Dice Roller & Probability Calculator
Type any dice expression to see its exact probability distribution, average and the odds of beating a target number. Then roll it with a fair, cryptographically random dice roller.
Examples: 2d6+3, 4d6dl1 (drop lowest), 2d20kh1 (keep highest), 1d20 adv, d%.
Roll history
Full probability table
| Result | Exactly | At least | At most |
|---|
How to read dice notation
Dice expressions use the standard NdS format: N is the number of dice and S is the number of sides. 3d6 means roll three six-sided dice and add them. You can combine dice and numbers with plus and minus signs, so 1d8+1d6+3 is a weapon hit with extra damage and a +3 modifier.
| Notation | Meaning | Example use |
|---|---|---|
2d6+3 | Roll two d6 and add 3 | Greatsword damage |
4d6dl1 | Roll four d6, drop the lowest | Rolling ability scores |
2d20kh1 or 1d20 adv | Roll two d20, keep the highest | Advantage |
2d20kl1 or 1d20 dis | Roll two d20, keep the lowest | Disadvantage |
d% | A percentile roll, 1–100 | Random tables, wild magic |
3d6-1d4 | Subtract a die from a roll | Any custom formula |
The calculator works out the exact probability of every result. It does not simulate thousands of rolls, so the numbers are precise even for rare outcomes.
Advantage and disadvantage odds
Advantage means rolling two d20s and using the higher one; disadvantage uses the lower one. The table shows the chance of rolling at least a given number on the d20 itself, before modifiers.
| Need at least | Normal | Advantage | Disadvantage | Advantage gain |
|---|---|---|---|---|
| 2 | 95% | 99.75% | 90.25% | +4.75% |
| 3 | 90% | 99% | 81% | +9% |
| 4 | 85% | 97.75% | 72.25% | +12.75% |
| 5 | 80% | 96% | 64% | +16% |
| 6 | 75% | 93.75% | 56.25% | +18.75% |
| 7 | 70% | 91% | 49% | +21% |
| 8 | 65% | 87.75% | 42.25% | +22.75% |
| 9 | 60% | 84% | 36% | +24% |
| 10 | 55% | 79.75% | 30.25% | +24.75% |
| 11 | 50% | 75% | 25% | +25% |
| 12 | 45% | 69.75% | 20.25% | +24.75% |
| 13 | 40% | 64% | 16% | +24% |
| 14 | 35% | 57.75% | 12.25% | +22.75% |
| 15 | 30% | 51% | 9% | +21% |
| 16 | 25% | 43.75% | 6.25% | +18.75% |
| 17 | 20% | 36% | 4% | +16% |
| 18 | 15% | 27.75% | 2.25% | +12.75% |
| 19 | 10% | 19% | 1% | +9% |
| 20 | 5% | 9.75% | 0.25% | +4.75% |
Advantage helps most when you need an 11 (a 25-point jump, roughly like a +5 bonus) and least at the extremes. On average it raises a d20 roll from 10.5 to about 13.8.
Average results of common rolls
| Roll | Average | Range | Typical use |
|---|---|---|---|
| 1d4 | 2.5 | 1–4 | Dagger, Bless, Guidance |
| 1d6 | 3.5 | 1–6 | Shortsword, Sneak Attack die |
| 1d8 | 4.5 | 1–8 | Longsword, Rapier |
| 1d10 | 5.5 | 1–10 | Fire Bolt, Heavy crossbow |
| 1d12 | 6.5 | 1–12 | Greataxe |
| 2d6 | 7 | 2–12 | Greatsword, Maul |
| 3d6 | 10.5 | 3–18 | Classic ability score roll |
| 4d6 drop lowest | 12.24 | 3–18 | Standard ability score roll |
| 8d6 | 28 | 8–48 | Fireball, Lightning Bolt |
| 1d20 | 10.5 | 1–20 | Attacks, checks and saves |
Why 2d6 and 1d12 feel different
Both 2d6 and 1d12 deal similar damage on average (7 and 6.5), but their shapes are very different. Every result on a d12 is equally likely, while 2d6 clusters around 7: you roll a 7 one time in six, but a 2 or a 12 only one time in 36. More dice means more consistent results. Type both expressions above and compare the charts.
Rolling ability scores: 4d6 drop the lowest
Rolling four d6 and dropping the lowest gives an average of about 12.24 per ability. The most likely single result is 13, and you have roughly a 1.6% chance of an 18 on any given roll. Compare that with the point buy calculator, where every player gets the same 27 points.
Is the dice roller fair?
Yes. Each die is rolled with your browser's cryptographic random number generator and rejection sampling, so every face has exactly the same chance. The roll history keeps your last ten results so you can check them at the table.