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Dice Roll Probability Calculator - Online Sum & Graph

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Dice Roll Probability Calculator

Calculate the probability distribution of sums when rolling multiple identical dice. Perfect for board games, D&D, and statistics.

Frequently Asked Questions

We use dynamic programming to count all possible combinations of dice faces that result in each sum. The probability of a specific sum equals the number of favorable combinations divided by the total number of outcomes (facesnumber of dice).

For 2d6, the most probable sum is 7, with a probability of about 16.67% (1/6). This is the peak of the symmetric triangular distribution.

This calculator handles multiple dice of the same type. For mixed dice (e.g., 1d4 + 1d6), you can combine the distributions manually or use a convolution method. We may add this feature in a future update.

The odds are shown as a percentage and a relative bar in the distribution table. For example, rolling a total of 4 with 2d6 has a probability of 8.33% (3/36).

In Dungeons & Dragons, you often roll multiple d20s, d6s for damage, or d8s for healing. Use this tool to understand the likelihood of meeting a target number or to balance homebrew rules.

The expected sum of n identical dice with s sides equals n Ă— (1 + s) / 2. For example, 3d6 has an average of 10.5. The actual distribution becomes more bell-shaped as n increases.

For fair dice with the same number of faces, the distribution of sums is always symmetric around the mean because each outcome (face value) is equally likely and the dice are independent.

Add up the probabilities of all sums equal to or greater than your target. Our table displays individual probabilities; you can quickly sum them manually or export the data for further analysis.
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