FF7/Battle/Damage Calculation

In Attacks, Items, and Weapons there exists a single byte that tells the Battle Engine how to calculate damage. This is a list of known values with their effects on Base Damage. They are classified into Physical, Magical, and Exact. Physical and Magical will rely on the caster's Strength and Magic stat respectively to calculate base damage. After modification it is multiplied by a random variance ([224..255]/256 or something similar). These will also trigger Physical and Magical Counter Attacks respectively. Exact is just what it sounds like. They do not have a base damage calculation. The entire damage comes from exactly the formula shown and is applied to the target without defense calculation (though element is still taken into account). These will not trigger Physical or Magical Counter Attacks, but will trigger General Counter Attacks such as Adamantoise's Light Shell.

For more details, these can be considered Base Damage Modifiers as described in Terence Fergusson's Battle Mechanics FAQ.
Akari has begun a more detailed damage formula page.

Value	Effect
0x00	No Damage Calculation
0x08	Exact target's HP & MP by (Strength / 32)%
0x11	Physical (Strength / 16)
0x22	Magical (Strength / 16)
0x23	Exact target's HP * (Strength / 32)
0x24	Exact target's MHP * (Strength / 32)
0x25	Magical +(Strength * 22)
0x26	Exact (Strength * 20)
0x29	Exact always 1 Damage(?)
0x37	Physical [Base] = (Strength * 16); Ignores Barrier
0x47	Magical [Base] = (Strength * 16); Ignores MBarrier
0x50	No Damage Calculation
0x60	Exact caster's HP
0x61	Exact caster's MHP - HP
0x68	Exact random x 100 (Dice)
0x69	Exact number of Escapes
0x6A	Exact reduces Target's HP to 1
0x6B	Exact number of minutes in game clock
0x6C	Exact 10 x Target's Kills
0x6D	Exact 1111 x Target's Materia
0x83	Exact HP * (Strength / 32) if level MOD Attack% = 0
0x96	Exact caster's HP/2 [Exact]
0xA0	Physical based on User's Status Effects*
0xA1	Physical Power up when Near-Death
0xA2	Physical (1 + Dead Allies)
0xA3	Physical (Target's Level / 16)
0xA4	Physical (1 + [48 * HP/MHP]) / 16
0xA5	Physical (1 + [48 * MP/MMP]) / 16
0xA6	Physical (1 + [AP on Weapon? / 10000]) / 16
0xA7	Physical (10 + [Character's Kills / 128]) / 16
0xA8	Physical (1 + [Limit Level * Limit Units / 16]) / 16
0xB1	Physical (Strength / 16); No random criticals

NOTE: For A0h base strength is multiplied by (1 + (Number of Status Effects User has out of the following: Near-death, Poison, Sadness, Silence, Slow, Darkness) + (2 * Number if Status Effects User has out of the following: D.Sentence, Slow-numb) )

As an exception to the above rules, 37h and 47h are used as damage calculations for items. Damage to target is calculated normally while ignoring M/Barrier.

Values 29h and 6Bh are not used in the game, but have been shown to produce those results.