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Dice Probability Calculator

Probabilities of rolling a chosen sum on multiple dice.

Compute the probability of rolling exactly, at least, or at most a chosen sum on N fair dice with S sides each.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

Generating function over dice sums computed via dynamic programming, then divided by Sⁿ to get probabilities.

In depth

Compute the probability of rolling exactly, at least, or at most a chosen sum on N fair dice with S sides each.