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Note that having only a bow or an arrow, but not both equipped will be a weapon with only 1 attack power.

Critical hits are one of the most common attack modifiers. When a character lands a critical hit, they get a bonus to their attack power depending on the character and type of weapon equipped. Critical hits are indicated visually by a screen flash, except for Jump, which gives no such indication. Note that this screen flash can be disabled in FE.

Crit rates

Doubled if one weapon equipped, tripled if bow and arrow.
Note that in vanilla, certain cutscenes disable crits, this is not present in FE (except in the Ordeals Mirror Room when Chero is enabled). However, starting a battle with a character dead will remove their ability to crit for the rest of the game.
As well, there is a weapon property that was thought to cause no crits, however, this is just a rumor, Weapons do not remove your ability to crit in vanilla or FE.

Crit bonus table
Each character gets a set bonus to their attack power on a crit, as well as a bonus depending on their equipment, summarized in the table below.

This is the final modification to the damage formula, before defense is subtracted.
Ex. Rosa with bows and charm arrows has a 6% chance to crit, which will increase base damage by 60 (base)+ 40 (arrow), or 100 extra damage per hit.

An attack can only hit 1 elemental weakness, and 1 race weakness. However, the two can be combined, such a using an ElvenBow with Ice Arrows against Rubicant in the Elements fight (a Mage with a strong weakness to Ice), resulting in a 16x damage multiplier.
Physicals hit weaknesses then resistances, spells hit resistances/absorbs, then weaknesses. IE rubi is weak and absorbs ice, weapons deal extra damage, spells get absorbed.

While attack damage is generally described as being Attack Power multiplied by a random number between 1 and 1.5, it is actually calculated as follows:

1. Divide the Attack Power by 2. If the result is greater than 255, set it to 255
2. Get a random number between 0 and this value
3. Add that number to the original (full) Attack Power

Because of this, the highest possible final result will be the original Attack Power + 255.

Note that this only comes into play when Attack Power is above 510 (255*2). In vanilla FF4, this may be most noticeable with Zeromus' Meteo, which can only deal between 800 and 1055 damage, instead of capping at the expected 1200. In the randomizer, it is most relevant with Kainazzo's Wave in certain boss locations with high HP.

NOTE: This random value applies to most forms of both physical and magical damage. It is applied after any bonuses from Berserk, Jump, etc. and bonuses due to a target having Mini or Toad status, but before any elemental and racial damage bonuses, before the target's defense is applied, and before the number of hits is applied.