DPS Calculator

What the DPS Calculator Measures (and Why “Average Hit” Matters)

DPS stands for damage per second: the most common way games summarize how quickly a build, weapon, or skill can deal damage over time. The catch is that many games include randomness—especially critical hits—so your real output is better represented by an expected value (an average over many attacks), not just your “normal hit” number.

ProCalc.ai’s DPS Calculator uses four inputs:

- Damage per hit (your non-crit base hit) - Attacks per second (how many hits you land each second) - Crit chance (%) (probability a hit is a crit) - Crit multiplier (×) (how much bigger a crit is than a normal hit)

From those, it computes:

- Average hit (expected damage per attack, including crits) - DPS (average hit × attacks per second) - Damage per minute (DPM) - Crit contribution (what percent of your average damage is coming from crits)

This is ideal for comparing gear upgrades, talent choices, buffs, and different attack-speed vs. crit-focused setups.

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The DPS Formula (Used by ProCalc.ai)

The calculator follows these steps.

### 1) Convert crit chance into a probability If your crit chance is C%, then:

- Crit probability = C / 100

Example: 25% crit chance → 0.25 probability.

### 2) Compute the expected (average) hit A crit multiplier of M× means: - Normal hit = damage - Crit hit = damage × M

Expected value blends them:

Average hit avg_hit = damage × (1 + (C/100) × (M − 1))

Why this works: - (M − 1) is the “extra” portion crits add beyond a normal hit - Multiply that extra by crit probability to get the average bonus from crits - Add 1 to include the base hit

### 3) Compute DPS DPS dps = avg_hit × attack_speed

Where attack speed is attacks per second (APS).

### 4) Compute damage per minute dpm = dps × 60

### 5) Compute crit contribution (share of damage due to crits) The calculator estimates what fraction of your average hit comes specifically from the crit bonus:

crit_contribution (%) = [( (C/100) × (M − 1) ) / ( 1 + (C/100) × (M − 1) )] × 100 (rounded to the nearest whole percent)

This tells you whether your build is mostly “base damage driven” or “crit driven.”

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Worked Example 1: Balanced Stats (Easy Baseline)

Inputs - Damage per hit = 120 - Attacks per second = 2.0 - Crit chance = 25% - Crit multiplier = 2.0×

Step 1: Average hit avg_hit = 120 × (1 + (25/100) × (2.0 − 1)) = 120 × (1 + 0.25 × 1) = 120 × 1.25 = 150

So your average hit is 150 damage per attack.

Step 2: DPS dps = 150 × 2.0 = 300

Step 3: DPM dpm = 300 × 60 = 18,000

Step 4: Crit contribution crit_contribution = [(0.25 × 1) / (1 + 0.25 × 1)] × 100 = (0.25 / 1.25) × 100 = 20%

Interpretation: Even with 25% crit chance and 2× crits, only about 20% of your average damage is coming from crits. Most of your output is still your base hit and attack speed.

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### Worked Example 2: High Crit Build (Same Base Damage, Different Feel)

Inputs - Damage per hit = 120 - Attacks per second = 2.0 - Crit chance = 50% - Crit multiplier = 2.5×

Average hit avg_hit = 120 × (1 + 0.50 × (2.5 − 1)) = 120 × (1 + 0.50 × 1.5) = 120 × (1 + 0.75) = 120 × 1.75 = 210

DPS dps = 210 × 2.0 = 420

DPM dpm = 420 × 60 = 25,200

Crit contribution crit_contribution = [(0.50 × 1.5) / (1 + 0.50 × 1.5)] × 100 = (0.75 / 1.75) × 100 ≈ 42.86% → 43%

Interpretation: This setup gains a lot from crits—about 43% of average damage is crit-driven. It will also “feel” swingier: long streaks of non-crits hurt more, but crit streaks spike hard.

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### Worked Example 3: Attack Speed vs. Bigger Hits (Comparing Two Options)

You’re choosing between two upgrades. Everything else stays the same: crit chance 30%, crit multiplier 2.0×.

### Option A (faster weapon) - Damage per hit = 90 - Attacks per second = 3.0 - Crit chance = 30% - Crit multiplier = 2.0×

avg_hit = 90 × (1 + 0.30 × (2.0 − 1)) = 90 × 1.30 = 117

dps = 117 × 3.0 = 351 dpm = 351 × 60 = 21,060

### Option B (heavier weapon) - Damage per hit = 130 - Attacks per second = 2.2 - Crit chance = 30% - Crit multiplier = 2.0×

avg_hit = 130 × 1.30 = 169

dps = 169 × 2.2 = 371.8 dpm = 371.8 × 60 = 22,308

Result: Option B wins on sustained DPS (371.8 vs 351), even though it attacks slower. If your game rewards burst windows, Option B may also align better with buffs—while Option A may feel smoother and more consistent for on-hit effects.

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### Pro Tips for Using DPS Correctly

1) Treat DPS as “long-run average,” not guaranteed output. With low crit chance, short fights can deviate a lot from the average.

2) Keep your units consistent. Attacks per second must be per second (not per minute). If your game shows attacks per minute, divide by 60 first.

3) Use the crit contribution to guide stat priorities. - If crit contribution is low (say 10–20%), adding more base damage or attack speed may be more reliable. - If it’s high (40%+), crit scaling is doing heavy lifting, and crit buffs can be extremely valuable.

4) Compare upgrades by changing one variable at a time. If you change damage, speed, and crit all at once, it’s hard to learn what actually improved your output.

5) Remember that many games have hidden modifiers (armor, resistances, headshots, damage falloff). This calculator is best for “sheet DPS” unless you plug in post-mitigation damage.

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### Common Mistakes (and How to Avoid Them)

- Confusing crit multiplier formats. Some games display “crit damage +100%” to mean 2.0× total. Others show “200% crit damage” meaning 2.0×. Make sure your crit multiplier is the total multiplier (like 1.5×, 2.0×, 2.5×), not the bonus percent.

- Entering crit chance as a decimal. If you type 0.25 thinking it means 25%, the calculator will treat it as 0.25%, massively underestimating DPS. Enter 25 for 25%.

- Using burst damage as “damage per hit.” If your skill hits multiple times, decide whether “damage per hit” is per projectile/tick or the whole cast. If it’s the whole cast, then “attacks per second” should be casts per second—not individual hits.

- Ignoring downtime and reloads. Real combat often includes movement, reloads, cooldowns, or target invulnerability. The calculator assumes continuous attacking. For realism, reduce attacks per second to an effective rate that includes downtime.

- Comparing builds with different on-hit effects using only DPS. Some setups win because they apply status effects, lifesteal, stuns, or armor shred. DPS is only one axis—still useful, but not the whole story.

If you plug your stats into ProCalc.ai’s DPS Calculator and focus on average hit, DPS, and crit contribution together, you’ll get a clear, practical view of what’s actually driving your damage—and what to upgrade next.

Calculating Damage Per Second (DPS) is a fundamental aspect of understanding combat effectiveness in many video games. It allows players to quantify how much damage a character, weapon, or ability can inflict over time, helping with gear choices, build optimization, and strategy. The ProCalc.ai DPS Calculator uses a straightforward method to estimate this crucial metric, taking into account critical hits, which are a common mechanic in many RPGs and action games.

The core idea behind DPS is to determine the average damage dealt per attack and then multiply that by how many attacks occur in a second. Critical hits complicate this slightly because they modify the damage of a certain percentage of attacks. To account for this, we first calculate the average damage per hit, considering the chance and magnitude of critical strikes.

The formula for the average damage per hit is: avg_hit = damage * (1 + (crit_chance / 100) * (crit_multiplier - 1))

Let's break down each variable in this formula. damage refers to the base damage dealt by a single hit, assuming no critical strike. This is typically a raw number, like 100 or 500. crit_chance is the probability, expressed as a percentage, that an attack will be a critical hit. For example, a 25% crit chance means one in four attacks, on average, will be critical. We divide crit_chance by 100 to convert it into a decimal for calculation purposes (e.g., 25% becomes 0.25). crit_multiplier is the factor by which critical hits increase your damage. A crit_multiplier of 2x means a critical hit deals double the base damage. The (crit_multiplier - 1) part isolates the *extra* damage gained from a critical hit. For instance, if a crit multiplier is 2x, then (2 - 1) means critical hits add 100% of the base damage. Multiplying this by (crit_chance / 100) gives us the average additional damage contributed by critical hits over many attacks. Adding 1 to this entire term ensures we're multiplying the base damage by a factor that includes both regular hits and the average bonus from critical hits.

Once we have the avg_hit, calculating DPS is simple: dps = avg_hit * attack_speed

Here, attack_speed represents how many attacks your character or weapon can perform in one second. This is typically expressed as attacks per second (e.g., 1.5 attacks/second).

We also provide Damage Per Minute (DPM) for those who prefer a longer-term view: dpm = dps * 60

Finally, to give you a clearer picture of critical hits' impact, the calculator also estimates the crit_contribution. This metric shows what percentage of your total average damage per hit is attributable solely to the critical hit mechanic. crit_contribution = Math.round(((crit_chance / 100) * (crit_multiplier - 1)) / (1 + (crit_chance / 100) * (crit_multiplier - 1)) * 100)

Let's walk through an example. Suppose you have a weapon that deals 100 damage per hit, attacks 1.5 times per second (attack_speed), has a 20% crit_chance, and a crit_multiplier of 2x.

First, calculate the average damage per hit: avg_hit = 100 * (1 + (20 / 100) * (2 - 1)) avg_hit = 100 * (1 + 0.20 * 1) avg_hit = 100 * (1 + 0.20) avg_hit = 100 * 1.20 avg_hit = 120

Now, calculate the DPS: dps = 120 * 1.5 dps = 180

Your Damage Per Second would be 180. The DPM would be 180 * 60 = 10,800. The critical contribution would be: crit_contribution = ((20 / 100) * (2 - 1)) / (1 + (20 / 100) * (2 - 1)) * 100 crit_contribution = (0.20 * 1) / (1 + 0.20 * 1) * 100 crit_contribution = 0.20 / 1.20 * 100 crit_contribution = 0.1666... * 100 crit_contribution = 17% (rounded)

For a second example, consider a slower, harder-hitting weapon: 500 damage, 0.8 attack_speed, 50% crit_chance, and a crit_multiplier of 1.5x.

avg_hit = 500 * (1 + (50 / 100) * (1.5 - 1)) avg_hit = 500 * (1 + 0.50 * 0.5) avg_hit = 500 * (1 + 0.25) avg_hit = 500 * 1.25 avg_hit = 625

dps = 625 * 0.8 dps = 500

In this case, the DPS is 500. The DPM is 500 * 60 = 30,000. The critical contribution would be: crit_contribution = ((50 / 100) * (1.5 - 1)) / (1 + (50 / 100) * (1.5 - 1)) * 100 crit_contribution = (0.50 * 0.5) / (1 + 0.50 * 0.5) * 100 crit_contribution = 0.25 / 1.25 * 100 crit_contribution = 0.20 * 100 crit_contribution = 20%

It's important to note some limitations and edge cases. This formula assumes a consistent attack speed and a simple critical hit mechanic. In games with variable attack speeds (e.g., due to buffs or debuffs), damage fall-off over distance, or more complex critical hit systems (like critical damage reduction on enemies, or headshot multipliers that stack differently), this basic DPS calculation might not capture the full picture. It also doesn't account for abilities that deal damage over time (DoTs), area-of-effect (AoE) damage, or proc-based damage that happens intermittently. For such scenarios, more complex simulations or game-specific formulas would be required. However, for direct damage from standard attacks, this formula provides a robust and widely applicable estimate.

• DigiPen Institute of Technology
• MIT Media Lab
• Gamasutra / Game Developer
• Investopedia
• Britannica