How OSRS DPS Is Calculated: Attack Bonus, Strength, and Prayer
Understand how OSRS damage per second is calculated from attack speed, accuracy, max hit, and prayer bonuses. Covers the effective level, roll, and hit damage formulas.
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The OSRS DPS Formula Overview
OSRS combat is based on two key calculations per hit: 1. Accuracy roll: Did the attack hit (vs. the monster's defence roll)? 2. Damage roll: If it hit, how much damage was dealt?
DPS = Hit Chance × Average Damage × (1 ÷ Attack Speed in seconds)
Attack Speed Reference
Attack speed in OSRS is measured in game ticks (1 tick = 0.6 seconds):
Effective Level Calculation
Before rolling accuracy or max hit, calculate the effective level which incorporates prayer and stance bonuses:
Effective Attack Level = floor(Attack Level × Prayer Multiplier) + Stance Bonus + 8 Effective Strength Level = floor(Strength Level × Prayer Multiplier) + Stance Bonus + 8
Prayer multipliers (melee): - Burst of Strength: ×1.05 - Superhuman Strength: ×1.10 - Ultimate Strength: ×1.15 - Piety: Attack ×1.20, Strength ×1.23, Defence ×1.25
Stance bonuses: - Aggressive: +3 to effective strength - Accurate: +3 to effective attack - Controlled: +1 to attack, strength, and defence
Max Hit Formula
Max Hit = floor(0.5 + Effective Strength Level × (Equipment Strength Bonus + 64) / 640)
Example: 99 Strength, Piety, Aggressive stance, +118 strength bonus (full bandos + abyssal whip): - Effective Strength = floor(99 × 1.23) + 3 + 8 = 121 + 3 + 8 = 132 - Max Hit = floor(0.5 + 132 × (118 + 64) / 640) = floor(0.5 + 132 × 182/640) = floor(0.5 + 37.6) = 38
Accuracy (Hit Chance) Calculation
Attacker's roll = floor(Effective Attack Level × (Equipment Attack Bonus + 64)) Defender's roll = floor(Effective Defence Level × (Defence Bonus + 64))
Hit Chance: - If Attacker's roll > Defender's roll: Hit Chance = 1 − (Defender's Roll + 2) ÷ (2 × Attacker's Roll + 1) - If Attacker's roll ≤ Defender's roll: Hit Chance = Attacker's Roll ÷ (2 × Defender's Roll + 1)
Average Damage Per Hit
If a hit lands (doesn't splash), damage is uniformly distributed between 0 and max hit: Average Damage = Max Hit / 2
Full DPS = Hit Chance × (Max Hit / 2) / Attack Speed (seconds)
Example continuation: 85% hit chance, max hit 38, whip attack speed (5 ticks = 3 seconds): DPS = 0.85 × (38/2) / 3 = 0.85 × 19 / 3 = 5.38 DPS
Related Guides
- OSRS Accuracy and Hit Chance Explained: How to Calculate if You'll HitUnderstand OSRS accuracy and hit chance calculation. Learn how attacker and defender rolls determine whether your attack lands, and how equipment bonuses and prayer affect accuracy.
- OSRS Attack Speed and Game Ticks: How Tick-Based Combat WorksUnderstand OSRS game ticks and attack speed. Every action in OSRS happens in 0.6-second tick intervals, and weapon speed determines how many ticks between attacks.
- OSRS Combat Level Formula: How Your Combat Level Is CalculatedCalculate your OSRS combat level from your stats. Covers the combat level formula for melee, ranged, and magic combat styles, and how Prayer and Hitpoints contribute.
- OSRS Drop Rate Probability: How to Use a Drop Rate CalculatorLearn to use OSRS drop rate probability calculations to find your dry streak odds, time to 50% chance, and cumulative probability at any kill count.
Frequently Asked Questions
- How is max hit calculated in OSRS?
- Max Hit = floor(0.5 + Effective Strength Level × (Strength Bonus + 64) / 640). Effective Strength = floor(Strength Level × Prayer Mult) + Stance Bonus + 8. Example: 99 Str, Piety (×1.23), Aggressive (+3), +118 str bonus: Effective = 132; Max Hit = 38.
- How does prayer affect OSRS DPS?
- Prayers multiply the effective level used in accuracy and max hit calculations. Piety boosts Attack by ×1.20 and Strength by ×1.23 — the most powerful melee prayer. At 99 Strength, Piety adds roughly equivalent to 20+ strength levels in terms of DPS boost.
- What is the best way to maximize OSRS DPS?
- In order of impact: (1) Use the best-in-slot weapon for the content. (2) Maximize strength bonus through equipment (Bandos armor, Torture amulet). (3) Use Piety (requires 70 Prayer, 65 Herblore). (4) Choose Aggressive stance for max hit. (5) Use Super Combat Potion (+13/+13/+13 to stats). Beyond these, damage reduction via defence becomes more valuable.
- Why do I sometimes hit 0 in OSRS?
- In OSRS, any hit — even from a fully accurate attack — has a chance of dealing 0 damage. This is because damage is rolled uniformly from 0 to max hit. Even a max hit of 30 gives each value from 0–30 equal probability. A 0-hit is not a miss — it landed but rolled the minimum damage value.
Last updated 7/28/2026