What is the formula for damage considering attacks and defenses?

Question

I understand the effects of held items, STAB etc.
But how do you calculate the damage done to the opposing pokemon using your pokemon's attack and the opponent's defense and HP?

Answer 1

I'm just going to quote a brilliant answer given by Pokemaster himself.

The actual damage done is a product
of the attack's base power, pokemon's
attack stat, its level, modifiers
(like super-effective) plus a little
random variation.

Apparently this is the exact formula.
I've broken it down into a few chunks
to make it easier:

DAMAGE = ( USER_ATTACK ÷ OPP_DEFENSE +
2 ) × MODIFIERS

where: USER_ATTACK = (2×USER_LEVEL +
10) × USER_ATTACK_STAT × BASE_POWER
OPP_DEFENSE = 250 × OPP_DEFENSE_STAT
MODIFIERS = SUPER_EFFECTIVE × STAB ×
RANDOM

variables: USER_LEVEL is the user's
current level USER_ATTACK_STAT is the
user's Attack (or Special Attack) stat
BASE_POWER is the power of the move,
given in the movedex OPP_DEFENSE_STAT
is your opponent's Defense (or Special
Defense) stat SUPER_EFFECTIVE is 2 for
single type advantage, etc like our
type chart STAB aka Same Type Attack
Bonus is 1.5 if you used a move type
same as your pokemon (e.g. Blastoise
using Surf) RANDOM is just a little
random variation which makes it more
interesting ;)

That's the formula for damage.