Dice Probability Calculator
Calculate the probability of rolling specific sums with multiple dice. Perfect for RPG players, board gamers, and probability students.
Dice Probability Calculator
Calculate the probability of rolling specific sums with multiple dice
Valid sums range from 2 to 12
Formula
P(sum) = favorable outcomes / total outcomesTotal outcomes for 2d6 = 6^2 = 36
Common Dice Probabilities
| Dice | Min | Max | Mean | Most Likely |
|---|---|---|---|---|
| 1d6 | 1 | 6 | 3.5 | All equal (16.7%) |
| 2d6 | 2 | 12 | 7 | 7 (16.7%) |
| 3d6 | 3 | 18 | 10.5 | 10, 11 (12.5%) |
| 1d20 | 1 | 20 | 10.5 | All equal (5%) |
| 4d6 (drop lowest) | 3 | 18 | 12.24 | 13 (13.3%) |
How to Use
- 1Select dice — Choose the number of dice and type (d4, d6, d8, d10, d12, d20, or d100).
- 2Set comparison — Choose whether you want exactly, at least, or at most the target sum.
- 3Enter target — Input the target sum you want to calculate probability for.
- 4View results — See the probability, odds, and distribution chart.
Frequently Asked Questions
What is the most likely roll with 2d6?
With 2d6 (two six-sided dice), the most likely sum is 7, which has a probability of about 16.67% (1 in 6). This is because there are 6 ways to roll a 7 out of 36 total combinations.
How do I calculate dice probability?
Dice probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For n dice with s sides, total outcomes = s^n.
What does "at least" mean for dice rolls?
"At least" means the target sum or higher. For example, "at least 10" on 2d6 includes rolling 10, 11, or 12.
Why is the distribution bell-shaped?
When rolling multiple dice, middle values have more combinations that produce them than extreme values. This creates a bell curve (normal distribution) centered around the mean.
What is the probability of rolling a natural 20?
On a single d20, the probability of rolling any specific number (including 20) is 1/20 = 5%. This is the famous "critical hit" probability in many RPGs.