Maximum melee hit

Maximum melee hit is the maximum damage a player can deal in a melee combat. It is affected by player's strength, equipment and other bonuses such as prayer, passive effects or potions.

Step one: Calculate the effective strength
$$Effective\ Strength=floor((Strength\ Level+PotionBonus)\times Prayer\ Bonus\times Other\ Bonus)+Style\ Bonus$$See the following table for the various bonuses values:

Remember that if you use the Dragon battleaxe special attack you cannot use another special attack right after unless you use restoration pool in POH or if another player casts Energy Transfer upon you. Also note that the dragon battleaxe special attack raises your strength depending on the other levels.

Step two: Calculate the base damage
$$Base\ Damage=1.3+\frac{Effective\ Strength}{10}+\frac{Strength\ Bonus}{80}+\frac{Effective\ Strength\times Strength\ Bonus}{640}$$If you are not using a special attack or effect:

$$Max\ Hit=floor(Base\ Damage)$$

Otherwise, continue to step three.

Step three: Calculate the bonus damage
$$Max\ Hit=floor(Base\ Damage\times Special\ Bonus)$$The following special attack/effect bonuses apply:

The Keris's maximum hits (against kalphites or scarabites) is as follows:
 * Special cases

$$Max\ Hit_{Keris,\ normal}=floor(Base\ Damage\times 1.25)$$ $$Max\ Hit_{Keris,\ critical}=floor(Base\ Damage)\times 3$$

This results in the maximum possible hit (outside of certain parts of quests) of 126 - using Keris, a player with 99 strength can hit up to 126 on assigned Kalphites, using the best strength equipment, the Piety prayer, a black mask, and drinking a super strength potion.

The Saradomin sword's special attack hit up to an extra 15 magic-based damage:

$$Max\ Hit_{Saradomin\ sword}=floor(Base\ Damage)+15$$

During quests/minigames
In the Dungeon of Tolna during A Soul's Bane quest, players could hit up to 200 on monsters in the rage room, however that damage is simply a player's normal damage times twenty, and doesn't give any experience.

In the Barbarian Assault minigame you can hit a possible of your max hit +5 if your attacker level is 5 on the penance rangers and fighters.