Dice Probability Calculator
Odds of an exact, at-least or at-most total on 1 to 100 dice from d4 to d20, of one or every die showing a value, or of a d20 with advantage. How it works
Use the Dice Probability Calculator
About the Dice Probability Calculator
Two six-sided dice have 36 equally likely results, and 6 of them add up to 7, so the chance of rolling a 7 is 6/36 = 1/6, or 16.67%. No other total on 2d6 comes up as often. This dice probability calculator counts the ways to reach a total on 1 to 100 dice of one size (d4, d6, d8, d10, d12 or d20) and gives the chance of that exact total, that total or more, or that total or less. With two or more dice it can instead give the chance that at least one die, or every die, shows a value: at least one 6 on two d6 is 11/36, or 30.56%.
2d6: chance of each total
| Total | Ways out of 36 | Exactly this total | This total or more |
|---|---|---|---|
| 2 | 1 | 2.78% | 100.00% |
| 3 | 2 | 5.56% | 97.22% |
| 4 | 3 | 8.33% | 91.67% |
| 5 | 4 | 11.11% | 83.33% |
| 6 | 5 | 13.89% | 72.22% |
| 7 | 6 | 16.67% | 58.33% |
| 8 | 5 | 13.89% | 41.67% |
| 9 | 4 | 11.11% | 27.78% |
| 10 | 3 | 8.33% | 16.67% |
| 11 | 2 | 5.56% | 8.33% |
| 12 | 1 | 2.78% | 2.78% |
Sum equals and At Least modes with 2 d6 dice. The chances of a total and of 14 minus that total are the same, so 6 and 8 are both 5/36.
1d20: chance of rolling the target or higher
| Target | Chance | Odds against |
|---|---|---|
| 2 | 95.00% | 0.05 : 1 |
| 5 | 80.00% | 0.25 : 1 |
| 10 | 55.00% | 0.82 : 1 |
| 11 | 50.00% | 1.00 : 1 |
| 15 | 30.00% | 2.33 : 1 |
| 18 | 15.00% | 5.67 : 1 |
| 20 | 5.00% | 19.00 : 1 |
At Least mode with one d20. Each step of 1 on the target moves the chance by 5 percentage points.
3d6: chance of a total or more
| Total | Exactly | This total or more |
|---|---|---|
| 8 | 9.72% | 83.80% |
| 10 | 12.50% | 62.50% |
| 11 | 12.50% | 50.00% |
| 12 | 11.57% | 37.50% |
| 14 | 6.94% | 16.20% |
| 15 | 4.63% | 9.26% |
| 18 | 0.46% | 0.46% |
216 results. 10 and 11 are the most likely totals, 27 ways each.
At least one die or every die showing a value
| Dice | Each die shows | At least one die | All dice |
|---|---|---|---|
| 2d6 | 6 | 11/36 (30.56%) | 1/36 (2.78%) |
| 3d6 | 6 | 91/216 (42.13%) | 1/216 (0.46%) |
| 4d6 | 6 | 671/1296 (51.77%) | 1/1296 (0.08%) |
| 2d6 | 5 or more | 5/9 (55.56%) | 1/9 (11.11%) |
| 2d20 | 20 | 39/400 (9.75%) | 1/400 (0.25%) |
| 2d20 | 15 or more | 51/100 (51.00%) | 9/100 (9.00%) |
| 2d20 | 10 or more | 319/400 (79.75%) | 121/400 (30.25%) |
What to match set to At least one die or All dice, with Exact (a single face) or At Least. Two d20 where at least one must reach the target is a roll with advantage; where both must reach it, a roll with disadvantage. Roll type gives the same figures directly.
How to use this tool
- Pick the die and type how many you roll, from 1 to 100.
- With two or more dice, choose What to match: the sum of the dice, at least one die showing the value, or all dice showing it. For two d20, Roll type can instead keep the higher die (advantage) or the lower die (disadvantage).
- Choose the roll mode. Two or more dice added together offer Sum equals, At Least and At Most, and Sum equals adds a chart of every total; one die offers Exact, At Least, At Most and Sum, which is Exact plus the chart.
- Type the target: a face for one die or for an at-least-one or all-dice match, otherwise the total of all the dice.
- Read the percentage, the fraction, the decimal and the odds against and in favor.
Frequently asked questions
- What are the odds of rolling a 7 with two dice?
- 1 in 6. Six of the 36 results add to 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), which is 16.67%, odds in favor 1 : 5 and odds against 5.00 : 1. A 2 or a 12 can only be rolled one way each, 2.78%.
- What is the difference between odds and probability?
- Probability is favorable results over all results: a 6 on 2d6 is 5/36, 13.89%. Odds compare favorable with unfavorable results: 5 : 31 in favor, or 6.20 : 1 against, which means 6.2 misses for every hit.
- How do I include a modifier, like 1d20 + 5 against 15?
- Subtract the modifier from the target and enter what the die alone must roll. 1d20 + 5 needs 10 or more on the die: At Least 10 on one d20 is 55.00%, or 11/20.
- What is the chance of a natural 20?
- 1/20, or 5.00%, on one d20. Choose d20, 1 die, Exact and target 20. Odds against are 19.00 : 1.
- Where is the chart of every total?
- With two or more dice added together, Sum equals shows the chance of that total and a bar chart of every possible total with your target highlighted: use it to see the bell shape of 3d6. With one die, Sum gives the same number as Exact and adds the chart, which shows how flat one d20 is.
- Can it work out advantage or at least one 6?
- Yes. Roll 2 d20 and set Roll type to Advantage (keep the higher die) or Disadvantage (keep the lower die), then choose At Least and the target. A 15 or more is 204/400, 51.00%, with advantage and 36/400, 9.00%, with disadvantage, against 30.00% on one d20; a natural 20 is 39/400, 9.75%, with advantage. For at least one 6, set What to match to At least one die shows the value: on four d6 it is 671/1296, 51.77%, which is 1 − (5/6)⁴. Dropping the lowest die, exploding dice and mixed sets such as 2d6 + 1d8 are not covered.
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