🎲Dice Cumulative Probability Calculator

Enter dice type, count, and target sum to calculate the exact probability of hitting it

dice

How to Use the Dice Cumulative Probability Calculator

This tool calculates the exact probability that the sum of multiple dice rolls meets a given condition: at least, at most, or exactly equal to a target. It uses dynamic programming (DP) to compute the full probability distribution rather than approximations.

Useful for tabletop RPGs like D&D and Pathfinder, board games, or probability studies. For 2d6, rolling 7 or higher has a 58.33% chance — the most likely single outcome is 7 at about 16.67%.

Frequently Asked Questions

How do I check if a d20 roll beats a DC 15?

Set dice type to d20, count to 1, target to 15, and comparison to "at least." The result shows the probability of rolling 15 or higher — which is 30%.

How many dice can this calculator handle?

Up to 20 dice are supported. With more dice, the distribution becomes increasingly bell-shaped and centered around the mean.

Why does the distribution cluster toward the middle with more dice?

By the Central Limit Theorem, summing independent random variables produces a distribution approaching a normal curve. Extreme values become increasingly rare with more dice.