Dice Probability Calculator
Calculate dice probability using your data.
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What this tool does
Calculate dice probability using your data. Fair six-sided dice, independent rolls. Sums near the middle are far more likely than extremes because many more combinations produce them.
How to use the Dice Probability Calculator
- Enter or select number of dice.
- Enter or select target sum.
- Read the calculated result; change any measurement to compare alternatives.
Formula
exact distribution of the sum by convolving single-die distributions; every face equally likely
- dice
- Number of dice
- target
- Target sum
Fair six-sided dice, independent rolls. Sums near the middle are far more likely than extremes because many more combinations produce them.
Worked example
For dice probability calculator, the following measurements illustrate the exact method: Number of dice: 2; Target sum: 7.
Inputs
- Number of dice2
- Target sum7
Result
- P(sum = target) (%)16.67
- Ways to roll the target6
- P(sum ≤ target) (%)58.33
- P(sum ≥ target) (%)58.33
- Total combinations36
Results explained
- P(sum = target) (%)
- P(sum = target) (%) from the formula above. Fair six-sided dice, independent rolls. Sums near the middle are far more likely than extremes because many more combinations produce them.
- Ways to roll the target
- Ways to roll the target from the formula above. Fair six-sided dice, independent rolls. Sums near the middle are far more likely than extremes because many more combinations produce them.
- P(sum ≤ target) (%)
- P(sum ≤ target) (%) from the formula above. Fair six-sided dice, independent rolls. Sums near the middle are far more likely than extremes because many more combinations produce them.
- P(sum ≥ target) (%)
- P(sum ≥ target) (%) from the formula above. Fair six-sided dice, independent rolls. Sums near the middle are far more likely than extremes because many more combinations produce them.
- Total combinations
- Total combinations from the formula above. Fair six-sided dice, independent rolls. Sums near the middle are far more likely than extremes because many more combinations produce them.
Frequently asked questions
exact distribution of the sum by convolving single-die distributions; every face equally likely
Fair six-sided dice, independent rolls. Sums near the middle are far more likely than extremes because many more combinations produce them.
Enter numbers only, in the units and format each label describes. Remove missing values rather than substituting zero, unless zero is a real observation.
No. Results describe the numbers you entered. Statistical inference also depends on sampling design, independence, model fit and interpretation; a p-value is not the probability that a hypothesis is true.
No. Every calculation, including the distribution algorithms, runs entirely in your browser.