How do I calculate the chance of at least one crit?

Use the complement rule: P(at least 1) = 1 − (1 − p)^N, where p is the crit chance per hit and N is the number of hits. At 25% crit over 10 hits, 1 − 0.75^10 = 94.37%. The chance of at least two crits is 1 − P(0) − P(1) = 1 − 0.0563 − 0.1877 = 75.60%.

How do crit rate and crit damage combine into average damage?

Average damage multiplier = 1 + p × (M − 1), where M is the damage of a crit relative to a normal hit. A 25% chance of ×2 crits gives 1.25× average damage. In Genshin Impact and Honkai: Star Rail, M = 1 + CRIT DMG, so 60% CRIT Rate with 120% CRIT DMG gives 1 + 0.6 × 1.2 = 1.72×.

How many attacks do I need to be 90% sure of a crit?

Solve 1 − (1 − p)^N ≥ 0.9, which gives N = ⌈ln(0.1) ÷ ln(1 − p)⌉. At 25% crit you need 9 attacks, at 10% you need 22 and at 5% you need 45. Under Dota 2 pseudo-random crits you need fewer attacks at 25% and above, because a proc is guaranteed after a fixed number of misses.

What is pseudo-random distribution (PRD) in Dota 2?

Dota 2 and Warcraft III roll many crits and bashes with PRD. The first attack has a chance C, each attack without a proc adds another C, and a proc resets the chance to C. C is chosen so the long-run rate equals the listed chance: for 25% it is about 8.47%, so a proc is guaranteed by the 12th attack. PRD keeps the average the same but makes long streaks of misses or procs much rarer.

What happens if my crit rate is above 100%?

In most games crit rate is capped at 100%, so every point above it is wasted. The calculator caps the rate at 100%, shows how much is wasted and keeps the rest of the maths correct. A few games convert overcapped crit into other stats, so check your game before stacking past the cap.

Does every game use independent crit rolls?

No. Most RPGs and looter games roll every hit independently, which is what the binomial results assume. Dota 2 uses PRD, League of Legends applies its own pseudo-random adjustment to crits, and some games add pity counters. Use the PRD panel only for Dota 2-style systems.

Crit Chance Calculator

Chance of at least one crit in N hits = 1 − (1 − p)^N. Average damage multiplier = 1 + p × (M − 1), where M is the crit multiplier (×2, or 1 + CRIT DMG% in Genshin-style games). Dota 2 uses a pseudo-random distribution instead: a 25% crit starts at 8.47% and rises by 8.47% per hit without a crit.

Crit Chance Parameters

Critical Hit Rate (%)

Per-hit chance. Values above 100% are capped.

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 Damage

Crit damage is entered as

Target chance of at least 1 crit (%)

Finds how many attacks you need

Quick Presets

Results (independent rolls)

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%

Dota 2 / Warcraft III pseudo-random (PRD)

Same nominal chance, rolled the Dota 2 way: chance on the Nth attack since the last proc = N × C.

C (1st attack)

—

Guaranteed by

—

At least 1 (PRD)

—

At least K (PRD)

—

Cumulative Crit Distribution

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

PRD constants vs true random

C is the proc chance on the first attack after a proc; each miss adds another C. Values computed to match Valve's Dota 2 constants (25% → 0.0847, 50% → 0.3021).

Nominal chance	C	Guaranteed by attack	≥1 in 5 hits (PRD)	≥1 in 5 hits (random)
5%	0.380%	264	5.58%	22.62%
10%	1.475%	68	20.34%	40.95%
15%	3.222%	32	40.23%	55.63%
20%	5.570%	18	60.81%	67.23%
25%	8.474%	12	78.41%	76.27%
30%	11.895%	9	90.83%	83.19%
40%	20.155%	5	100.00%	92.22%
50%	30.210%	4	100.00%	96.88%
60%	42.265%	3	100.00%	98.98%
70%	57.143%	2	100.00%	99.76%
80%	75.000%	2	100.00%	99.97%

Worked examples

25% crit, 10 hits. No crits: 0.75¹⁰ = 5.63%, so at least one crit = 94.37%. Exactly one: 10 × 0.25 × 0.75⁹ = 18.77%, so at least two = 100 − 5.63 − 18.77 = 75.60%. Expected crits = 10 × 0.25 = 2.5.

Crit rate vs crit damage (Genshin / HSR). 60% CRIT Rate and 120% CRIT DMG: M = 1 + 1.20 = 2.2, average multiplier = 1 + 0.6 × 1.2 = 1.72×. Swapping to 70% / 100% gives 1 + 0.7 × 1.0 = 1.70×, slightly worse.

Hits for 90% odds. At 25% crit: ln(0.1) ÷ ln(0.75) = 8.004, rounded up to 9 hits (1 − 0.75⁹ = 92.5%). With Dota 2 PRD, 25% reaches 90% sooner because the chance climbs 8.47% per miss.

Model: binomial (fixed number of independent hits with the same chance) for the main results; PRD panel follows Dota 2 / Warcraft III rules. Armor, caps on crit damage and game-specific rounding are not modelled.

NIST binomial distribution Penn State binomial conditions Dota 2 wiki: pseudo-random distribution

Summary

The Crit Chance Calculator works out how often a critical hit system pays off. With independent rolls (most RPGs, Genshin Impact, Path of Exile) it gives the binomial chance of zero, exactly K and at least K crits in N attacks, the expected number of crits, and how many attacks you need for a chosen chance of at least one crit. It turns crit rate and crit damage into an average damage multiplier, caps crit rate above 100%, and adds a separate Dota 2 / Warcraft III pseudo-random distribution (PRD) panel built on Valve's C constants.

How it works

Enter the crit rate per hit. Values above 100% are capped and the wasted amount is shown.
Enter the number of attacks and a target number of crits K.
Chance of at least one crit = 1 − (1 − p)^N; chance of exactly K = C(N, K) · p^K · (1 − p)^(N − K).
Expected crits = N × p. Attacks needed for a chance c of at least one crit = ⌈ln(1 − c) ÷ ln(1 − p)⌉.
Enter crit damage as a total multiplier (×2) or as a bonus percentage (CRIT DMG 50% = ×1.5). Average hit multiplier = 1 + p × (M − 1).
The PRD panel finds the constant C for your nominal chance (the chance on the first attack, raised by C after every miss) and recomputes the odds for Dota 2-style pseudo-random crits.

Use cases

Checking the odds of landing at least one crit in a short burst or a boss rotation.
Comparing crit rate against crit damage upgrades in Genshin Impact, Honkai: Star Rail or Path of Exile.
Seeing how much crit rate is wasted above the 100% cap.
Working out how many attacks you need for a 90% or 99% chance of a crit.
Understanding why Dota 2 crits and bashes feel more consistent than true random rolls.
Teaching the binomial distribution with a gaming example.

Frequently Asked Questions

Last updated: 2026-10-10 · Reviewed by Nham Vu