Hong Life CalculatorsUnderstanding the D&D advantage and disadvantage probability calculator — concept and principle
In Dungeons & Dragons 5th edition, an ability check, attack roll or saving throw succeeds when one twenty-sided die (d20) plus your modifier meets or beats a target number such as a Difficulty Class (DC) or Armor Class. Advantage lets you roll two d20s and keep the higher; disadvantage makes you keep the lower. This calculator shows your chance of success in all three situations, plus the chance of rolling at least one natural 20 when you have advantage so you can judge what a spell or help action is worth.
How it is calculated
- Number needed on the die: need = target − modifier.
- Single-roll chance: p = (21 − need) ÷ 20, because the faces need, need + 1, … 20 succeed. For the default attack roll, the calculator clamps p between 5% and 95%, matching the rule that a natural 20 always hits and a natural 1 always misses; for ability checks and saving throws it does not.
- Advantage: 1 − (1 − p)². You fail only if both dice fail.
- Disadvantage: p². You succeed only if both dice succeed.
- Natural 20 with advantage: 1 − 0.95² = 9.75%, the chance that at least one of two dice shows 20.
The principle
The two dice are independent, so probabilities multiply. With disadvantage both dice must succeed, which gives p × p. With advantage it is easier to count the opposite: the only way to fail is that both dice fail, with probability (1 − p)², so success is one minus that. Advantage helps most when p is near 50%: there the gain is p(1 − p) = 25 percentage points, roughly equal to +5 on a single roll.
Worked example
- Inputs: target 15, modifier +3, so you need 15 − 3 = 12 or higher on the d20.
- Faces 12 to 20 are 9 faces, so p = 9 ÷ 20 = 45% (normal roll).
- Advantage: 1 − 0.55² = 1 − 0.3025 = 69.75%.
- Disadvantage: 0.45² = 20.25%.
- Natural 20 with advantage: 1 − 0.95² = 9.75%.
| Target number on d20 (roll ≥) | Normal |
|---|---|
| 3.75 | 95% |
| 7.5 | 82.5% |
| 11.2 | 63.75% |
| 15 | 45% |
| 18.8 | 26.25% |
| 22.5 | 7.5% |
| 30 | 5% |
How to read the result
Compare advantage with normal: here it adds 24.75 points, about the same as a +5 bonus. Disadvantage cuts the chance by the same amount. A spread like 45% / 70% / 20% shows why denying an enemy advantage or imposing disadvantage on them is one of the strongest tactical choices in the game.
Common mistakes
- Forgetting that ties succeed: meeting the DC exactly is a success, which is why the formula uses 21 − need.
- Adding advantage and disadvantage together; in 5e they cancel and you roll one die.
- Leaving the roll type on attack for an ability check or save: the 5% and 95% caps are an attack-roll rule, so checks can be 0% or 100%.
Frequently asked questions
Is advantage really worth +5?
Only near a 50% chance. At p = 0.9 advantage adds just 9 points, and at p = 0.1 it also adds only 9 points.
What is the chance of a natural 1 with disadvantage?
Also 1 − 0.95² = 9.75%, the same as rolling a 20 with advantage.
Do multiple sources of advantage stack?
No. In 5e several sources still give only two dice, and any single source of disadvantage cancels all advantage.
Sources: Wizards of the Coast, Dungeons & Dragons Player's Handbook (5th edition), chapter 7 "Using Ability Scores" (advantage and disadvantage)