Summon with the Summoner's !Summon command, or !Call if you're feeling lucky. Summon magic can NOT be reflected.

 

For brevity's sake, on this page I'm shortening magic defense to MDef, evade rate to evade, magic evade rate to MEvd, and magic power to magic.

The basic damage formula for pretty much everything is Damage = (A - D) * M. It's what goes into A, D, and M that makes things interesting.

Since M acts as a damage multiplier, anything that modifies M modifies final damage. Modifiers to A and D have more complicated effects on final damage because A and D are compared to each other on the way to computing final damage. Note that most calculations are truncated (rounded down).

If a summon does not automatically hit, then it has a (hit rate)% chance per target to succeed. Each target then has an additional MEvd% chance to avoid it even if a success is determined.

 

Summon Creatures
　チョコボ　　 ChocoboMP: 4

Optional. Chobobo is one of the few summons that is bought (for 300 gil) rather than won.
チョコボキック　　Chocobo Kick

Physical damage to one enemy.

A = Random(30, 33), D = defense, M = (level * magic)/256 + 4.

Hit rate = 100%. However, for this effect, use physical evade% for dodging rather than MEvd%.
デブチョコボ　　　Fatso Chocobo

Physical damage to all enemies. Always hits. 8% chance of occurring instead of Chocobo Kick.

A = Random(75, 84), D = defense, M = (level * magic)/256 + 4.
　シルフ　　　 SylphMP: 8

Optional. Sylph is one of the few summons that is bought (for 350 gil) rather than won.
かぜのささやき　　Wind's Murmur

Damages one enemy, slightly healing the party based on the damage it does. Always hits, except that the Aegis Shield can block it.

A = Random(30, 33), D = MDef, M = (level * magic)/256 + 4. Heals each party member by damage/4 unless 'petrified' or 'incapacitated'.

Despite being a draining attack of sorts, Wind's Murmur works normally against Undead targets. The recovery also works normally on the Undead, unlike most healing, so feel free to use it when someone's wearing Bonemail.
　レモラ　　　 RemoraMP: 2

Optional. Remora is one of the few summons that is bought (for 250 gil) rather than won.
まとわりつき　　　Latch On

Sets 'paralysis' status on one enemy. No damage.

Hit rate = (100 + user's level - target's level)%.
　シヴァ　　　 ShivaMP: 10

Optional. Beat Shiva (and three henchmen) in the Worus Castle Water Supply Tower for the summon.
ダイアモンドダストDiamond Dust

Ice damage to all enemies. Always hits, except that the Aegis Shield can block it.

A = Random(38, 42), D = MDef, M = (level * magic)/256 + 4
　ラムウ　　　 RamuhMP: 12

Optional. Beat Ramuh in the forest east of Istory Village for an item to learn the summon.
さばきのいかづち　Thunder of Judgment

Thunder damage to all enemies. Always hits, except that the Aegis Shield can block it.

A = Random(53, 59), D = MDef, M = (level * magic)/256 + 4
　イフリート　 IfritMP: 11

Required. Beat Ifrit under the Ancient Library for the summon.
じごくのかえん　　Flames of Hell

Flame damage to all enemies. Always hits, except that the Aegis Shield can block it.

A = Random(45, 50), D = MDef, M = (level * magic)/256 + 4
　タイタン　　 TitanMP: 25

Required. Beat Titan in the Karnak Meteorite for the summon.
だいちのいかり　　Wrath of the Earth

Earth damage to all enemies. Misses any target with 'levitate' (usually flying monsters), but always hits otherwise.

A = Random(110, 123), D = MDef, M = (level * magic)/256 + 4
　ゴーレム　　 GolemMP: 18

Optional. Rescue Golem from his attackers in the Wyvern Valley for an item to learn the summon.
アースウォール　　Earth Wall

Protects the party from physical damage until exhausted. Does nothing if cast when already in effect.

Blocks the next (caster's level + 20) * 50 physical damage against the party.
　カトブレパス CatoblepasMP: 33

Optional. Beat Catoblepas in {the northwest island} in World 2 for an item to learn the summon.
あくまのひとみ　　Demon's Eye

Sets 'petrified' status on one enemy, effectively killing it. No damage.

Hit rate = (99 + user's level - target's level)%.
　カーバンクル CarbuncleMP: 45

Optional. Beat Carbuncle in {Castle Exdeath} for the summon.
ルビーのひかり　　Ruby Light

Sets 'reflect' status on all allies. Always hits.
　シルドラ　　 SyldraMP: 32

Optional. Visit the Pirate Hideout with Lenna and Faris in World 3 for a scene and the summon.
サンダーストーム　Thunderstorm

Wind damage to all enemies. Always hits, except that the Aegis Shield can block it.

A = Random(165, 185), D = MDef, M = (level * magic)/256 + 4
　オーディン　 OdinMP: 48

Optional. Beat Odin within a minute in the {Bal} Castle Basement in World 3 for the summon.
ざんてつけん　　　Zantetsuken

Kills all enemies, regardless of immunities. Fails against each Heavy target, but always succeeds otherwise.

As long as at least one target is not Heavy, Odin has a (80 + user level - target level)% chance to use Zantetsuken, though I'm not sure how it determines which target level to pick. He uses Gungnir instead if all targets are Heavy or if the Zantetsuken check fails.
グングニル　　　　Gungnir

Physical damage to one random enemy. Always hits.

A = Random(255, 286), D = defense, M = (level * magic)/256 + 4.
　フェニックス PhoenixMP: 99

Optional. Clear the {Phoenix Tower} for the summon. When summoned, both of the following effects occur.
てんせいのほのお　Flames of Reincarnation

Flame damage to all enemies. Always hits, except that the Aegis Shield can block it.

A = Random(105, 118), D = MDef, M = (level * magic)/256 + 4
てんせいのほのお　Flames of Reincarnation

Removes 'incapacitated' and recovers all HP and MP for a single ally. Inflicts 'incapacitated' instead against the Undead. Always hits 'incapacitated' targets that are not Undead, and always misses live targets that are not Undead.

Always hits the Undead unless also Heavy, in which case it always fails. Ignores 'incapacitated' immunity.
　リバイアサン LeviathanMP: 39

Required(?). Beat Leviathan in {Istory Falls} for the summon.
だいかいしょう　　Great Tidal Wave

Water damage to all enemies. Always hits, except that the Aegis Shield can block it.

A = Random(195, 219), D = MDef, M = (level * magic)/256 + 4
　バハムート　 BahamutMP: 66

Optional. Beat Bahamut at the Northern Mountain after unsealing him for the summon.
メガフレア　　　　Megaflare

Magic damage to all enemies. Always hits, except that the Aegis Shield can block it.

A = Random(250, 281), D = MDef, M = (level * magic)/256 + 4

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