🎲 Dice Probability Calculator
Choose the number of dice, sides and a target sum to see the exact odds, plus the full probability distribution.
Exactly 7
16.67%
7 or more
58.33%
7 or less
58.33%
Possible sums: 2 to 12. Each bar is a sum's probability; the target is highlighted.
How the dice probability calculator works
Rolling several dice and adding them produces a bell-shaped distribution, not a flat one, because middle sums can be made many ways while extremes can be made only one way. This calculator computes the exact distribution for any number of dice with any number of sides by counting every combination, then gives you the probability of hitting a target sum exactly, at least, or at most, and draws the full distribution. It is ideal for tabletop RPGs and board games, and it runs in your browser.
The classic example is 2d6: a sum of 7 is the most likely (six ways to make it) while 2 and 12 are rarest (one way each). Adding more dice makes the distribution narrower and more sharply peaked around the average. This covers independent, fair dice; weighted or exploding dice are not modelled.
Frequently asked questions
What are the odds of rolling a 7 with two dice?
With two six-sided dice there are 36 equally likely outcomes and six of them sum to 7, so the probability is 6 ÷ 36 = 16.67%, the highest of any sum. This calculator shows this and the odds for every other sum.
Why is 7 more likely than 2 or 12 on 2d6?
Because there are more ways to make a middle sum. A 7 can be rolled as 1+6, 2+5, 3+4 and their reverses (six ways), while a 2 can only be 1+1 (one way). More combinations means higher probability.
How do I calculate probability for multiple dice?
Count the number of combinations that produce each sum and divide by the total number of outcomes (sides^dice). This tool does the counting for any number of dice and sides and shows exact, at-least and at-most probabilities.
What does the chart show?
The full probability distribution: each bar is the chance of that sum, with your target highlighted. It makes the bell shape of multi-dice rolls obvious at a glance.
Is anything uploaded?
No. The distribution is computed in your browser.