Toolzy

Dice Probability Calculator

Calculate the probability distribution of dice roll sums for any number of dice and sides.

Probability of rolling 8 or more

41.67%

SumWaysProbabilityChart
212.78%
325.56%
438.33%
5411.11%
6513.89%
7616.67%
8513.89%
9411.11%
1038.33%
1125.56%
1212.78%

See the exact probability of every possible sum when rolling multiple dice, computed with combinatorial math rather than simulation. Set the number of dice, sides per die, and a target sum to see the chance of reaching or beating it.

How to use

  1. Enter the number of dice and sides per die.
  2. Enter a target sum to see the probability of rolling that or higher.
  3. Browse the full distribution table and bar chart below.

Frequently asked questions

How is this calculated?
It uses dynamic programming to count the exact number of ways each sum can occur across all dice combinations, then divides by the total number of possible outcomes — no simulation or randomness involved.
What's the most likely sum for two six-sided dice?
7 is the most likely sum for 2d6, since there are 6 ways to make it (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of 36 total outcomes.
What does "probability of X or more" mean?
It's the combined probability of every sum from your target value up to the maximum possible sum, useful for game mechanics like "roll 8+ to succeed".

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