Dice Probability Calculator
Calculate the probability of an exact, maximum or minimum sum for identical fair independent dice.
Calculations stay in your browser.
- Probability (approximate)
- Exact fraction
- Possible sum range
Each die has faces numbered 1 through m, all equally likely. Dice are identical and independent. This model does not determine whether real dice are fair or whether cheating occurred.
Dynamic programming combines the equally likely faces for each die. It counts outcomes exactly; the displayed percentage is rounded. No random simulation is used.
The sum ranges from n to n × m. Targets outside this range give 0% or 100% according to the selected event.
A QUICK WALKTHROUGH
How to use this tool
- Enter the number of dice, sides per die and target sum.
- Choose exactly, at most or at least, then calculate.
- Read the exact fraction and approximate percentage.
Probability model
Each die has faces numbered 1 through m, all equally likely. Dice are identical and independent. This model does not determine whether real dice are fair or whether cheating occurred.
Calculation and limits
Dynamic programming combines the equally likely faces for each die. It counts outcomes exactly; the displayed percentage is rounded. No random simulation is used. The sum ranges from n to n × m. Targets outside this range give 0% or 100% according to the selected event. Calculations stay in your browser.
GOOD TO KNOW
Common questions
Can the target be outside the possible range?
Yes. Impossible events return 0%; certain events return 100%.