Critical Hit Calculator

A critical hit is a special attack outcome found in almost every modern video game, from action RPGs and MOBAs to turn-based strategy games and shooters. When a critical hit lands, the attack deals bonus damage beyond the normal value, giving players a powerful spike of output that can shift the momentum of any encounter.

Critical hits are governed by two core statistics: crit chance (the probability that any single attack will be a critical hit, expressed as a percentage) and crit multiplier (the factor by which base damage is multiplied when a crit lands). A third modifier — bonus crit damage — stacks additively with the base multiplier to further amplify the spike. Understanding exactly how these values interact is the first step to optimizing your damage output.

This critical hit calculator handles the full range of calculations: raw crit damage, expected damage per hit, DPS increase from your crit stats, multi-attack totals, armor mitigation, and the probability of landing at least one critical hit in a given number of attacks. Whether you are theorycrafting an ARPG build, evaluating gear upgrades, or studying game design math, every result here follows the exact arithmetic used in the page above.

Games implement crit systems differently — some cap crit chance at 100%, some use pseudorandom distribution (PRD) to prevent long streaks, and some apply crit multipliers before armor rather than after. This calculator models the most common independent-probability system where each attack rolls independently, and armor is applied uniformly to both normal and critical hits.

Every output this calculator produces derives from a small set of formulas. Mastering them lets you make faster decisions during gameplay or build planning without opening the tool every time.

Critical Hit Damage is the most fundamental value. The effective multiplier combines the base crit multiplier with any bonus crit damage, both expressed as percentages and divided by 100 to convert to a decimal factor:

Once you have the crit damage value, the Expected Damage per Attack is a probability-weighted average of the normal hit and the critical hit. This is the figure that actually matters for sustained DPS comparisons, because over a long fight your average output converges to this number.

The DPS Increase is the percentage improvement of expected damage over raw base damage. This is the cleanest single number for comparing two gear sets: whichever configuration produces a higher DPS increase percentage simply deals more damage on average, regardless of attack speed.

After applying armor, both normal and critical damage are reduced by the same fraction. This means armor does not change your relative DPS increase from crits — it scales both down proportionally.

Knowing your crit chance per hit is useful, but players often want to know the probability of seeing at least one critical hit within a burst combo or a skill rotation. This calculator computes three key probability metrics across N attacks, assuming each attack is an independent Bernoulli trial.

Probability of zero crits in N attacks is (1 − p)^N. For example, at 25% crit chance over 10 attacks, the chance of hitting zero crits is 0.75^10 ≈ 5.63%. That sounds low, but it means roughly one in eighteen combos will produce no crits at all — a real variance concern for short fights.

Probability of at least one crit is the complement: 1 − (1 − p)^N. At 25% over 10 attacks this equals approximately 94.37%. Most players perceive crits as "always happening" once crit chance climbs past 20–25%, and these numbers explain why: even modest crit chance produces near-certain crit appearances over a full rotation.

Probability of all crits is p^N, which collapses quickly. At 50% crit chance across 8 attacks, every hit being a crit has probability 0.5^8 = 0.39% — spectacular when it happens, but extremely rare.

These probabilities underpin the Damage Range output. The minimum possible damage assumes zero crits (every hit deals base damage), while the maximum assumes all crits. High variance between those extremes means your actual fight-to-fight damage fluctuates heavily — relevant for burst DPS checks and speed runs where consistency matters as much as average output.

Most games apply armor or damage reduction as a flat percentage subtracted from final damage. This calculator models that as a multiplicative factor: damageAfterArmor = damage × (1 − armorReduction / 100). The same factor applies to both normal hits and critical hits, so the relative benefit of crit stats is unchanged by armor — your DPS increase percentage is identical before and after armor reduction.

Where armor matters is in the absolute totals. A 20% armor reduction that seems minor on a 100-damage normal hit becomes a 70-point swing on a 350-damage critical hit. Understanding that armor scales with damage magnitude helps you evaluate the trade-off between stacking offensive crit stats and investing in armor penetration items.

The Total Expected Damage After Armor output combines the expected-per-hit math with the armor multiplier across all N attacks, giving you the realistic projected damage for a full ability rotation against a defended target. Use this value when comparing builds against tanky enemies with high mitigation.

Some games separate physical armor from magical or elemental resistance, applying different reduction values to different damage types. In those cases, run this calculator once per damage type with the relevant armor figure, then sum the results for a complete picture of your effective output.

The core question in any crit build is: which is worth more — more crit chance or a higher crit multiplier? The answer depends on your current stats.

From the expected damage formula, both stats scale multiplicatively with base damage, but they interact with each other. When crit chance is very low, increasing the crit multiplier has diminishing impact because crits land rarely. Conversely, when the multiplier is already very high (say 300%+), adding another 5% crit chance delivers a larger absolute improvement than adding another 25% multiplier. A useful rule of thumb: if your crit multiplier is more than four times your crit chance (in their respective natural units), prioritizing crit chance is usually more efficient.

The DPS Increase output makes this comparison easy. Plug in two gear configurations and compare the percentages directly — no theory needed. The configuration with the higher DPS increase wins, regardless of which individual stat changed.

Beyond the raw numbers, consider diminishing returns from game-specific caps. Many games cap crit chance at 100% (this calculator enforces that cap via Math.min(chance, 100)), making further investment in crit chance wasted past that threshold. At that point every point should go toward crit multiplier or bonus crit damage. Some games also implement soft caps on multiplier scaling, so always test the live numbers rather than relying purely on formula extrapolation.

Finally, remember that expected damage is a long-run average. In short fights, variance matters. A 50% crit chance build will feel wildly inconsistent compared to a 20% crit chance, higher multiplier build that still produces the same expected DPS. Match your build philosophy to your content: burst boss phases reward high expected damage, while sustained farm speed rewards low variance and consistent crits.

Different games implement critical hits in meaningfully different ways, and knowing the conventions helps you enter the right numbers into this calculator.

Use this table to identify the standard multiplier for your game, then enter your actual stat values for precise calculations. When a game uses pseudorandom distribution, the average crit chance over many attacks still matches the stated value, so the expected damage formula remains valid for planning purposes even though individual attack sequences differ from the pure-probability model.