Probability
Dice Probability Calculator
Calculate exact probabilities for a selected total when rolling standard fair dice. Inspect the complete distribution, compare at-least and at-most probabilities, visualize every possible sum, and export a professional PDF analysis.
Exact target probability0%
Favorable outcomes0 of 0
Probability at least target0%
Probability at most target0%
Expected sum0
Exact distribution
Probability of every possible total
Dice-sum distributionFair independent dice
| Total | Outcome count | Exact probability | Cumulative at most | Cumulative at least |
|---|
Dice distribution
Target total inside the dice-sum distribution
The target, favorable outcomes, and at-least or at-most context are visible together.
Target total inside the dice-sum distribution
1
2
7
...
Exact target0%
Favorable0
At least target0%
At most target0%
How to use Dice Probability Calculator
- Enter number of dice, sides per die, and the target total.
- Review exact target probability, favorable outcomes, at-least probability, at-most probability, and expected sum.
- Use the distribution table to see whether the target is near the center of the distribution or in a tail.
Calculator guide
Understanding Dice Probability Calculator
The sum of fair dice is not uniformly distributed because middle totals can be formed in more ways than extreme totals. Enumerating outcomes produces exact probabilities for each possible sum.
Calculation method
How the calculation works
Probability of a total = favorable equally likely outcomes / total outcomes, where total outcomes = sides^dice. Build the sum distribution one die at a time, count the outcomes for every total, and divide each count by sides raised to the number of dice.
Dice probability method
Fair dice limits
Worked situations
Practical examples
- Find the probability of rolling a total of 7 with two six-sided dice.
- Compare the probability of rolling at least a selected total.
- See how the sum distribution changes as the number of dice increases.
Better inputs
Useful tips
- Use at-least probability for thresholds and exact probability for a single total.
- Remember that identical-looking sums may have different numbers of ordered combinations.
- Compare the target with the mean sum before interpreting whether it is unusual.
Before relying on the result
Limitations and common mistakes
- Dice are assumed independent, fair, and identical.
- Only totals are modeled, not patterns such as doubles or specific faces.
- Large dice pools are limited to keep the interactive distribution readable.
Reference
Key terms
- Sample space
- The complete set of possible outcomes.
- Favorable outcome
- An outcome satisfying the selected event.
- Exact probability
- Chance of one specific total.
- Cumulative probability
- Combined chance across a range of totals.
Important note
Calculated directly from the entered values using the displayed formula and rounding settings.
Frequently asked questions
Why is 7 common with two six-sided dice?
Six ordered outcomes sum to 7, more than for any other total.
Are all totals equally likely?
No. Individual dice faces are uniform, but sums have different numbers of combinations.
What does at least mean?
It includes the selected total and every larger possible total.
Does the order of dice matter?
Ordered outcomes are counted because each physical die can show its own result.