Use NdM±k notation, for example 2d6, 3d6+2 or 4d8-1. Choose a comparison and target to see those odds.
About this tool
The Dice Probability Calculator takes standard dice notation such as "2d6", "3d6+2" or "4d8-1" and works out the exact probability of every possible total. Everything is computed in your browser with integer array math and no random rolling, so the numbers are the true theoretical odds rather than a simulation.
It parses the notation into a count N, a die size M and a modifier. It then builds the probability mass function by convolving the uniform distribution [1…M] with itself N times using dynamic programming over an array of sums, and finally shifts the whole curve by the modifier. The mean is N·(M+1)/2 + modifier, the minimum is N + modifier, the maximum is N·M + modifier, and the most likely total is the peak of the curve. For your target it sums the exact-total probabilities for "exactly", "at least" or "at most".
Type a notation string, choose a comparison and a target number, and the results update live. For 2d6 the chance of rolling exactly 7 is 6/36 = 16.67% and the average is 7. Blank or malformed notation shows an invalid-input message instead of a wrong answer.
Frequently asked questions
How is the probability computed — is it a simulation?
No. It builds the exact probability mass function by convolving the single-die uniform distribution N times, so the odds are the true mathematical values, not sampled estimates that would drift from run to run.
What dice notation is supported?
The standard NdM±k form: a die count, the letter d, the number of sides, and an optional +k or −k modifier. Examples: 2d6, 3d6+2, 4d8-1, 1d20. Spaces are ignored and case does not matter.
What does 'most likely total' mean?
It is the total with the single highest probability — the peak of the distribution. For a symmetric roll like 2d6 that is 7; for 3d6 it is 10 or 11. It is the mode, which for symmetric dice equals the mean.
What is the difference between 'at least' and 'at most'?
'At least' sums the probabilities of every total greater than or equal to your target; 'at most' sums every total less than or equal to it. 'Exactly' uses only the single target total's probability.
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