What formula is used for "at least one crit"?

The complement rule: P(at least 1) = 1 - (1 - p)^N, where p is the per-hit crit probability and N is the number of attacks. This is exact, not an approximation.

How is expected crits calculated?

Expected crits = N × p. For example, 10 attacks at 25% crit rate yields an expected value of 2.5 crits. This is the long-run average over many sessions.

Does this account for crit damage multipliers?

Yes, optionally. Enter normal-hit damage and the total damage multiplier applied on a crit. The estimate is an average under the same independent-roll assumptions; it does not model armor, buffs, caps or game-specific rounding.

What if my game uses pseudo-random or pity mechanics?

The binomial results will not apply. This calculator assumes every attack is an independent roll with the same crit probability. Use the game-specific probability rules when rolls influence later rolls.

What is a good crit rate to aim for?

There is no universal target. Compare the exact or at-least-K probability over your real rotation and, where appropriate, the expected-damage result against the alternative stats available in that game.

Crit Chance Calculator

Enter the per-hit crit rate, attacks and a target number of crits to calculate exact and cumulative binomial probabilities. The crit multiplier shows relative average damage even when base damage is unknown.

Crit Chance Parameters

Critical Hit Rate (%)

Enter a value from 0 to 100

Number of Attacks

How many hits in your rotation (1 – 10,000)

Target Critical Hits (K)

Used for exactly K and at least K probability

Normal Damage (optional)

Crit Multiplier

Quick Presets

Results

At Least 1 Crit

—

probability

Expected Crits

—

average per rotation

Zero Crits Chance

—

probability of no crits

Exactly K Crits

—

target probability

At Least K Crits

—

target probability

Average Hit Multiplier

—

relative to a normal hit

Expected Total Damage

Optional

independent-roll average

At Least 1 Crit — Visual

—

0% 50% 100%

Cumulative Crit Distribution

Crits	Exact Prob.	At Least N Crits
Enter values above to see breakdown

Model and sources

The probabilities use a binomial model: a fixed number of independent attacks, two outcomes per attack, and the same crit probability on every attack.

This does not model pity counters, pseudo-random distributions, changing proc rates, armor, caps, game-specific rounding, or patch-specific rating conversions.

NIST binomial distribution Penn State binomial conditions

Summary

How it works

Enter your base critical hit rate as a percentage (e.g. 25 for 25%).
Enter the number of attacks you plan to make in a burst or rotation.
The calculator applies the formula P(at least 1 crit) = 1 - (1 - p)^N.
Expected crits is calculated as N * p.
Results update instantly — no submit button needed.
Choose a target K to see the probability of exactly K and at least K critical hits.
Optionally enter normal-hit damage and the total crit multiplier to estimate average damage.
The effective average-hit multiplier is 1 + p × (M − 1), where M is the total crit multiplier.

Use cases

Evaluating whether increasing crit rate is worthwhile for your build.
Comparing two weapons with different crit stats in RPGs like Genshin Impact or Path of Exile.
Estimating burst damage reliability over a skill rotation in MMORPGs.
Planning ability cooldowns around expected crit windows.
Understanding crit variance in card games or tabletop RPGs.
Teaching probability concepts with an intuitive gaming context.

Frequently Asked Questions

Last updated: 2026-09-22 · Reviewed by Nham Vu