Dice Probability Calculator: Any Dice, Any Sides, Chart

This dice probability calculator gives the chance of any total for any number of dice with any number of sides: exactly a number, at least it, or at most it. For two six-sided dice there are 36 equally likely outcomes, and a 7 is the most common total at 6 in 36, or one roll in six. Set your own dice below and the full chart updates with it.

Two dice probability chart: all 36 outcomes

Roll two fair six-sided dice and each die shows 1 to 6 independently, so there are 6 × 6 = 36 equally likely pairs. This grid shows the total of every pair. The first die is down the side and the second is across the top.

Count how often each total appears and you get the chart people look for. The 7s run along the diagonal, six of them, and the 2 and the 12 appear once each.

The chances add up to 36 in 36, which is the total probability of two dice: one. Cumulative figures come from the same chart. A total of 6 or less can be made 15 ways in 36 (41.67%), and a total of 8 or more also 15 ways (41.67%).

How to calculate dice probability

1. Count the equally likely outcomes: sides to the power of dice. Two six-sided dice: 6 × 6 = 36.
2. Count the outcomes that give the result you want. A total of 7: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1, which is 6 outcomes.
3. Divide. 6 ÷ 36 = 1/6, or 16.67%.

For "at least" and "at most", add up the counts for every total that qualifies before you divide. For a question about one die inside a larger roll, the dice are independent, so you multiply their chances: two 6s in a row on two dice is 1/6 × 1/6 = 1/36.

What is the probability of rolling doubles or at least one 6?

Doubles on two six-sided dice: 6 of the 36 pairs, so 1 in 6 (16.67%). At least one 6: it is easier to count the pairs with no 6, which is 5 × 5 = 25, so 36 − 25 = 11 pairs have at least one 6, or 30.56%. The calculator shows the "at least one" chance for whatever dice you set.

3 dice probability

Three six-sided dice have 6 × 6 × 6 = 216 outcomes, totals run from 3 to 18, and the most likely totals are 10 and 11, each with 27 ways (12.50%). The chart becomes a smoother bell shape with every die you add, because there are more ways to reach the middle than the edges. Set the dice to 3 above to see the whole table.

Chances of rolling 1, 2, 3, 4, 5 and 6 with 6 dice

That is one of each face. There are 6! = 720 orders that show every face once, out of 6 to the power of 6 = 46,656 outcomes, so the chance is 720 ÷ 46,656 = 1.54%, about 1 roll in 65.

Dice odds: chance versus odds

A chance of 1/6 is the same thing as odds of 5 to 1 against: 5 ways to miss for every way to hit. The stat card shows the chance as a percentage and as "1 in N". To convert, odds against are (1 − chance) ÷ chance, so a 25% chance is 3 to 1 against. Our gambling odds explained article covers the conversions in full.

Dice in Gift Club

Gift Club has two dice games, and this page is neutral maths for fair dice, not a description of either. Each game's guide has its own rules and tables: Dice Duel and Roll Over.

Frequently asked questions