Damage per second/Ranged

See also: OSRS Wiki DPS calculator

This article is about calculating ranged damage output. Range damage is affected by the Equipment used, prayer, skill boosts and the monster being attacked.

There are various methods by which players can increase their potential Ranged damage. The effects of most equipped items can be seen in the stats window (labelled as Range: +x and Ranged strength: +x).

Calculating your ranged damage output

Step one: Calculate the effective ranged strength

${\text{Effective Ranged Strength }}={\Bigg \lfloor }{\bigg (}{\Big \lfloor }{\big (}{\text{Ranged Level}}+{\text{Boost}}{\big )}*{\text{Prayer Bonus}}{\Big \rfloor }+{\text{Atk Style}}+8{\bigg )}*{\text{Void Modifier}}{\Bigg \rfloor }$

If you are using the accurate attack style Atk Style is 3 while all other styles are 0.

Void Modifier is 1 if not wearing void, 1.1 if wearing full ranged void, or 1.125 if wearing full elite ranged void.

Ranged Level boost:

Main article: Temporary skill boost

Boost		Level increase	Visibility	Other info
	Ranging cape	1	Visible	When the ranging cape is equipped, it grants players the ammo-saving effects of Ava's accumulator.
	Wild pie	4	Visible	Hitpoints 11 per bite. Slayer 5
	Lizardkicker	4	Visible	Strength - floor(CurrentLevel * 0.04) - 2 Magic - floor(CurrentLevel * 0.04) - 2
	Spicy stew (red spice)	±0-5	Visible	Hitpoints 11 Depending on type of stew, any skill except Hitpoints can be boosted or reduced by 0 to 5 levels randomly.
File:Ranging potion.png	Ranging potion	4-13	Visible	Ranged 4 + floor(StaticLevel * 0.1)
File:Ranging mix.png	Ranging mix	4-13	Visible	Hitpoints 6 per dose. Ranged 4 + floor(StaticLevel * 0.1) Requires Barbarian training.
File:Divine ranging potion.png	Divine ranging potion	4-13	Visible	Ranged 4 + floor(StaticLevel * 0.1) Stat draining for ranged is disabled for 5 minutes, meaning the player's Ranged level will stay fully boosted. After the 5 minutes are over, Ranged level will be restored to its base level.
File:Bastion potion.png	Bastion potion	4-13	Visible	Defence 5 + floor(StaticLevel * 0.15) Ranged 4 + floor(StaticLevel * 0.1) Acts as a ranging and super defence potion in one dose.
File:Divine bastion potion.png	Divine bastion potion	4-13	Visible	Defence 5 + floor(StaticLevel * 0.15) Ranged 4 + floor(StaticLevel * 0.1) Stat draining for Ranged and Defence is disabled for 5 minutes, meaning the player's Ranged and Defence levels will stay fully boosted. After the 5 minutes are over, Ranged and Defence levels will be restored to its base level.
	Bandages (Theatre of Blood)	4-13	Visible	Hitpoints 20 Attack 4 + floor(StaticLevel * 0.15) Defence 4 + floor(StaticLevel * 0.15) Strength 4 + floor(StaticLevel * 0.15) Magic 4 Ranged 4 + floor(StaticLevel * 0.1)
File:Twisted (-).png	Twisted (-)	4-13	Visible	Ranged 4 + floor(StaticLevel * 0.1) Only usable within the Chambers of Xeric.
File:Overload (-).png	Overload (-)	4-13	Visible	Acts as an elder (-), twisted (-), and kodai (-) potion in one dose. Hitpoints - 50 Attack 4 + floor(StaticLevel * 0.1) Defence 4 + floor(StaticLevel * 0.1) Strength 4 + floor(StaticLevel * 0.1) Ranged 4 + floor(StaticLevel * 0.1) Magic 4 + floor(StaticLevel * 0.1) The boost is reapplied every 15 seconds for 5 minutes. (This lost health is refunded after the overload ends). Only usable within the Chambers of Xeric.
File:Twisted potion.png	Twisted potion	5-17	Visible	Ranged 5 + floor(StaticLevel * 0.13) Only usable within the Chambers of Xeric.
File:Overload (Chambers of Xeric).png	Overload (Chambers of Xeric)	5-17	Visible	Acts as an elder, twisted, and kodai potion in one dose. Hitpoints - 50 Attack 5 + floor(StaticLevel * 0.13) Defence 5 + floor(StaticLevel * 0.13) Strength 5 + floor(StaticLevel * 0.13) Ranged 5 + floor(StaticLevel * 0.13) Magic 5 + floor(StaticLevel * 0.13) The boost is reapplied every 15 seconds for 5 minutes. (This lost health is refunded after the overload ends). Only usable within the Chambers of Xeric.
File:Potion of power.png	Potion of power	5-19	Visible	Ranged 5 + floor(StaticLevel * 0.15) Only usable within the Soul Wars minigame.
File:Super ranging.png	Super ranging	5-19	Visible	Ranged 5 + floor(StaticLevel * 0.15) Only usable within the Nightmare Zone.
File:Overload (Nightmare Zone).png	Overload (Nightmare Zone)	5-19	Visible	Acts as a super combat, super ranging, and super magic potion in one dose. Hitpoints - 50 Attack 5 + floor(StaticLevel * 0.15) Defence 5 + floor(StaticLevel * 0.15) Strength 5 + floor(StaticLevel * 0.15) Ranged 5 + floor(StaticLevel * 0.15) Magic 5 + floor(StaticLevel * 0.15) The boost is reapplied every 15 seconds for 5 minutes. (This lost health is refunded after the overload ends). Only usable within the Nightmare Zone.
File:Twisted (+).png	Twisted (+)	6-21	Visible	Ranged 6 + floor(StaticLevel * 0.16) Only usable within the Chambers of Xeric.
File:Overload (+).png	Overload (+)	6-21	Visible	Acts as an elder (+), twisted (+), and kodai (+) potion in one dose. Hitpoints - 50 Attack 6 + floor(StaticLevel * 0.16) Defence 6 + floor(StaticLevel * 0.16) Strength 6 + floor(StaticLevel * 0.16) Ranged 6 + floor(StaticLevel * 0.16) Magic 6 + floor(StaticLevel * 0.16) The boost is reapplied every 15 seconds for 5 minutes. (This lost health is refunded after the overload ends). Only usable within the Chambers of Xeric.
	Smelling salts	11-26	Visible	Attack 11 + floor(StaticLevel * 0.16) Defence 11 + floor(StaticLevel * 0.16) Strength 11 + floor(StaticLevel * 0.16) Ranged 11 + floor(StaticLevel * 0.16) Magic 11 + floor(StaticLevel * 0.16) Restores run energy by 25%. The boost is reapplied every 15 seconds for 8 minutes. Only usable within the Tombs of Amascut.

Prayer Multiplier:

Prayer
Sharp Eye	1.05
Hawk Eye	1.10
Eagle Eye	1.15
Rigour	1.23

Step two: Calculate the maximum hit

${\text{Maximum Hit}}=\left\lfloor \left\lfloor 0.5+{\frac {{\text{Effective Ranged Strength}}*({\text{Equipment Ranged Strength}}+64)}{640}}\right\rfloor *{\text{Gear Bonus}}\right\rfloor$

The maximum hit is the largest hit you can possibly do with the current setup. It can be tested by using the Combat dummy in a Player-owned house.

The Equipment Ranged Strength can be found in the Equipment Stats window under 'Other bonuses'.

If slaying monsters on task while wearing a Black mask (i) or Slayer helm (i), the gear bonus is 1.15.

If killing Undead monsters while wearing a Salve amulet (i) or Salve amulet (ei), the gear bonus is 7/6 (1.167) or 1.2 respectively.

Note that these two bonuses DO NOT stack.

In the wilderness, Craw's bow and Webweaver bow give a gear bonus of 1.5. This bonus stacks additively with a Black mask(i) or Slayer helm (i), for a total of 1.65, and multiplicatively with the Salve amulet (i) or (ei).

Twisted bow damage modifier is also included in the gear bonus and does stack with slayer/salve (multiply by both modifiers). However, the tbow modifier is less straightforward to calculate as it is not constant: see its page here to calculate it based on your opponent.

Step three: Calculate the bonus damage

${\text{Max Hit}}={\big \lfloor }{\text{Base Damage}}\times {\text{Special Bonus}}{\big \rfloor }$

The following special attack/effect bonuses apply, bolts only apply when the special effect activates:

Attack/Effect	Multiplier
Special attacks
Dark bow (dragon arrows)	1.5
Dark bow (other arrows)	1.3
Zaryte crossbow (enchanted bolts)	1.1
Bolts' Special effects
Diamond bolts (e)	1.15
Dragonstone bolts (e)	1.45
Onyx bolts (e)	1.15
Opal bolts (e)	1.25

Step four: Calculate the effective ranged attack

${\text{Effective Ranged Attack}}=\left\lfloor (\left\lfloor ({\text{Ranged Level}}+{\text{Boost}})*{\text{Prayer Bonus}}\right\rfloor +{\text{Atk Style}}+8)*{\text{Void Modifier}}\right\rfloor$

If you are using the accurate attack style Atk Style is 3 while all other styles are 0.

Void Modifier is 1 if not wearing void, 1.1 if wearing either full ranged void or full elite ranged void.

Prayer Multiplier:

Prayer
Sharp Eye	1.05
Hawk Eye	1.10
Eagle Eye	1.15
Rigour	1.20

Note that the only difference between effective ranged strength and effective ranged attack is the value for Rigour and void.

Step five: Calculate the Attack roll

${\text{Atk roll}}=\left\lfloor {\text{Effective Ranged Attack}}*({\text{Equipment Ranged Attack}}+64)*{\text{Gear Bonus}}\right\rfloor$

The Equipment Attack bonus can be found in the Equipment Stats window under the heading 'Attack Bonus'.

The gear bonus is the same as in Step 2.

Twisted bow accuracy modifier is also included in the gear bonus and does stack with slayer/salve (multiply by both modifiers). However, the tbow modifier is less straightforward to calculate as it is not constant: see it's page here to calculate it based on your opponent. Thus it does not multiply your accuracy output, it just multiplies your attack roll.

Step six: Calculate the Defence roll

${\text{Def roll}}=({\text{Target Defence Level}}+9)*({\text{Target Ranged Defence Bonus}}+64)$

Target's Defence is denoted by a shield icon on the target's wiki page.

Target's ranged defence can be found under the 'Defensive stats' heading.

Step seven: Calculate the hit chance

If Attack Roll > Defence roll:

${\text{Hit Chance}}=1-{\frac {{\text{Def roll}}+2}{2*({\text{Atk roll}}+1)}}$

Else

${\text{Hit Chance}}={\frac {\text{Atk roll}}{2*({\text{Def roll}}+1)}}$

Step eight: Calculate the ranged damage output

${\text{Damage per hit}}={\text{Hit Chance}}*{\Biggl (}{\frac {\text{Maximum hit}}{2}}+{\frac {1}{{\text{Maximum hit}}+1}}{\Biggr )}$

To calculate the Damage Per Second, divide the Damage Per hit by the attack speed of the weapon in seconds. Note that the rapid attack style decreases the attack speed by 1 tick.