Damage

This article covers information on the damage that can be delivered and received during battle. The formulas vary between games.
==Overview==
===Shin Megami Tensei III: Nocturne===
====Physical Attack====
(\text{Level} + \text{Strength}) \times \text{Skill Power} \div 15
====Weapon Attack====
\text{Max HP} \times \text{Skill Power} \times 0.0114
====Magic Attack Peak====
((\text{Limit} - \text{Complement}) \div \text{Skill Power})) \times \frac{255}{24}
====Magic Attack====
If user's level is below peak:
0.004 \times (5 \times (\text{Magic} + 36) - \text{Level}) \times ((24 \times \text{Skill Power} \times (\text{Level} \div 255) + \text{Complement}))
If user's level is at peak:
0.004 \times (5 \times (\text{Magic} + 36) - \text{Peak}) \times \text{Limit}
If user's level is above peak, but below 160:
0.004 \times (5 \times (\text{Magic} + 36) - \text{Level}) \times \text{Limit}
If user's level is above 160:
0.004 \times (5 \times (\text{Magic} + 36) - 160) \times \text{Limit}
===Shin Megami Tensei V===
The variance of the damage is likely 5% (can be 5% lower and 5% higher; difference overall is 10%.)
One trait about stat increases is that, as the distance between the offensive Strength/Magic stat and Vitality grows higher, the multiplier will grow at a progressively smaller rate.
Although the user's stats influence their damage in a curved line as they increase, the base power of the attacks themselves are still straightforward and aren't complicated by the formula of the stats. For example, an attack with a base power of 40 will deal twice the damage against an attack with 20, should the rest of the circumstances match. 
The two ranks of a single type buff do not stack with one another, but rather the second rank transforms it into a slightly stronger buff instead. Different types of buffs do stack multiplicatevely. (e.g. Tarukaja & Rakunda; 1*1.4*1.4)
Pleromas, such as Phys Pleroma, boost the user's attack by x1.2. High Pleromas, such as High Phys Pleroma, instead boost it to x1.35. Both multipliers stack accumulatively against each-other, generating a result of x1.55.https://hyperwiki.jp/smt5/passive/https://game8.jp/megaten5/411987
The maximum damage that can be dealt in the game is 99,999.真・女神転生Ⅴ 最大ダメージを狙う, hyperts.net (2021-11-23)
Damage from Poison is pre-determined, causing it to deal 100 damage by default. Poison Adept doubles it, Poison Master triples it, while stacking both multiplies it by 5. The attack doesn't follow any other formulas, but it still has variance; however, this variance presumably only goes higher than the base value.
===Megami Ibunroku Persona===
====Party Regular Attack====
\frac{\text{(Weapon Attack)}^2}{4} \div (\text{Target's Defense} \times 1.5) \times \text{Target's Resistance} + \text{Random Number}
====Party Physical Skills====
(\text{Attack})^2 \div (\text{Target's Defense} \times 1.5) \times (1 + \frac{\text{Skill Power}}{100}) \times \text{Target's Resistance} + \text{Random Number}
====Gun Damage====
\frac{\text{(Gun Attack)}^2}{4} \div (\text{Target's Defense} \times 1.5) \times \text{Target's Resistance} + \text{Random Number}
====Enemy Regular Attack====
\frac{\text{(Attack)}^2 \times 2.25}{4} \div (1 + \text{Target's Defense}) \times \text{Target's Resistance} + \text{Random Number}
====Enemy Physical Skills====
\frac{\text{(Attack)}^2 \times 2.25}{4} \div \text{Target's Defense} \times (1 + \frac{\text{Skill Power}}{100}) \times \text{Target's Resistance} + \text{Random Number}
====Magic Damage====
\frac{\text{(Magic Attack)}^2 \times (\text{Skill Power} + 1)}{120} \div \text{Target's Magic Defense} \times \text{Target's Resistance} + \text{Random Number}
===Persona 5 / Royal===
====Attack Power====
=====Melee and Gun Attacks=====
If the user is inflicting a basic melee or gun attack, the related weapon and the user's Strength stat will be taken into account.
The formula multiplies the square root of half the user's weapon power and the square root of the user's Strength stat by each-other. Whether the weapon is melee or ranged ultimately depends on the type of attack that is being used. The formula is as follows:裏技・小技など, ペルソナ5総合攻略Wiki P5攻略 Wiki*攻撃ダメージ量の変化, ペルソナ5ザ･ロイヤル総合攻略Wiki P5R攻略 Wiki*
\sqrt{\frac{1}{2} \times \text{Weapon Power}} \times \sqrt{\text{Strength Stat}}
When the user's Strength stat is doubled, the modifier will be multiplied by approximately 1.4.
If the user's Strength stat is at the maximum of 99, the damage total of the attack will be nearly multiplied by x10 compared to a Strength stat of 1.
=====Skills=====
If the user is wielding a physical skill, the base power of the skill and the user's Strength/Magic stat are taken into consideration. 
Similarly to Melee and Gun attacks, the square root of the base power of the skill is multiplied by the square root of the Strength stat. This means that you can expect Heat Wave to deal a bit less damage than Paradise Lost R while using the same persona, as will -dyne skills if your persona has equal St and Ma.
The formula is as follows:
\sqrt{\text{Skill Power}} \times \sqrt{\text{Stat}}
Where the Phys/Gun skills use St as their stat, and Fire/Ice/Elec/Wind/Psi/Nuke/Bless/Curse/Almighty use Ma as their stat. Both Strength and Magic-based skills use the same formula.https://www.reddit.com/r/Persona5/comments/zcnzbe/the_wikis_damage_formula_for_magic_attacks_is/
====Defense Subtraction====
After the total power of the attack has been calculated, it is divided against the square root of the sum of the target's armor defense and their Endurance stat. The formula is as follows:
\text{Base Power} \div \sqrt{\left ( \left ( \text{Endurance} \times \text{8} \right ) + \text{Armor Defense} \right )}
If the defense and endurance stats are doubled, the damage taken will be multiplied by approximately x0.7.
====Miscellaneous Modifiers====
There are several other criteria that factor in affecting the damage output of attacks besides the user's stats, weapon and attack power. These include Critical hits, Technical attacks, the effects of certain ailments, the target's elemental resistance or weakness against the attack, Baton Pass, temporary buff and debuff skills, certain passive skills and traits, whether the target is guarding or not, the difficulty setting, and so on.
If an attack exploits a weakness, the attack will be unable to deal Technical damage, so the two multipliers can't stack.
One unique factor in damage calculation is that certain types of Passive buff skills, such as Fire Boost, Fire Amp and Magic Ability, and the trait Pagan Allure, although they can stack with each-other to boost damage (via multiplication), the multiplier is capped to x2. However, the limitation only applies to said passive abilities, with the exception of Tyrant's Mind and the Country Maker trait, which ignore the limit. Additionally, accessories stack in the same way and follow the same restrictions, but accessories and skills with matching effects (Ice Boost and Blue Band) cannot stack.スキル効果重複について, ペルソナ5総合攻略Wiki P5攻略 Wiki*スキル効果重複について, ペルソナ5ザ･ロイヤル総合攻略Wiki P5R攻略 Wiki* The traits Mighty Gaze, Intense Focus, Striking Weight and Undying Fury's multipliers are not applied to the cap.
One important factor would be the Level difference between the attacker and the opponent. There is no change if the attacker is 4 levels lower or 1 level higher than its target, but the attack power will gradually be multiplied over time, with 10 levels and higher being capped at x1.5. Otherwise, if the attacker is 15 levels lower or more, their power will be x0.5.
The same applies for the damage taken as well. There is no change if the target is 2 levels lower and 3 levels higher, but the defense will increase if the target's level is higher, where at 10 levels or more, the damage will be x0.5, but at 10 levels less, the damage will be multiplied to x1.5.
For the protagonist, the level calculated is his own, rather than the one of his equipped Persona.
The final calculation is randomized between numbers that are close to the default result. The variance is approximately 5% (can be 5% smaller or larger at most.)
==Trophies & Awards==
Trophy 	Icon	Description 	For 	Reward
Devastating Blow 	 	Deal 999 damage in a single blow. 	SMT3NHD trophy	
Destroyer 	 	Dealt over 1,000 damage to an enemy in a single hit. 	SH2 trophy 	
Going Nova 	 	Deal over 999 damage in 1 attack. 	P3P trophy 	
Get a Load of Those Numbers!	 	Dealt over 999 damage in a single attack (All-Out Attacks excluded).	P3R trophy 	
Going Nova 	 	Deal over 999 damage in 1 attack 	P4G trophy 	
The Ultimate Strike 	 	Deal over 999 damage in a single attack. 	P5 trophy 	
Ultimate Attack 	 	Deal over 9999 damage in battle without using an All-out Attack. 	Thieves Den 	50P
Ultimate Strike 	 	Dealt 2,000 damage in a single attack. 	P5T trophy 	
==References==
Category:Attack Properties