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Critical Hit Probability in D&D: Math Behind the Natural 20

The complete mathematics of critical hits in Dungeons & Dragons — probability of critting, critical damage calculations, features that improve crit chance, and Lucky vs Advantage.

Quick Answer: A natural 20 (critical hit) occurs 5% of the time — 1 in every 20 attacks. With Advantage, the probability rises to 9.75% (1 - (19/20)² = 9.75%). A Champion Fighter's Improved Critical hit on 19-20 gives 10% base, and with Advantage: approximately 19%.

Base Critical Hit Probability

In D&D 5e, a natural 20 on an attack roll is always a critical hit regardless of the target's Armor Class. The probability is always 1/20 = 5%. Additionally, attacks always miss on a natural 1 and always hit on a natural 20 — these are absolute rules that modifiers cannot override.

ConditionCrit RangeBase ProbabilityWith Advantage
Standard205%9.75%
Champion Fighter (3rd level)19-2010%19%
Champion Fighter (15th level)18-2015%27.75%
Hexblade Warlock (Hex Warrior)205%9.75%
Paladin Divine Smite on Crit205%Bonus damage doubling

Critical Hit Damage Calculation

On a critical hit, you roll all the weapon's damage dice twice. A longsword normally does 1d8 damage — on a crit, you roll 2d8 + modifier. A greatsword (2d6) crits for 4d6 + modifier. Spell attacks also crit and double their damage dice.

Lucky Feat vs Advantage for Crits

The Lucky feat lets you add a third d20 to any roll and choose which to use. This gives you three chances at a 20 rather than two. P(crit with Lucky) = 1 - (19/20)³ ≈ 14.3% — higher than Advantage's 9.75%. However Lucky is limited to 3 uses per long rest, while Advantage can apply every attack.

Frequently Asked Questions

What is the probability of rolling a critical hit in D&D?

Exactly 5% (1 in 20) for a standard character. With Advantage (rolling 2d20, taking the higher): 9.75%. With Champion Fighter's Improved Critical (19-20 range): 10%, or 19% with Advantage.

How does Advantage affect critical hit chance?

With Advantage, P(crit) = 1 - (19/20)² = 9.75% — approximately double the base 5%. Rolling two dice and taking the higher significantly boosts crit probability.

What is the most damage on a critical hit in D&D 5e?

High damage crits typically involve Barbarian's Brutal Critical (extra damage die), Paladin Divine Smite, or Rogue Sneak Attack damage — all doubled on a crit. A high-level Paladin with Divine Smite on a crit can deal 10d8 + weapon damage in a single hit.