Table probability reference
Read the odds before the dice land.
A d20 is flat, two d6 form a curve, and a d100 maps directly to percentages. Use the table that matches the roll instead of treating every total the same way.
D20 target-at-or-above reference
On a fair d20, each face has a 5% chance. For target T and modifier M, the natural face needed is N = T − M. For ordinary target-at-or-above arithmetic, successful faces = max(0, min(20, 21 − N)), and chance = successful faces ÷ 20. This formula does not add special natural-1 or natural-20 rules.
| Target total | Modifier | Natural face needed | Successful faces | Chance |
|---|---|---|---|---|
| 5 | +0 | 5 | 16 of 20 | 80% |
| 10 | +0 | 10 | 11 of 20 | 55% |
| 15 | +0 | 15 | 6 of 20 | 30% |
| 15 | +5 | 10 | 11 of 20 | 55% |
| 20 | +3 | 17 | 4 of 20 | 20% |
A modifier changes the face needed, not the die. Advantage and disadvantage are outside that single-d20 formula: if a single-roll success chance is p, advantage is 1 − (1 − p)² and disadvantage is p², assuming two independent d20s and a keep-high or keep-low rule. At 55%, those are 79.75% and 30.25%. Rerolls and special natural-face rules need their own calculation.
Complete 2d6 total distribution
Two six-sided dice produce 36 equally likely face pairs, but the totals are not equally likely. Six pairs total 7; only one pair totals 2 and one totals 12.
| Total | Ways out of 36 | Chance |
|---|---|---|
| 2 | 1 | 2.78% |
| 3 | 2 | 5.56% |
| 4 | 3 | 8.33% |
| 5 | 4 | 11.11% |
| 6 | 5 | 13.89% |
| 7 | 6 | 16.67% |
| 8 | 5 | 13.89% |
| 9 | 4 | 11.11% |
| 10 | 3 | 8.33% |
| 11 | 2 | 5.56% |
| 12 | 1 | 2.78% |
Use 2d6 when a game intentionally makes middle totals more common than extremes. The roller shows both dice and their sum; the game determines what that total means.
D100 roll-under examples
A uniform d100 gives every integer from 1 to 100 a 1% chance. With an inclusive “roll equal to or under” rule, target 25 succeeds on 1–25 (25%), target 50 on 1–50 (50%), and target 73 on 1–73 (73%). If a table uses strictly under instead, target 73 succeeds only on 1–72 (72%); declare that boundary before rolling.
The tool supports one physical 100-sided die and two-d10 percentile mode. Both cover 1–100, but the visible dice are read differently. The d100 guide explains 00 + 0 = 100, 00 + 7 = 7 and when to choose each mode.
Worked interpretations
- D20: target 15 with
+5needs a natural 10. Eleven faces, 10 through 20, succeed, so the chance is 55% before any special face rule. - 2d6: a game that succeeds on 8 or higher accepts totals 8–12: 5 + 4 + 3 + 2 + 1 = 15 outcomes out of 36, or 41.67%.
- D100: an inclusive roll-under target of 37 has 37 successful values. A result of 38 misses by one; it is not a 38% chance after the roll.
What these numbers assume
- Each face is equally likely within the selected result path.
- Each die is treated as an independent roll.
- No reroll, keep-high, keep-low or exploding-die rule has been applied.
- Modifiers change totals or thresholds; they do not change a fair die's face probabilities.
For accepted input formats, read the dice notation guide. For the physical and fallback result paths, read How It Works.