Dice Odds Calculator
Exact average, range, and hit chance for any dice pool.
What it does
Dice odds count exact combinations instead of simulating rolls. Two six sided dice make 36 ordered pairs, and counting how many reach each total gives probabilities that never wobble with sample size.
The tool above takes dice count, sides, and a target sum. It returns the average roll, the min to max range, and the exact chance of reaching the target or more across all combos.
The default of 2d6 against 9 counts 10 winning pairs out of 36 (four ways to 9, three to 10, two to 11, one to 12): 27.78%. The average 7 sits mid range with 2 and 12 at the far ends.
The counting follows Khan Academy probability units with the same combination tables in LibreTexts statistics references. Both treat fair dice as uniform: every face lands with equal chance on every roll.
How to use
- Enter how many dice roll together, 1 to 10.
- Enter the sides per die, 2 to 20.
- Enter the target sum you need to reach or beat.
- Read the average first for the typical roll.
- Read the chance for the exact hit rate.
Formula
- (sides+1)/2
- Mean of one fair die.
- sides^dice
- Total ordered outcomes counted exactly.
- target+
- Sums at or above the entered target.
Pools past 100,000 combos are rejected to keep counting exact instead of sampled. Modifier bonuses (like +3) shift the target down by the bonus before entering.
Worked example
Example: 2d6, target 9+
Two six sided dice, need 9 or more.
- Combos: 6^2 = 36 ordered pairs.
- Average: 2 x 7 / 2 = 7. Range 2 to 12.
- Winners: 9 has 4, 10 has 3, 11 has 2, 12 has 1: 10 total.
- Chance: 10 / 36 = 27.78%.
- Tool shows 7, 2 to 12, 27.78%.
Reference table
| Target+ | Winners | Chance |
|---|---|---|
| 7+ | 21 of 36 | 58.33% |
| 9+ | 10 of 36 | 27.78% |
| 11+ | 3 of 36 | 8.33% |
| 12 | 1 of 36 | 2.78% |
Limits
- Fair dice only; weighting breaks uniformity.
- Exact counting capped at 100,000 combos.
- Sums only; keep highest or drop lowest need other math.
- Independent rolls assumed every throw.
Common mistakes
- Reading 7 as the most common single die face instead of the pair average.
- Counting 12 as likely as 7 on 2d6 (1 vs 6 ways).
- Adding averages of different dice wrongly.
- Trusting short hot streaks over exact odds.
- Entering the bonus into sides instead of shifting target.
Try it yourself
Quick checks. Answers sit tucked under each question.
1d20 target 15+?
6 of 20 faces: 30%, average 10.5.
1d6 target 4+?
3 of 6 faces: 50%, average 3.5.
2d6 target 7+?
21 of 36: 58.33%.
Questions
What are the odds of rolling 9 on 2d6?
Exactly 9 lands 4 of 36 (11.11%); 9 or more lands 10 of 36 (27.78%).
Why is 7 the average of 2d6?
Each die averages 3.5, and averages add: 3.5 + 3.5 = 7.
Most common 2d6 total?
7 with 6 ways. Ends 2 and 12 hold one way each.
How does a +3 bonus fit?
Lower the target by 3 first, then read the chance for the shifted number.
Does past rolling matter?
No. Dice hold no memory, so every throw reruns the same odds.
Why cap combos?
Exact counting grows as sides^dice; past 100,000 the page refuses instead of sampling.