At its core, Emerald uses a fixed formula then layers modifiers for weather, items, abilities, type, and more. Because rounding down happens many times, order matters.

The core formula

For a successful hit that is not a fixed-damage move, base damage is:

Damage = floor( floor( floor( ((2 × Level) / 5) + 2 ) × Power × A / D / 50 ) + 2 )

• Level is the attacker’s level.
• Power is the move’s listed power after any power changes that apply before damage (for example, SolarBeam in rain or sand).
• A is the relevant attacking stat and D is the relevant defending stat. In Generation III, the move’s category depends on its type, not the move itself:
  • Physical types: Normal, Fighting, Flying, Ground, Rock, Bug, Ghost, Poison, Steel
  • Special types: Water, Fire, Grass, Electric, Ice, Psychic, Dragon, Dark

After base damage is found, the game multiplies by a combined Modifier and rounds down again.

The modifier stack (in order used in Emerald)

1. Targets

• If the move hits multiple targets in a double battle, multiply by 0.5.

2. Weather

• Rain: Water moves ×1.5, Fire moves ×0.5.
• Sun: Fire moves ×1.5, Water moves ×0.5.
• Sand: SolarBeam power halves, and some recovery moves are reduced; no global damage boost.
• Hail: no boost to Ice moves in Gen III, but chip damage applies separately to most non-Ice Pokémon.

3. Critical

• Critical hits multiply damage by 2.
• They ignore negative Attack or Sp. Atk stages on the attacker and ignore positive Defense or Sp. Def stages on the defender. They also ignore Reflect or Light Screen.

4. Random factor

• Multiply by a random value uniformly chosen between 0.85 and 1.00.

5. STAB

• Same-type attack bonus is ×1.5 if the user’s type matches the move.

6. Type effectiveness

• Multiply by 0, 0.25, 0.5, 1, 2, or 4 depending on the defender’s types.

7. Burn

• If the attacker is burned, physical damage is halved unless the attacker has Guts.

8. Other field, item, and ability modifiers

• Reflect or Light Screen: halve physical or special damage respectively.
• Choice Band: ×1.5 to the user’s Attack (applies to A before the main fraction).
• Type-boosting items like Charcoal, Mystic Water, etc.: ×1.1 to damage of that type.
• Huge Power or Pure Power: double Attack (affects A).
• Blaze, Overgrow, Torrent, Swarm at low HP: ×1.5 to matching move types.
• Flash Fire (after activation): ×1.5 to Fire moves.
• Thick Club on Cubone/Marowak or Light Ball on Pikachu: double the listed stat as noted.
• Helping Hand: ×1.5 to the ally’s move that turn.
• Charge: ×2 to the user’s next Electric move.

Finally, after multiplying all applicable modifiers, the result is floored. If the target is not immune, minimum damage is 1.

Important Gen III specifics

• Weather from Drizzle and Sand Stream is indefinite until replaced.
• Rock types do not gain a Special Defense boost in sandstorm in Gen III.
• Category is tied to type, so every Water move is special and every Fighting move is physical.
• Natures and EVs alter stats before battle, which then feed into A and D.
• Accuracy and evasion are checked before damage; if a move misses, the damage formula is not used.

Worked example

Level 50 Swampert uses Surf (Power 95) in rain on a neutral target, no items, no crit, single target.

1. Base damage from the core formula using Swampert’s Sp. Atk as A and the foe’s Sp. Def as D.
2. Targets: ×1 (single target).
3. Weather: ×1.5 (rain boosts Water).
4. Critical: ×1.
5. Random: ×0.85 to ×1.00.
6. STAB: ×1.5 (Water user with a Water move).
7. Type: ×1 (neutral).
8. Other: none.

Net multiplicative modifier range = 1.5 × 1.5 × [0.85..1.00] = [1.9125..2.25] applied to the base damage, then floored.

Bottom line

Emerald computes base damage from level, power, and the appropriate attacking and defending stats, then applies a precise sequence of modifiers with frequent rounding down. Because order and flooring matter, small differences in items, weather, or abilities can swing outcomes dramatically.