Dice probability calculator
Why is 7 the most common roll with two dice? Because more combinations add up to it. Add dice and watch the bars turn into a bell.
Counting combinations
Every face combination of fair dice is equally likely: two six-sided dice have 6 × 6 = 36 outcomes. The probability of a sum is simply the number of combinations that produce it divided by 36. A sum of 2 needs 1 + 1 (one way); a sum of 7 has six ways. That is why the two-dice chart is a triangle peaking at 7.
Adding dice makes a bell
Set the number of dice to 3, then 5, then 10. The triangle rounds into a bell curve. Each die adds an independent random amount, and sums of many independent amounts tend to be normal: the central limit theorem at work.
How the exact answer is computed
The calculator builds the distribution one die at a time: the number of ways to reach each sum with d dice is the sum of the ways to reach it with d − 1 dice plus each possible face. This convolution gives exact counts rather than an estimate, and the simulator lets you compare them with actual random rolls.
At least one six
For "at least one" questions, use the complement: P(at least one six in n rolls) = 1 − (5/6)ⁿ. With 4 rolls that is 51.8%; the Chevalier de Méré's puzzles about this bet led Pascal and Fermat to found probability theory in 1654.
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Questions students ask
What is the probability of rolling a 7 with two dice?
6 of the 36 equally likely outcomes sum to 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), so the probability is 6/36 = 1/6 ≈ 16.67%. No other sum has as many combinations.
How do you calculate the probability of a dice sum?
Count the outcomes that give the sum and divide by the total number of outcomes, sides^dice. This calculator counts them exactly by convolution rather than by simulation.
What is the probability of rolling at least one six in four rolls?
1 − (5/6)^4 ≈ 51.8%. This was the bet in the famous 1654 letters between Pascal and Fermat.
Why does the distribution look like a bell with more dice?
A sum of many independent random values tends towards a normal distribution. That is the central limit theorem, visible here with only 3 or 4 dice.