base Damage
 30% Weapon Card Crit
 Being Jakobs, the weapon has an innate 10% Crit Boost
 Being a Sniper, the weapon has an innate 20% Crit Boost
And that our build has:
 25% Weapon Damage from The Fast And The Furryous
 50% V1 from The Power Inside
 35% V2 from DE4DEYE
 10% Elemental Damage from Scorcher Spiderant
 15% Crit from Galactic Shadow
 30% Post Add Crit: Hunter’s Eye vs. Human bonus
 275% Post Add Crit: Base Fade and 1 Stack of Unblinking Eye
 Guardian Rank Off
 Target is a human
 No Hunt Power boosts (would affect Hunter’s Eye in this case)
 We’ll be ignoring the elemental multipliers (vs. Flesh, Armor and Shield) and assume neutrality for the sake of finding our final multiplier. That, or you can just assume this is Kinetic vs. Flesh , which would be neutral anyway.
This grants us the following final formula that we’ll use for the examples:
Final Damage Output = Base Damage x (1 + FastFurryous) x (1 + PowerInside) x (1 + DE4DEYE) x (1 + ScorcherAnt) x [2 x [(1 + SniperBonus) x (1 + WeaponCardBonus) x (1 + ManufacturerBonus) x (1 + GalacticShadow)] + (Fade + UnblinkingEye) + (HuntersEyeHuman)]
Weak point hit/Megavore proc without Fade Away:
Final Damage Output = 1000 x (1 + 0.25) x (1 + 0.50) x (1 + 0.35) x (1 + 0.10) x [2 x [(1 + 0.20) x (1 + 0.30) x (1 + 0.10) x (1 + 0.15)] + 0.30]
Final Damage Output = 1000 x 1.25 x 1.50 x 1.35 x 1.10 x [2 x [1.20 x 1.30 x 1.10 x 1.15] + 0.30]
Final Damage Output = 1000 x 1.25 x 1.50 x 1.35 x 1.10 x 4.2468
Final Damage Output = 11824.68375
Weak point hit/Megavore proc with Fade Away:
Final Damage Output = 1000 x (1 + 0.25) x (1 + 0.50) x (1 + 0.35) x (1 + 0.10) x [color=#f44][2 x [(1 + 0.20) x (1 + 0.30) x (1 + 0.10) x (1 + 0.15)] + 2.75 + 0.30]
Final Damage Output = 1000 x 1.25 x 1.50 x 1.35 x 1.10 x [2 x [1.20 x 1.30 x 1.10 x 1.15] + 2.75 + 0.30]
Final Damage Output = 1000 x 1.25 x 1.50 x 1.35 x 1.10 x 6.9968
Final Damage Output = 19481.715
Nonweak point hit with Fade Away:
Nonweak point hits with Fade Away don’t get anything fro mthe actual main crit formula. That leaves us with a diferent base formula:
Final Damage Output = Base Damage x (1 + FastFurryous) x (1 + PowerInside) x (1 + DE4DEYE) x (1 + ScorcherAnt) x (1 + Fade + UnblinkingEye)
It then translates into:
Final Damage Output = 1000 x (1 + 0.25) x (1 + 0.50) x (1 + 0.35) x (1 + 0.10) x (1 + 2 + 0.75)
Final Damage Output = 1000 x 1.25 x 1.50 x 1.35 x 1.10 x 3.75
Final Damage Output = 10441.40625
GRENADE/SHIELD BONUS ELEMENT ON WEAPON
Receives no Splash or Weapon Type Damage boosts
Final Damage Output = %BonusElement x Gun Damage x V1 x V2 x Pearl Stacks x Slide/Airborne Damage Anoints x Elemental Multiplier x Crit x Guardian Rank Gun Damage x Amp Shield x Harmageddon
V2 = (1 + HiddenMachine + HuntersEyeArmor + DE4DEYE + RakkSlag + IceBreaker + GrenadeThrowAnoint + HighHealthBreaker)
Splash = None.
 Follows the General Formula except for: receives no Splash Multipliers and no Weapon Type Boosts on V2. These anointments are the 50% Bonus Element for 10s that can spawn on Shields and Grenades.
On nonweak point hits, this damage can independently crit via Megavore. Each instance of bonus element has its own 20% chance at a Megavore proc. Leave No Trace and Head Count will only trigger on crits coming from the main damage of the gun.
When hitting a weak point, both the main damage and any bonus elements will crit. Fade Away crits apply correctly to this damage, and works in accordance to what is described in the Fade Away section.
WEAPON BONUS ELEMENT ON WEAPON
Receives no Splash Damage boosts
Final Damage Output = %WeaponBonusElement x Gun Damage x V1 x V2 x Pearl Stacks x Slide/Airborne Damage Anoints x Elemental Multiplier x Crit x Guardian Rank Gun Damage x Amp Shield x Harmageddon
Follows the General Formula except for: receives no Splash multipliers. These do receive Weapon Type Damage boosts on V2. For FL4K, these anointments are:
 100% Element on Next 2 Magazines
 Gamma Burst 115% Bonus Radiation
 150% Radiation damage when below 50% health
 125%/75% vs. Badass/Named/Boss (it’s a kinetic bonus element)
On nonweak point hits, this damage can independently crit via Megavore. Each instance of bonus element has its own 20% chance at a Megavore proc. Leave No Trace and Head Count will only trigger on crits coming from the main damage of the gun (not bonus elements).
When hitting a weak point, both the main damage and any bonus elements will crit. Fade Away crits apply correctly to this damage, and works in accordance to what is described in the Fade Away section.
ACTION SKILL FORMULA
Rakk Attack/Gamma Rift Explosion
Final Damage Output = Action Skill Base Damage x Mayhem Scaling x Action Skill Damage Boosts x V1 x V2 x Splash x Elemental Multiplier x Harmageddon
Action Skill Base Damage = Base Card damage listed on the skill tree.
Action Skill Damage Boosts = (1 + GrimHarvest + IntStalkerHuman + ClassModActionSkillDmg)
V1 = (1 + Frenzy + EmpathicRage + PackTactics + SkagDmg + Interplanetary + PowerInside + VictoryRush)
V2 = (1 + HiddenMachine + HuntersEyeArmor + DE4DEYE + IceBreaker + GrenadeThrowAnoint + HighHealthBreaker)
Splash = (1 + ClassModSplashDmg + ArtifactAreaDmg + SplashDamageAnoint)
Elemental Multiplier = [Elemental Bonus Multiplier x (1 + ArtifactElementalDmg + IntStalkerCorrosive + ScorcherAnt + GRank Elemental + OldGod)]
GRENADE/SHIELD BONUS ELEMENT ON ACTION SKILL/MELEE/OTHERS
Receives no Splash or Weapon Type Damage boosts

The bonus elements from Shield and Grenade anointments apply universally to these types of damage. This damage includes Grenades, Melee, Action Skills, and Slam.

These bonus elements currently do not receive Mayhem Scaling when applied to the listed damage types, except for Grenades, which have their own base damage scaled through the Mayhem loot level.

When applied to a source that uses damage dealt for its calculation, there will be no scaling problems. Example: White Elephant bombs have their damage based on the main, nonbonus element damage dealt by the Melee attack, which means the bonus elements on the White Elephant explosion will scale from the White Elephant’s damage. However, the bonus elements on the Melee attack get no scaling.
Final Damage Output = Elemental% Base Damage x V1 x V2 x Elemental Multiplier x Crit x Guardian Rank Gun Damage x Harmageddon
Elemental% Base Damage = The % of Base Damage used as Bonus Element. This is 50% of base damage for Shield/Grenade ASE Bonus Elements.

The Shield/Grenade anoints are consistent with their usage on weapons, meaning they don’t get Weapon Type Damage boosts on V2 or Splash Damage boosts.

Melee and Action Skill Damage boosts do not apply to these bonus elements.

Crit formula applies fully.
On nonweak point hits, this damage can independently crit via Megavore. Each instance of bonus element has its own 20% chance at a Megavore proc. Leave No Trace and Head Count will only trigger on crits coming from the main damage source.
When hitting a weak point, both the main damage and any bonus elements will crit, but only if the main damage source can crit in the first place.
WEAPON BONUS ELEMENT ON ACTION SKILL/MELEE/OTHERS
Receives no Splash or Weapon Type Damage boosts

The bonus element from the 150% Radiation while below 50% Health and Terror Cryo anointments apply universally to these types of damage. This includes Grenades, Melee, Action Skills, and Slam.

These bonus element receives Mayhem Scaling on applicable sources. Grenades have their own scaling through the Mayhem loot level.
Final Damage Output = Elemental% Base Damage x Mayhem Scaling x Damage Source Boost x V1 x V2 x Elemental Multiplier x Crit x Harmageddon
Elemental% Base Damage = The % of Base Damage used as Bonus Element. This is 150% of base damage for the URad anointment.
Damage Source Boost = Melee/Action Skill/Grenade Damage

Depending on which damage the element is being applied to, it can receive boosts that are specific to that damage source. This means it can get Melee damage when applied to Melee, Action Skill Damage when applied to an Action Skill and Grenade Damage when applied to a Grenade.

Does not receive Weapon type Damage boosts, since it’s being applied to a nongun source. Does not receive Splash Damage boosts.

Crit formula applies fully.
On nonweakpoint hits, this damage cannot independently crit via Megavore. This is likely due to some key differences in how bonus elements on the player’s Weapon are handled compared to bonus elements on Shield/Grenade. Leave No Trace and Head Count will only trigger on crits coming from the main damage source.
When hitting a weakpoint, both the main damage and any bonus elements will crit, but only if the main damage source can crit in the first place.
PET DAMAGE FORMULA
Final Damage Output = Base Damage x Mayhem Scaling x Pet Damage x Sic’ Em x DE4DEYE x Go For The Eyes x Splash x Elemental Multiplier x Harmageddon
Base Damage = (BaseHit + 75%GammaBurstRad)
Pet Damage = (1 + FuriousAttack + LickTheWounds + Furryous + PowerInside + Ferocity + Frenzy + PsychoHead + Endurance + PackTactics + IntStalker + DangerousGame + GrimHarvest)
 All the Pet Damage present in Hunter Skills (Furious Attack, Interplanetary Stalker, Dangerous Game) does not get boosted by Big Game/Hunt Power sources, with the exception of Frenzy and Psycho Head On A Stick.
Sic’ Em = (1 + SicEm). (1 + 0.30) at 3/3, up to (1 + 0.60) at 6/3
 Sic’ Em applies to Attack Commands only.
DE4DEYE = (1 + DE4DEYE). The 35% damage bonus against targets above 75% health. So, (1 + 0.35)
Go For The Eyes = (1 + GFTE). (1 + 0.75) at 5/5, up to (1 + 1.50) at 10/5
 Go For The Eyes doesn’t seem to apply to the extra Radiation Damage from Gamma Burst.
Splash = (1 + ClassModSplashDmg + ArtifactAreaDmg + SplashDamageAnoint)
 Splash applies to Attack Commands only.
Elemental Multiplier = (ElementalDamageMultiplier)
Harmageddon = [(1 + 0.05)], up to [(1 + 0.20)]
Each unique status instance is an additional + 0.05, which goes up to 0.20 for a x1.20 multiplier.
HUNT POWER AND SKILL VALUES
 Essentially, it’s a simple formula of:
Skill Value x Hunt Power
 Furious Attack at 5/5 totals 20% Gun Damage. With 30% Hunt Power, this is:
0.20 * 1.30 = 0.26 (26% Gun Damage)
 Apart from Frenzy and Psycho Head On A Stick, Pet Damage boosts on Hunter Skills do not receive an increase from Hunt Power. This only affects the damage added to the skills on that older hotfix that attempted to buff pets.
Some Hunt Power boosted skill values and extra class mod rolls:
3/3 BIG GAME BOOSTED HUNTER GUN DAMAGE/DAMAGE SKILLS:
(0.x * 1.30)

Furious Attack 5/5: 0.26 at 10 stacks / 0.026 per stack

Interplanetary 5/5: 0.39 at 3 stacks / 0.13 per stack

Hunter’s Eye 5/5: 0.39 Critical, 0.39 Robot Damage

Dangerous Game 3/3: 0.325 Gun Damage, 0.13 Crit

Frenzy 5/5: 0.52 at 10 stacks / 0.052 per stack
6/3 BIG GAME BOOSTED HUNTER GUN DAMAGE/DAMAGE SKILLS:
(0.x * 1.60)

Furious Attack 5/5: 0.32 at 10 stacks / 0.032 per stack

Interplanetary 5/5: 0.48 at 3 stacks / 0.16 per stack

Hunter’s Eye 5/5: 0.48 Critical, 0.48 Robot Damage

Dangerous Game 3/3: 0.40 Gun Damage, 0.16 Crit

Frenzy 5/5: 0.64 at 10 stacks / 0.064 per stack
6/3 BIG GAME BOOSTED HUNTER GUN DAMAGE/DAMAGE SKILLS + STALKER COM WITH +3 BIG GAME +2 INTERPLANETARY:
(0.x * 1.85)

Furious Attack 5/5: 0.37 at 10 stacks / 0.037 per stack

Interplanetary 7/5: 0.78 at 3 stacks / 0.26 per stack

Hunter’s Eye 5/5: 0.555 Critical , 0.555 Robot Damage

Dangerous Game 3/3: 0.4625 Gun Damage, 0.185 Crit

Frenzy 5/5: 0.74 at 10 stacks / 0.074 per stack
BOUNTY HUNTER ROLLS WITHOUT BIG GAME BOOST

Hunter’s Eye 10/5: 0.60 Critical, 0.60 Robot Damage

Hunter’s Eye 7/5: 0.42 Critical, 0.42 Robot Damage

Frenzy 10/5: 0.80 at 10 stacks / 0.080 per stack

Frenzy 7/5: 0.56 at 10 stacks / 0.056 per stack

Dangerous Game 6/3: 0.50 Gun Damage, 0.20 Crit
BOUNTY HUNTER ROLLS WITH 3/3 BIG GAME BOOST
(0.x * 1.30)

Hunter’s Eye 10/5: 0.78 Critical, 0.78 Robot Damage

Hunter’s Eye 7/5: 0.546 Critical, 0.546 Robot Damage

Frenzy 10/5: 1.04 at 10 stacks / 0.104 per stack

Frenzy 7/5: 0.73 at 10 stacks / 0.073 per stack

Dangerous Game 6/3: 0.65 Gun Damage, 0.26 Crit
BARBARIC YAWP PET BONUSES
Pet Bonus x Yawp
This one’s pretty simple, it’s just the base pet bonus multiplied by the % increase from Yawp.
 Example with Horned Skag and 5/5 Yawp:
Horned Skag Gun Damage
(SkagGunDmg) x (1 + Yawp) = Final Gun Damage
(0.10) x (1 + 2) = 0.30 (30% Gun Damage)
Horned Skag Damage
(SkagDmg) x (1 + Yawp) = Final Damage
(0.05) x (1 + 2) = 0.15 (15% V1)
FINAL NOTES
Thanks for reading, and i hope this comes of use! The discovered math/formulas in this game right now are ever so slightly changing in accordance to what is discovered. So when something comes up, i’ll be updating whatever needs updating here.