Damage Formula/Detailed Damage Formula
Attack Types: Normal Attack | Charge Attack
Other Damage: Plain Damage | Destruction Damage | Bonus Damage | Critical Damage | Supplemental Damage | DMG Taken Amplified
Damage Formula: Basic Concepts | Detailed Formula | Damage Cap
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Apart from fixed damage instances, all damage in Granblue Fantasy is based on the characters' ATK stat, which is then affected by a series of modifiers coming from skills effects, weapon skills, summon calls, etc.
For computations, the notion of Base Damage is useful to factor in all these modifiers. It is then used to compute actual damage values such of normal attacks, charge attacks, etc.
Base damage
Base damage is a virtual damage value that is used as a basis in the computation of the actual damage values for in-game attack types (normal, counters, charge attacks, etc.).
It can be expressed as:
Base damage = Character total ATK × Elemental boost × NormalOmegaEx boosts × Char Enmity boost × Char Stamina boost × Perpetuity boost × Unique Stackable boost × Assassin boost × Total Char Unique ATK boosts × Crew Ship boost × Crew Skills boost × ATK down debuff effect
NormalOmegaEx boosts is a composite value:
NormalOmegaEX boosts = ( Normal ATK boost × Normal Enmity boost × Normal Stamina boost × Omega ATK boost × Omega Enmity boost × Omega Stamina boost × EX ATK boost × EX Enmity boost ) - Fixed ATK Modifiers
The different boost categories that appear in these formulas are detailed below. Within a boost category, the modifiers always stack additively. Sometimes, two modifiers will not stack with each other: in that case, priority rules appear, which depend on the type of modifiers.[Citation needed]
Character total ATK
The sum of the character's base ATK, grid weapons' ATK values, and summon ATK values. If a weapon matches the character's weapon specialty, it contributes at 120% of its base ATK instead of 100%.
Elemental boost
Elemental boost = 1 + Elem superiority + Elem summon mod + Elem EMP buffs + Elem ATK buffs - Elem ATK debuffs
Elemental superiority is 50% when the character is element-superior to the enemy, -25% when element-inferior, 0% otherwise.
Elemental summon modifiers are auras of the type X% boost to [Element] Elemental ATK.
Elemental EMP buffs are EMPs of the type [Element] ATK up.
Elemental ATK buffs and debuffs are the [Element] ATK up/down effects that can come from skills, weapons, enemies or summon calls.
Normal ATK boost
Normal ATK boost = 1 + Norm ATK mod × (1 + Optimus aura) + Bahamut mod + Ultima mod + NormSummon aura + Norm buffs - Norm debuffs
Normal ATK modifier encompasses all the Normal weapon skills that increase ATK with no requirement on character HP level.
Optimus aura is the modifier from the Optimus Series summons aura (and their Demi Optimus counterparts): Agni, Varuna, Titan, Zephyrus, Zeus and Hades.
Normal summon aura is the X% boost to Normal ATK modifer from summons such as Grand Order.
Normal buffs/debuffs are the ATK up/down effects that can come from skills, enemies or summon calls.
Omega ATK boost
Omega ATK boost = 1 + Omega ATK mod × (1 + Omega aura)
Omega ATK modifiers encompass all the Omega weapon skills that increase ATK with no requirement on character HP level.
Omega aura is the modifier from the Omega Series SSR summons aura: Colossus, Leviathan, Yggdrasil, Tiamat, Luminiera and Celeste.
EX ATK boost
EX ATK boost = 1 + Usual EX ATK mod + Mysterious EX ATK mod × (1 + Ranko aura)
Usual EX ATK modifiers encompass all the EX weapon skills that increase ATK with no requirement on character HP level, excluding the iDOLM@STER event weapon Mysterious EX skills.
The Ranko Kanzaki aura affects the Mysterious EX ATK modifiers from iDOLM@STER event EX weapons.
Normal/Omega/EX Enmity and Stamina boosts
Normal Enmity boost = 1 + Norm Enmity mod × (1 + Optimus aura) Normal Stamina boost = 1 + Norm Stamina mod × (1 + Optimus aura) Omega Enmity boost = 1 + Omega Enmity mod × (1 + Omega aura) Omega Stamina boost = 1 + Omega Stamina mod × (1 + Omega aura) EX Enmity boost = 1 + EX Enmity mod EX Stamina boost = 1 + EX Stamina mod
Enmity and Stamina modifiers are the ATK up weapon skill modifiers that depend on the HP level of the character. They are present on Normal, Omega and EX weapons.
Normal and Omega Enmity/Stamina modifiers are affected by the Optimus/Omega auras, but not the EX modifiers.
Fixed ATK Modifiers
Absolute modifiers of the ATK computation, such as the 15% ATK cut from Qinglong Manewhip.
Char Enmity/Stamina boost
Char Enmity boost = 1 + Jammed mod + Enmity EMP mod + Ring Enmity mod + AX Enmity mod Char Stamina boost = 1 + Strength mod + Stamina EMP mod + Ring Stamina mod + AX Stamina mod
Jammed and Strength are character buffs originating from skills, weapons, summons or charge attacks.
EMP modifiers and Ring modifiers respectively come from the EMP perks and the Coronation Rings, Lineage Rings, and Intricacy Rings associated to the character.
AX modifiers come from AX skill in the grid that's currently being used and is added to all characters.
Perpetuity boost
Perpetuity boost = 1 + Perpetuity mod
Perpetuity modifiers are ATK up effects originating from the Perpetuity Ring, the Shield of Eternal Splendor, the Divine Stamp Book, and some buffs, such as 
.
Unique Stackable boost
Unique Stackable boosts = 1 + Unique Stackable mod
Unique Stackable modifiers are ATK up effects that come from 
Multiplier: Unique Stackable and its variants. Unique Stackable boosts that use the same frame will stack additively and count toward the same cap. The cap used is dependent on highest active effect. Unique Stackable boosts will only count to the cap if it is applied while the current boost is below its individual cap (e.g. If 
Gain
Strength: 10% (Max: 100%)Multiplier: Unique StackableDuration: IndefiniteStacking: Single Target and
Strength: 10% (Max: 100%)Duration: IndefiniteStacking: Single Target.
Restore all allies' HP based on damage dealt (Healing cap: 2000) and remove 1 debuff. 5 times then 
At level 55:
Damage increased to 400%-500%.
At level 100:
Also inflict 
Strength: 10% (Max: 40%)Base Accuracy: 90%Duration: 180 seconds and 
Strength: 10% (Max: 40%)Base Accuracy: 90%Duration: 180 seconds.
Gain
Strength: 10% (Max: 50%)Multiplier: Unique StackableDuration: IndefiniteStacking: Single. 1 time, she will have a 50% boost. If the order of copied skills is switched, she will have a 60% boost.) Unique Stackable boosts in separate frames count toward separate caps (e.g. at max stacks,
Gain
Strength: 10% (Max: 100%)Multiplier: Unique StackableDuration: IndefiniteStacking: Single Target and
Strength: 10% (Max: 100%)Duration: IndefiniteStacking: Single Target.
Restore all allies' HP based on damage dealt (Healing cap: 2000) and remove 1 debuff. and 
Assassin boost
- See also: Assassin (Buff)
Assassin boosts = 1 + Assassin mod
Assassin modifiers are ATK up effects that come from buffs such 
,
, 
and other variants. In addition to the boost, all known assassin boosts also increase the damage cap.
Total Char Unique ATK boosts
Total Char Unique ATK boosts is the product of all the Unique ATK up effects present on a character. Essentially, each Unique ATK up effect behaves like its own boost category, applied multiplicatively in the damage formula.
Each Char Unique ATK boost = 1 + Unique ATK mod
Crew Ship boost / Crew Skills boost
Crew Ship boost = 1 + Crew Ship mod Crew Skill boost = 1 + Crew Skill mod
Crew Ship modifier is the X% [Element] ATK up effect present on the active crew airship.
Crew Skill boost is the X% [Element] ATK up effect triggered by certain crew skills.
ATK down debuff effect
ATK down debuff effect = 1 - ATK down mod
ATK down modifier encompasses all non-elemental X% ATK down debuffs present on the character.
Final Damage
Supplemental Damage
Supplemental Damage is an effect present on certain skills, such as Halluel and Malluel's 
Local status effect debuff, Pact Weapons' Pact skills, or the Hollowsky Weapons's Covenant skills and are directly added without taking into account Base Damage or Defense.
Please refer to Supplemental Damage for more information.
Seraphic boost
Seraphic boost is an effect present on some characters' passive skills (Eternals, for instance), and on the Seraphic Weapons skills.
It is applied after every other modifier has been applied, on every damage instance, and also affects the character's damage cap. However, Supplemental Damage is only boosted by Seraphic boosts for skill damage and C.A. Damage. Normal Attacks will not get their Supplemental Damage increased by a Seraphic boost.
Therefore, in all the following subsections describing the different instances of damage (excluding the exception described above), the final damage will be computed as such if a Seraphic modifier is present:
Final Damage = Instance Damage × (1 + Seraphic mod) Final Damage cap = Instance Damage cap × (1 + Seraphic mod)
Normal Damage
Normal damage is the damage of one hit of a normal attack. For multiattacks, each hit will be computed independently.
Normal Damage = (Base Damage × Sleeping boost × Random Modifier / Enemy DEF)
Random Modifier is a random number between 0.95 and 1.05 (step size 0.01); in other words, there is a 5% variance in the expected value for each hit.
Every enemy has an innate defense stat, which is then modified by the DEF up buffs and DEF down debuffs.
Enemy DEF = Innate DEF × Total DEF mods Total DEF mods = 1 + DEF up mods - DEF down mods - Unique DEF down mods
Innate DEF has a nominal value of 10, with high defense enemies using higher values and low defense enemies using lower values.
DEF up mods are all the DEF up effects present on the enemy. Damage Cuts and Repel effects are not taken into account.
DEF down mods encompass all the DEF down or [Element] DEF down debuffs present on the enemy.
Note that the total value of DEF up and DEF down mods is hard capped at 50%.
Unique DEF down mods are DEF down effects that are not affected by the hard DEF down cap. These include for instance Feower's 
and Gabriel (Summon)'s 
Local status effect (10% each, but don't stack).
Sleeping boost is associated to the 
Takes 10% more damage
Local status effect, 
Takes 25% more damage and
(Chance to end upon taking DMG)
Takes 50% more damage
Local status effect status effects applied to the enemy. The boost depends on the status:
Takes 10% more damage
Local status effect = 10%,
Takes 25% more damage = 25%,
(Chance to end upon taking DMG)
Takes 50% more damage
Local status effect = 50%.
Critical Damage
Critical attacks have a chance to replace Normal attacks when using an element-superior team (or under certain field effects). They are described by a chance and a multiplier, usually labeled X% chance to deal Y% supplemental damage.
Critical Damage = Normal Damage × (1 + Critical mods)
Critical mods is the sum of every multiplier linked to the critical skills that have successfully triggered for this damage instance (since critical damage only has a fixed chance to happen for each critical skill).
Bonus Damage
Bonus Damage = Normal Damage without Supplemental × Bonus multiplier
Bonus Damage, colloquially referred to as "echo", originates from certain skills, charge attacks, summons or weapons. It is another instance of damage present alongside the normal attacks. Each echo is computed independently.
Bonus multiplier is the X% Bonus Damage description of the echo-providing skills.
Counterattack damage
Counterattack Damage = Normal Damage × (1 + Counter multiplier)
Counter multiplier is the percentage value present on the Counter skill description.
Charge Attack damage
Charge Attack damage = ( Normal Damage × CA modifier × Weapon CA DMG boost x Buff CA DMG boost ) + Fixed CA damage
Weapon CA DMG boost = 1 + CA DMG from Weapon Grid Buff CA DMG boost = 1 + CA DMG Up from all other sources
Charge Attack modifier is a percentage value associated with the "strength" of the Charge Attack (medium, big, massive, unworldly). The most common modifier for SSR Characters is 450% for Massive Charge Attacks and 1,250% for Unwordly Charge Attacks.[1].
Weapon CA DMG is the sum of all weapon skills that provide . Check Weapon Skills for which weapons skills provide this.
Buff CA DMG Up is the sum of all Boost to Charge Attack Damage effects that are not from weapon skills. This includes EMPs, visible buffs granted by summon calls or skills, and character support skill effects.
Fixed CA damage is a value added to charge attack damage after all multiplicative mods are applied to ensure that Charge Attacks deal a minimum amount of damage. This value is very low, typically 2,000 for characters and between 2,000-4,000 for weapons when used a main weapon. It is affected by critical hit multipliers and damage amplification multipliers as those are applied later in the formula.
Chain Burst damage
Burst damage = Total party Charge Attack damage × Burst constant × Elem superiority × Burst boost
Burst constant depends on the number of Charge Attacks involved in the Chain Burst: 25% for 2 CA, 33.3% for 3 CA, 50% for 4 CA and more.
Element superiority is the same modifier as in the Elemental boost: +50%, -25% or 0%.
Burst boost is the sum of all stacking Boost to Chain burst DMG effects from skills, weapons or summons.
Skill Damage
Skill Damage = Normal Damage [or Critical Damage] × (Specific skill's damage modifier + Total boost to skill damage mod)
Skill Damage Cap Mod = 1 + General damage cap + Skill damage cap
Soft cap(Skill Damage) =
Skill Damage from 0 up to (Skill Damage limit 1 × SDCM) × 100 %
+ Skill Damage from limit 1 up to (Skill Damage limit 2 × SDCM) × Skill Damage limit 1 deduction %
+ Skill Damage from limit 2 up to (Skill Damage limit 3 × SDCM) × Skill Damage limit 2 deduction %
+ Skill Damage from limit 3 up to (Skill Damage limit 4 × SDCM) × Skill Damage limit 3 deduction %
+ Skill Damage from limit 4 to infinity × Skill Damage limit 4 deduction %
The values for skill damage cap thresholds and skill damage cap deduction percentages depend on the specific skill.[2] The value displayed on the wiki is not the Skill Damage limit 4 threshold, but is the resulting value after which it can be deduced that damage is being added at the final deduction %. Not all skill limits and deduction rates are recorded.
Skill Damage examples[2]
examples with confirmed numbers:
assumed Skill Damage = 1million, no skill cap buffs
Charlotte's Sword of Lumiel
= from 0 up to 500k * 100%
+= from 500k to 600k * 60%
+= from 600k to 700k * 40%
+= from 700k to 1mil * 5%
+= from 1million onwards * 1%.
=> 500k + 60k + 40k + 15k + 0 = 615k
(this is the value displayed on the wiki page next to the skill as damage cap)
assumed Skill Damage = 1million, no skill cap buffs
Vaseraga's Instinction
= from 0 up to 700k * 100%
+= from 700k to 800k * 70%
+= from 800k to 900k * 25%
+= from 900k to 1million * 5%
+= from 1million onwards * 1%
=> 700k + 70k + 25k + 5k + 0 = 800k
(this is the value displayed on the wiki page next to the skill as damage cap)
Vaseraga's Instinction with Aubade Grynoth buff (all skill damage limits x2, Skill Damage 500% up meaning Instinctions' 800% mod becomes 1300%, or an increase of 62.5%. This means the same 1million skill dmg becomes 1.625million skill dmg)
= from 0 up to 1.4million * 100%
+= from 1.4million to 1.6million * 70%
+= from 1.6million to 1.8million * 25%
+= from 1.8million to 2million * 5%
+= from 2million onwards * 1%
=> 1.4mil + 140k + 6250 + 0 + 0 = 1.546.250
The way Seraphic boost and Supplemental Damage is applied differs between Normal attacks and other damage types.
DMG taken amplified debuffs are a type of supplemental damage based on damage done, unlike most supplemental damage which is based upon an enemy's max health, or a flat amount.
This can make it seem like DMG Taken boosted debuffs work like another type of 'Seraphic Boost' that multiplies with Seraphic Boost, but that's not strictly true.
The difference is visible here:
Final Skill Damage = [Soft Cap(Skill Damage) + (Soft Cap(Skill Damage) * Sum of stackable DMG Taken Amplified Mods) + Supplemental Damage ] × (1 + Seraphic Modifier) (up to the hard cap) Final Normal Attack Damage = Soft Cap(Normal/Critical Damage) × (1 + Seraphic Modifier) (up to the hard cap) + [(Soft Cap(Normal/Critical Damage) * (1 + Seraphic Modifier)) * (sum of stackable DMG Taken Amplified Mods)] + Supplemental Damage
DMG Taken Amplified does not amplify other supplemental damage at all, unlike Seraphic Boost which does when it's Skill Damage. It is also is able to break the hard cap in Normal Attacks, unlike Seraphic Boost.
Sources for "DMG Taken Amplified" which are not raid specific like Defied and Fated Chain[4] can be found here
Resources
Further reading:
- Weapon / Summon Optimization and Progression (ProBoards)
- Damage Calculations Explained (reddit)
References
- ↑ Kamigame, list of CA modifiers. https://kamigame.jp/グラブル/ゲーム知識/奥義倍率.html
- ↑ 2.0 2.1 https://docs.google.com/spreadsheets/d/1SUhqwiq3UC7ba7jh22s0mhHJ_33Zi443aRywe-CmURQ/edit?gid=1119495962#gid=1119495962
- ↑ source for open wide (damage taken amplified only applying after hard cap on normal attacks and being applied before on skill damage): https://x.com/Tamo_GBF/status/1873615091641590032
- ↑ 4.0 4.1 source for confirmed dmg taken amplifiers https://x.com/Lysts_Sin/status/1829832116059980074