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This article covers information on the damage (ダメージ*)? that can be delivered and received during battle. The formulas vary between games.

## Overview

### Shin Megami Tensei III: Nocturne

#### Physical Attack

${\displaystyle (\text{Level} + \text{Strength}) \times \text{Skill Power} \div 15}$

#### Weapon Attack

${\displaystyle \text{Max HP} \times \text{Skill Power} \times 0.0114}$

#### Magic Attack Peak

${\displaystyle ((\text{Limit} - \text{Complement}) \div \text{Skill Power})) \times \frac{255}{24}}$

#### Magic Attack

If user's level is below peak:

${\displaystyle 0.004 \times (5 \times (\text{Magic} + 36) - \text{Level}) \times ((24 \times \text{Skill Power} \times (\text{Level} \div 255) + \text{Complement}))}$

If user's level is at peak:

${\displaystyle 0.004 \times (5 \times (\text{Magic} + 36) - \text{Peak}) \times \text{Limit}}$

If user's level is above peak, but below 160:

${\displaystyle 0.004 \times (5 \times (\text{Magic} + 36) - \text{Level}) \times \text{Limit}}$

If user's level is above 160:

${\displaystyle 0.004 \times (5 \times (\text{Magic} + 36) - 160) \times \text{Limit}}$

### 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.[1][2]

The maximum damage that can be dealt in the game is 99,999.[3]

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

${\displaystyle \frac{\text{(Weapon Attack)}^2}{4} \div (\text{Target's Defense} \times 1.5) \times \text{Target's Resistance} + \text{Random Number}}$

#### Party Physical Skills

${\displaystyle (\text{Attack})^2 \div (\text{Target's Defense} \times 1.5) \times (1 + \frac{\text{Skill Power}}{100}) \times \text{Target's Resistance} + \text{Random Number}}$

#### Gun Damage

${\displaystyle \frac{\text{(Gun Attack)}^2}{4} \div (\text{Target's Defense} \times 1.5) \times \text{Target's Resistance} + \text{Random Number}}$

#### Enemy Regular Attack

${\displaystyle \frac{\text{(Attack)}^2 \times 2.25}{4} \div (1 + \text{Target's Defense}) \times \text{Target's Resistance} + \text{Random Number}}$

#### Enemy Physical Skills

${\displaystyle \frac{\text{(Attack)}^2 \times 2.25}{4} \div \text{Target's Defense} \times (1 + \frac{\text{Skill Power}}{100}) \times \text{Target's Resistance} + \text{Random Number}}$

#### Magic Damage

${\displaystyle \frac{\text{(Magic Attack)}^2 \times (\text{Skill Power} + 1)}{120} \div \text{Target's Magic Defense} \times \text{Target's Resistance} + \text{Random Number}}$

### 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:[4][5]

${\displaystyle \sqrt{\frac{1}{2} \times \text{Weapon Power}} \times \sqrt{\text{Strength Stat}}}$

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:

${\displaystyle \sqrt{\text{Skill Power}} \times \sqrt{\text{Stat}}}$

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.[6]

#### 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:[4][5]

${\displaystyle \text{Base Power} \div \sqrt{\left ( \left ( \text{Endurance} \times \text{8} \right ) + \text{Armor Defense} \right )}}$

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.[7][8] The traits Mighty Gaze, Intense Focus, Striking Weight and Undying Fury's multipliers are not applied to the cap.[citation needed]

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.[4][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.[4][5]

For the protagonist, the level calculated is his own, rather than the one of his equipped Persona.[4][5]

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.)[4][5]

## Trophies & Awards

Trophy Icon Description For Reward
Devastating Blow Deal 999 damage in a single blow. SMT3NHD trophy
Omnipotent Strike Dealt over 9999 damage in a single blow. SMT5V 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

1. https://hyperwiki.jp/smt5/passive/
2. https://game8.jp/megaten5/411987
3. 真・女神転生Ⅴ 最大ダメージを狙う, hyperts.net (2021-11-23)
4. 裏技・小技など, ペルソナ5総合攻略Wiki P5攻略 Wiki*
5. 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*
7. 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*
8. 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*

General
Dungeon - Combat - Turn - Action - Level - Experience - Party - Stats - Skills - Items - Equipment - Melee Attack - Ranged Attack - Damage (Fixed) - Guard - Escape - Accuracy - Critical - Multi-hit - Insta-Kill - Ailments - Drops - Encounter - Random Encounters - Symbol Encounters - Ambush - Difficulty
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Shin Megami Tensei series
Terminal - Guardian (if...) - Tactical Battle (NINE) - Capacity (NINE) - RTS (NINE) - Reinforcements (NINE) - Race Shift (NINE) - Modules (NINE) - Magatama (3) - Reason (3) - Demon Co-Op (SJ) - EX Missions (SJ) - Challenge Quest (4) - Skill Potential (4/A-5) - Smirk (4) - Barrier (4) - Partners (4A) - Jade Dagger (4A) - Magatsuhi Skills (5) - Essence (5) - Glory (5) - Miracles (5) - Demon Statues (5) - Abscess (5)
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Persona series
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Devil Children series
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Digital Devil Saga series
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Characters
Playable Protagonist - Morgana - Ryuji Sakamoto - Ann Takamaki - Yusuke Kitagawa - Makoto Niijima - Futaba Sakura - Haru Okumura - Goro Akechi - Sumire Yoshizawa
Confidant Igor - Sojiro Sakura - Chihaya Mifune - Munehisa Iwai - Tae Takemi - Sadayo Kawakami - Ichiko Ohya - Shinya Oda - Hifumi Togo - Yuuki Mishima - Toranosuke Yoshida - Caroline & Justine - Sae Niijima - Takuto Maruki
Major Targets Suguru Kamoshida - Ichiryusai Madarame - Junya Kaneshiro - Shadow Futaba - Kunikazu Okumura - Masayoshi Shido - Holy Grail / Yaldabaoth - Azathoth / Adam Kadmon
Other Principal Kobayakawa - SIU Director - Shiho Suzui - Natsuhiko Nakanohara - Mika - Lala Escargot - Angel and Julian - Medjed - Wakaba Isshiki - Sugimura - President Tanaka - Kazuya Makigami - Naoya Makigami - Shadow Mishima - Shinichi Yoshizawa - Rumi - Shibusawa - Jose - Kasumi Yoshizawa - Coach Hiraguchi
Locations
Tokyo Yongen-Jaya (Café Leblanc) - Shibuya - Aoyama-Itchome (Shujin Academy) - Shinjuku - Akihabara - Kichijoji - Ogikubo - Inokashira Park - Tsukishima - Akasaka Mitsuke - Suidobashi - Odaiba Seaside Park - Ichigaya - Ikebukuro - Ginza - Harajuku - Meiji Shrine - Jinbocho - Miura Beach - Maihama (Tokyo Destinyland) - Kanda - Roppongi - Ueno - Asakusa - Chinatown - Nagatacho - Shinagawa - Nakano - Kosei High School
Metaverse Kamoshida's Palace - Madarame's Palace - Kaneshiro's Palace - Futaba's Palace - Okumura's Palace - Niijima's Palace - Shido's Palace - Mementos (Path of Qimranut - Path of Aiyatsbus - Path of Chemdah - Path of Kaitul - Path of Akzeriyyuth - Path of Adyeshach - Path of Sheriruth - Depths of Mementos - Qliphoth World - Path of Da'at) - Maruki's Palace
Other Velvet Room - Hawaii - Thieves Den
Music
Albums Original Soundtrack (Persona 5 / Royal (JP / EN))
Songs "Wake Up, Get Up, Get Out There" - "Life Will Change" - "Beneath the Mask" - "Last Surprise" - "Rivers in the Desert" - "The Whims of Fate" - "Tokyo Daylight" - "Hoshi To Bokura To" - "Break In To Break Out" - "Infinity" - "Dark Sun..." - "Autonomy" - "Found a Light" - "IT'S TOO LATE" - "Colors Flying High" - "Take Over" - "He's a Trickster☆" - "I Believe" - "No More What Ifs" - "Throw Away Your Mask" - "Bokura no Hikari (Our Light)"
Archives
Story Persona - Persona user - Shadow - Shadow Self - Second Awakening - Picaro Persona - I am thou - Cognition - P. A. D. - Metaverse - Metaverse Navigator - Mask - Wild Card - Phantom Thieves of Hearts - Phantom Aficionado Website - Antisocial Force - Treasure - Police - Calling Card - Change of Heart - Psychotic breakdown - Mental shutdown - General Public - Seven Deadly Sins - Sea of Souls - Bond - Featherman
School Life Calendar - Weather - Seasons
Confidant - Social Stats - Hideout - Class - Train - Invitations - Gifts - Decorations
Activities Bathhouse - Studying - Diner - Cleaning - Maid Café - Billiards - Books - DVDs - Retro Games - Movie Theater - Big Bang Challenge - Crane Game - Bed - Batting Cages - Fishing Pond - Crossword Puzzles - Darts - Infiltration Tools - Cooking - Training - Old Temple - Laundry - Part-time Jobs - Shrine - Confessional - Jazz Jin - Houseplant - Refrigerator - TV Quiz Show - Blackboard - Drink Stand - Lottery - Cultivation - Fortune Telling
Vendors Shops: (Persona 5 / Royal) - Vending Machines - Takemi Medical Clinic - Untouchable - Jose's Shop - Home Shopping Program - Tanaka's Shady Commodities - Military Vending Machine - Trading
Phantom Life Mementos Requests - Third Eye - Security Level - Search Objects - Treasure Chests - Safe Room - Thieves Guild - List of Shadows (Treasure Demon - Disaster Shadow - Savage Shadow) - List of Bosses - Skill Card - Will Seeds - Deviations - Slot Machines
Battle Items: (Persona 5 / Royal) - Skills: (Persona 5 / Royal) - Difficulty - Status Changes - Weaknesses - Traits - Navigator - Tactics - Guard - Party Switch - Baton Pass - One More - Critical - Technical - Showtime - Cut-in - All-out Attack - Hold Up - Personality - Drops - Game Over
Follow Up - Harisen Recovery - Endure - Protect - Pickpocket - Crocodile Tears - Sexy Technique - Down Shot - Bullet Hail - Oda Special - Kakoi Kuzushi - Sleuthing Instinct - Detox X - Mindfulness - Flow - Tumbling
Velvet Room List of Personas: (Persona 5 / Royal) - Fusion - Special Fusion - Hanging - Lockdown - Electric Chair - Arcana - Skill Inheritance - Fusion Accident - Fusion alarm - Challenge Battle
System Trophies: (Persona 5 / Royal) - Cutscenes - New Game Plus - Patches and Updates - Steam Profile Items
Unused Content: (Persona 5 / Royal)
Development
Corporate Atlus Co., Ltd. - Sega
Personnel Katsura Hashino - Shigenori Soejima - Shoji Meguro - Lyn Inaizumi - Atsushi Kitajoh - Ryota Kozuka - Kenichi Tsuchiya - Toshiki Konishi - Kazuhisa Wada - Lotus Juice
Other Media
Games Royal - Dancing in Starlight - Strikers - Tactica - The Phantom X
Productions Persona 5 The Animation The Day Breakers - Persona 5 The Animation (Episodes - Dark Sun... - Stars and Ours - Proof of Justice - A Magical Valentine's Day) - Persona O.A. - Persona 5 The Night Breakers - Persona Stalker Club V - PERSORA AWARDS 3 - Persora -The Golden Best 5- - Persona 20th Anniversary All Time Best Album - Persona 5 The Stage - Persona VS
Publications Manga - Dengeki Comic Anthology - Comic à La Carte - Comic Anthology (DNA Media Comics) - Tartarus Theater Wild - the Animation Dengeki Comic Anthology - Mementos Mission - Mementos Report - Persona Magazine
Events Night of the Phantom - Super Live 2017 - Super Live 2019 - TGS 2021 - 25th Anniversary Symphonic Concert
20th Anniversary Festival - 25th Anniversary - 25th FES
TGS 2015 - Take Tokyo Tower - E3 2016 - Take the Treasure - TGS 2016 - Morgana's Report - DJ Morgana
Miscellaneous Merchandise - Catherine: Full Body - Super Smash Bros. Ultimate