Ability damage

In combat, ability damage is a number based on your skills, weapons, and armour, which is used by almost all abilities to determine how high they can hit. Ability damage has different formulas for each combat style, and is affected by prayers and damage-boosting items. It is closely related to the auto-attack damage shown in the combat interface, but it varies in notable and significant ways.

Magic
$$ d_{m} = \begin{cases} {\color{white}1.5} l_m + \min\{9.6 l_{mh},d_s\}             + b_a& \mbox{for single-wielding}\\ 1.5 l_m + \min\{9.6 l_{mh},d_s\} + 5.2 l_{oh} + 1.5b_a& \mbox{for dual-wielding}\\ 1.5 l_m + \min\{9.6 l_{mh},d_s\} + 5.2 l_{mh} + b_a& \mbox{for 2h-wielding}\\ \end{cases} $$

Where:
 * $$d_m$$ is your damage with magic abilities.
 * $$l_m$$ is your level in Magic, including boosts.
 * $$l_{mh}$$ is the required level to use the weapon in your main hand.
 * $$l_{oh}$$ is the required level to use the weapon in your off hand.
 * $$d_s$$ is the stated damage of your spell.
 * $$b_a$$ is the sum of all damage boosts from armour.

It is important to note the dual-wielding formula is not yet known for the case where a different spell is used in each hand. The stated formula does not apply in this case, indeed it seems that dual wielding your highest level spell twice causes less damage than dual wielding your highest level spell with a lower one. This is almost certainly a bug.

Melee
$$ d_{w} = \begin{cases} {\color{white}1.5} l_s + d_{mh}s_{mh}               + b_a & \mbox{for single-wielding}\\ 1.5 l_s + d_{mh}s_{mh} + d_{oh}s_{oh} + 1.5b_a& \mbox{for dual-wielding}\\ 1.5 l_s + d_{mh}s_{mh} + 1.5b_a& \mbox{for 2h-wielding}\\ \end{cases} $$

Where:
 * $$d_w$$ is your damage with warrior abilities
 * $$l_s$$ is your level in Strength, including boosts.
 * $$d_{mh}$$ and $$d_{oh}$$ are the stated damage from your main and off hand weapons, respectively.
 * $$s_{mh}$$ and $$s_{oh}$$ are multipliers based on the speed of your main and off hand weapons:
 * For Average weapons, this is 0.65.
 * For Fast weapons, this is 0.7875.
 * For Fastest weapons, this is 1.
 * $$b_a$$ is the sum of all damage boosts from armour.

Ranged
$$ d_{r} = \begin{cases} {\color{white}1.5} l_r + \min\{9.6 l_{mh},d_a\}             + b_a & \mbox{for single-wielding}\\ 1.5 l_r + \min\{9.6 l_{mh},d_a\} + 4.8 l_{oh} + 1.5b_a & \mbox{for dual-wielding}\\ 1.5 l_r + \min\{9.6 l_{mh},d_a\} + 4.8 l_{oh} + 1.5b_a& \mbox{for 2h-wielding}\\ \end{cases} $$

Where:
 * $$d_r$$ is your damage with ranged abilities.
 * $$l_r$$ is your level in Ranged, including boosts.
 * $$l_{mh}$$ is the required level to use the weapon in your main hand (or two-handed).
 * $$l_{oh}$$ is the required level to use the weapon in your off hand (or two-handed).
 * $$d_a$$ is the stated damage of your ammo.
 * $$b_a$$ is the sum of all damage boosts from armour.

Prayer
Prayers increase your ability damage by a set percentage, which can be found on the Prayer page. Prayers do not affect the damage of bleed abilities.

Potions
The effect of potions is twofold: for one, it increases your visible Magic, Strength and Ranged levels, so that small amount is added to your ability damage at the beginning. In addition, each boosted level provides 8 extra damage. However, this occurs after any other multipliers including ability, critical hit and prayer multipliers, so it essentially just adds  to your damage. This extra damage has no effect on bleed abilities.

Other boosts
There are many miscellaneous items and situations that can boost your ability damage. All of them work on bleeds except for void armour and the slayer helmet and equivalents.
 * Void armour increases ability damage by 5% when used with the correct class.
 * Black mask, Focus sight, Hexcrest, Full slayer helmet and Slayer helmet boost your ability damage by 12.5% when on a Slayer task.
 * Ferocious ring boosts ability damage by 4% when on a task in Kuradal's Dungeon.
 * Balmung boosts ability damage by 45% against Dagannoths.
 * Bane ammunition increases ability damage by 18.75% against appropriate monsters.
 * TokKul-Zo increases ability damage by 10% against TzHaar creatures.
 * Keris increases damage by 33% against Kalphites, and occasionally increases it by 200%.
 * Brine sabre and Brackish blade increase damage by 40% against 'rum'-pumped crabs.
 * Silverlight and Darklight double ability damage against demons.
 * Using the portal to the King Black Dragon in the Lava Maze increases ability damage by 10%.

Abilities
Abilities use the ability damage number to determine their max hit. In general, the damage is multiplied by a particular number that is stated on the interface (for example, Assault's maximum hit is .) As mentioned earlier, the potion boost is then added to this. A non-critical hit (with the exception of bleeds and Unload/Frenzy) will hit between 33% and 100% of its maximum damage. Critical hits will hit between 100% and 105% damage.