Critical Hit Calculator
Calculate the average damage output of an attack given base damage, critical hit chance, and critical hit multiplier — the expected-value formula every theorycrafter uses to compare crit-heavy builds against flat damage builds. Use it to decide whether to stack crit chance, crit damage, or raw damage stats on your gear.
Last updated: May 2026
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About this calculator
The formula is: average damage = base damage × (1 + (critical chance / 100) × (critical multiplier − 1)). At 30% crit chance and 2.0× multiplier, average damage = base × (1 + 0.3 × 1.0) = base × 1.30 — a 30% effective damage increase. The formula derives from probability: 30% of hits are crits (dealing base × 2.0), 70% are non-crits (dealing base × 1.0), so average = 0.3 × 2.0 + 0.7 × 1.0 = 1.3, multiplied by base. The general formula handles any crit multiplier: at 100% crit chance and 2.5× multiplier, average = base × (1 + 1.0 × 1.5) = base × 2.5 (every hit crits for full multiplier). Edge cases: 0% crit chance returns base damage unchanged (no crit benefit); 100% crit chance returns base × multiplier (every hit is a crit, no probability dilution); 0% crit multiplier (or < 1) would produce average damage less than base (negative crit, which is unusual but mathematically valid). The expected-value formula gives accurate averages over many hits but doesn't capture variance — at 30% crit chance, you may go 10 hits without a crit (probability ~2.8%, real). For boss fights and long encounters, the average is what matters; for short PvP fights and burst rotations, variance can decide outcomes. Crit-stat allocation tradeoff: at low crit chance, +crit chance is usually more valuable than +crit damage (until 50–70% chance); after that breakpoint, +crit damage scales linearly while +crit chance hits diminishing returns. Many games have specific breakpoints where additional crit chance is wasted (cap at 100%, or "Always Crit" thresholds for boss vulnerabilities); always check your game's mechanics before stat-stacking.
How to use
Example 1 — Comparing two gear setups. Build A: base damage 1,000, 40% crit chance, 2.0× crit multiplier. Enter 1000 for Base Damage, 40 for Crit Chance, and 2 for Crit Multiplier. Result: 1,400 average damage. Verify: 1000 × (1 + 0.4 × 1.0) = 1000 × 1.4 = 1,400. ✓ Build B: base damage 1,150, 25% crit chance, 2.5× crit multiplier: 1150 × (1 + 0.25 × 1.5) = 1150 × 1.375 ≈ 1,581 average damage. Build B beats Build A by ~13% despite lower crit chance, because the higher base damage and higher crit multiplier compound favorably. Example 2 — Stat-priority decision. Your current build deals 800 base damage at 50% crit chance and 2.0× multiplier: 800 × (1 + 0.5 × 1.0) = 800 × 1.5 = 1,200 average damage. You can either add 10% crit chance OR 0.3× crit multiplier with the same item upgrade. Adding crit chance: 800 × (1 + 0.6 × 1.0) = 800 × 1.6 = 1,280 average (+6.67% gain). Adding crit damage: 800 × (1 + 0.5 × 1.3) = 800 × 1.65 = 1,320 average (+10% gain). Crit damage wins at this crit chance level — beyond 50% crit chance, +crit damage typically scales better than +crit chance. The breakpoint where they cross depends on your specific multiplier values; computing both alternatives is always faster than memorizing rules.
Frequently asked questions
Should I stack crit chance or crit damage?
Depends on your current values. At low crit chance (under 30%), +crit chance usually provides more % damage increase per stat point than +crit damage. As crit chance climbs (50–70%+), the relative benefit of +crit damage grows because each crit gets stronger while additional crit chance has fewer "wasted" non-crit hits to convert. The optimal stat ratio depends on your game's specific scaling: in Path of Exile, the rule of thumb is to balance crit chance and crit multi so that "effective multiplier" (1 + crit% × (multi − 1)) gain is roughly equal from each. In WoW, gear has fixed crit chance/damage values per item budget, so the question becomes which is more available on your itemization tier. Always compute both alternatives with the formula and pick the larger gain rather than relying on rules of thumb. As crit chance approaches the 100% cap, additional crit chance is completely wasted, and 100% of stat budget should shift to crit damage.
What's the difference between average damage and effective DPS?
Average damage (this calculator) is per-hit expected damage including crit probability. Effective DPS is average damage multiplied by attacks per second, plus modifiers for buffs, debuffs, and damage-over-time effects. So this calculator gives you the per-swing average; multiplying by attack speed gives baseline eDPS. For comprehensive damage modeling, you also need: damage-over-time tick rates, area-of-effect damage spread across targets, conditional bonuses (target HP%, debuff stacks, positional damage), and rotation efficiency (downtime, cooldown management). Top-tier theorycrafting tools (SimulationCraft for WoW, Path of Building for PoE) handle all of these via Monte Carlo simulation across millions of combat ticks. This simple expected-value formula is excellent for comparing individual stat allocations or gear pieces; for full character optimization, use a simulation tool that models the full combat loop.
Why do my actual damage numbers vary so much from the average?
Because the "average" is over many hits, but any single hit either crits or doesn't — there's no partial-crit. Variance follows a binomial distribution: at 30% crit chance over 10 hits, you expect 3 crits but might get 0–8 with non-trivial probability. Specific variance facts: over 10 hits at 30% crit, you have ~2.8% chance of zero crits (severe unlucky); over 100 hits at 30% crit, the standard deviation is about 4.6 crits, so 95% confidence interval is roughly 21–39 crits. For sustained combat (boss fights of 30+ seconds), the average converges quickly and variance shrinks. For burst windows (5–10 second cooldown phases), variance dominates and a single unlucky stretch can fail a damage check. To reduce variance, stack crit chance toward 100% (when every hit crits, variance disappears) or use abilities that guarantee crits (procs, talents, "always crit" debuffs). Variance-resistant builds favor higher base damage and consistent procs over RNG-heavy crit stacking.
What are the most common mistakes people make optimizing crit?
The biggest is stacking crit chance past the 100% cap without realizing additional points are wasted — many games allow crit chance to display above 100% but cap real benefit at 100%. The second is forgetting that some abilities and bosses ignore crit (mechanic-tagged "always normal hit" attacks) or have crit-immune phases. The third is comparing builds based on tooltip damage without applying the crit formula — a 1500 tooltip damage with 0% crit is identical average to 1000 tooltip with 50% crit at 2× multiplier. The fourth is over-stacking crit damage when crit chance is low; at 20% crit chance, doubling crit damage from 2× to 4× only lifts average damage by 20%, often less than what an equivalent base-damage upgrade would provide. The fifth is using crit numbers from PvP testing in PvE contexts (or vice versa); player-vs-player and player-vs-monster systems often have different crit reduction or armor scaling. The sixth is ignoring crit-related effects: many games have abilities that proc on crit (lifesteal, cooldown reduction, status effects), making crit chance more valuable than the simple damage formula suggests.
When should I not use this calculator?
Skip it for games without crit mechanics — most fighting games, puzzle games, and racing games don't use crit. It is the wrong tool for guaranteed-crit abilities (Path of Exile assassinations, WoW Subtlety Rogue's opener mechanics) where the per-hit damage is the multiplied value, not an expected average. Do not use it when calculating burst damage for kill-window planning; for those, use the worst-case (no crits) and best-case (all crits) bounds rather than the average, since burst windows are too short for the average to apply. It also doesn't handle multi-hit abilities where each individual hit rolls crit separately (channeled spells, multi-shot abilities) — those have lower variance than single-hit attacks at the same crit chance. For games with critical-hit-reduction mechanics on enemies (armor scaling, boss-only damage reduction), the formula needs additional terms for crit-reduced damage. And for complex stat interactions in modern ARPGs (Path of Exile, Last Epoch, Diablo 4), use a character-specific simulator that handles all the interaction layers rather than this simplified expected-value model.