Every number here is exact, worked out from every possible roll rather than estimated from random samples. For a roll like 2d6+3, the calculator lists every total, how likely each one is, and your chance of rolling at least a target number. The expected value is the average total: N × (sides + 1) ÷ 2 + modifier, so 2d6+3 averages 10 and 8d6 averages 28.
Chance to hit, advantage and disadvantage
For a d20 roll, work out the number you need on the die: the DC or AC minus your bonus. Each face is 5%, so a +5 attack against AC 15 needs a 10 or higher, which is 11 faces, or 55%.
- •Advantage rolls two d20s and keeps the higher one. Your chance becomes 1 − (1 − p)². At 55% that is 79.75%.
- •Disadvantage keeps the lower one: p². At 55% that is 30.25%.
- •Elven Accuracy (a feat from Xanathar’s Guide to Everything, not in either SRD) lets you reroll one of your advantage dice. Rerolling the lower die works out the same as rolling three d20s and keeping the highest: 1 − (1 − p)³, or 90.9% at 55%.
On an attack roll, a natural 20 always hits and a natural 1 always misses, whatever the bonus. Ability checks and saving throws have no automatic success or failure, so you can switch that rule off.
Critical hits
A normal attack crits on a natural 20: 5%. With advantage it is 9.75%, and with Elven Accuracy 14.3%. The Champion’s Improved Critical crits on 19–20 (10%, or 19% with advantage), and Superior Critical on 18–20 (15%). A roll in your crit range is a critical hit, so the calculator counts it as a hit even when the total would miss.
Worked example
A ranger at +7 attacks an AC 16 creature. She needs a 9 on the d20: 12 faces, 60%. With advantage she hits 84% of the time and crits 9.75% of the time. Under disadvantage she hits only 36%. Her 1d8+4 arrow averages 8.5 damage, or 13 on a crit, since a crit rolls the damage dice twice.
To turn those odds into damage per round across several attacks, use the damage calculator. To roll the dice, open the dice roller. Bless adds a d4 to the roll, which you can model here as 1d20+1d4+7 against the AC.
Sources: SRD 5.1 and SRD 5.2.1 by Wizards of the Coast (CC-BY-4.0): "Advantage and Disadvantage", "Rolling 1 or 20" and "Critical Hits", and the Champion’s Improved Critical and Superior Critical. Elven Accuracy: Xanathar’s Guide to Everything p. 74.