How does D&D 5e calculate critical hit damage?

On a critical hit you roll all of the attack's damage dice twice and add them together, then add the modifier once. For example, a 1d8+4 attack crits for 2d8+4. The modifier is never doubled — only the dice are.

Does sneak attack damage double on a critical hit?

Yes. Sneak Attack is part of the attack's damage roll, so all of its dice are doubled on a crit. A Rogue with 3d6 Sneak Attack and a 1d6 shortsword deals 2d6 (weapon) + 6d6 (sneak) + modifier on a crit.

Does Divine Smite double on a critical hit?

Yes. The PHB specifies that all damage dice from the attack — including Divine Smite dice — are doubled on a critical hit. A 3rd-level spell slot smite (normally 4d8) becomes 8d8 on a crit.

What is the Savage Attacks / Brutal Critical extra die?

Half-Orc Savage Attacks and Barbarian Brutal Critical each add one (or more at higher levels) weapon damage die on a crit. Crucially, this extra die is added once — it does not get doubled a second time because the base dice are already doubled. Use the Extra Critical Dice fields for these.

What is the expected value formula for dice?

The expected value of rolling k dice each with n sides is k times (n plus 1) divided by 2, written E[kdn] = k(n+1)/2. A 1d8 averages 4.5, a 2d6 averages 7, and their doubled crit versions are simply twice those amounts, plus modifier once.

Does the modifier double on a critical hit?

No. Per the 5e rules, only the damage dice are doubled. Flat bonuses — ability score modifier, proficiency (for attack cantrips), magic weapon bonus — are added once, exactly as in a normal hit.

D&D Critical Hit Calculator

A critical hit in Dungeons and Dragons 5th Edition is one of the most exciting moments at the table. When a d20 shows a natural 20 — or a lower number if you have an Improved Critical feature — you roll all the attack’s damage dice twice and add the result. Sounds simple enough, but once you factor in Sneak Attack, Divine Smite, Savage Attacks, Brutal Critical, magic weapon bonuses, and a lowered crit threshold, the arithmetic gets surprisingly involved. This calculator does all of it instantly and shows you the full probability distribution so you know exactly how explosive that crit can be.

How the maths works

Every damage roll has two components: dice and flat modifiers. On a critical hit the rules say to roll the dice twice (not to multiply the total — only the dice). The modifier is added once, just as it is on any normal hit.

The expected value of rolling k dice each with n faces is:

E[kdn] = k(n+1)/2

A 1d8 weapon averages 4.5; on a crit you roll 2d8, so the average becomes 9 — double the dice, not double the whole damage expression. Add a +4 STR modifier and you get a normal average of 8.5 and a crit average of 13.

When you add extra dice — say 3d6 Sneak Attack — those dice also double on a crit (they are part of the attack’s damage roll). So a Rogue with a 1d6 shortsword and 3d6 Sneak Attack hits for 4d6 + modifier normally and 8d6 + modifier on a crit, giving a normal average of 14 + modifier and a crit average of 28 + modifier.

Probability distribution

The calculator goes beyond averages. It performs an exact probability convolution across all possible dice combinations. The bar charts you see are the true probability mass functions — not approximations. You can read off the most likely damage value (the peak of the chart), see how wide the spread is, and understand how a lower crit threshold changes your expected damage per round.

Worked example — Rogue / Paladin multiclass

Suppose you are playing a level 7 Rogue (4 Sneak Attack dice = 4d6) multiclassed with 1 level of Paladin, using a 1d8 rapier with a +4 DEX modifier. You burn a 2nd-level spell slot on Divine Smite (3d8 radiant). On a regular hit:

Weapon: 1d8 (avg 4.5)
Sneak Attack: 4d6 (avg 14)
Divine Smite: 3d8 (avg 13.5)
Modifier: +4
Normal total avg: 36

On a crit (all dice doubled):

Weapon crit: 2d8 (avg 9)
Sneak Attack crit: 8d6 (avg 28)
Divine Smite crit: 6d8 (avg 27)
Modifier: +4 (once)
Crit total avg: 68 — nearly twice the normal hit

The maximum possible roll is 16 (max 2d8) + 48 (max 8d6) + 48 (max 6d8) + 4 = 116 damage from a single attack. Enter these exact numbers into the calculator to see the full distribution.

Formula note

The complete formula for a critical hit roll is:

Crit damage = (2 x base dice) + (2 x doubled-group dice) + extra-crit-only dice + modifier

where “extra-crit-only dice” means features like Savage Attacks (Half-Orc racial) or Brutal Critical (Barbarian class feature at levels 9, 13, 17) that add one weapon damage die on a crit but do not themselves get doubled. The calculator models both types correctly via the “Doubles on crit?” toggle for each extra dice group.