Dice Probability Calculator

Written byOleh Soloninupdated 5 October 2026

How many dice

Faces on a die

Target sum

Condition

Result

Probability16.67%
Odds1 in 6
Average roll7
Commonest sum7
Possible outcomes36
Distribution of sums
2: 2.78% 3: 5.56% 4: 8.33% 5: 11.11% 6: 13.89% 7: 16.67% 8: 13.89% 9: 11.11% 10: 8.33% 11: 5.56% 12: 2.78%

Why seven turns up so often

Calculates the chance of rolling a given sum on any number of dice and shows the full distribution of totals.

One die is flat: every face is equally likely. Two dice are not, because there are six ways to make seven and only one to make twelve, and that asymmetry is what every dice game is built on.

Add more dice and the sum's distribution takes the shape of a bell — its absolute spread grows, while the spread of the average per die narrows. Three six-sided dice almost never total four or seventeen, and that is what makes 3d6 a usable stand-in for an average.

How to use

Enter the number of dice and how many sides each has.
Enter the total you are after.
Read the whole distribution, not just the probability of your target.
Compare the target against the mean roll: the further from the middle, the rarer the total.

The distribution of two six-sided dice

Each row is a run of this calculator with two six-sided dice. There are 36 equally likely outcomes, and the probability of a total is the share of outcomes that produce it.

The distribution is symmetric around seven and triangular in shape: seven can be made six ways, while two and twelve have one each. Hence the rule players feel but rarely count — the middle is six times likelier than the edge.

Runs of this calculator with two six-sided dice.
Total	Ways	Probability	Odds
2	1	2.78%	1 in 36
5	4	11.11%	1 in 9
7	6	16.67%	1 in 6
10	3	8.33%	1 in 12
12	1	2.78%	1 in 36

What this calculator shows

The probability of the sum you ask for, exactly, at least or at most
The average roll and the commonest total
The full distribution of every possible sum

What to keep in mind

The dice are fair and independent, and the sum is the plain total with no rerolls or modifiers.
The distribution is computed exactly rather than simulated, so the percentages are the true values.

FAQs

What is the chance of rolling 7 on two dice?

One in six, or 16.67 percent. It is the commonest total because six different pairs of faces make it.

What is the average roll?

Half the number of faces plus a half, times the number of dice. For 2d6 that is 7; for 3d6 it is 10.5.

What changes as more dice are added?

The sum becomes more bell-shaped and extreme totals get rarer, because they need every die to agree. The absolute spread still grows, with the square root of the number of dice; what narrows is the spread relative to the average. It is the central limit theorem showing up on a table.

Does 2d6 differ from 1d12?

Completely. A d12 gives every number from 1 to 12 equal weight; 2d6 makes 7 six times as likely as 12 and cannot produce a 1 at all.

Why is seven the most common total?

Because six different pairs make it: 1+6, 2+5, 3+4 and the same three reversed. Two can only be made one way — 1+1 — and so comes up six times less often.

How does the picture change with more dice?

The distribution grows more bell-shaped and the edges rarer still. With three dice the extreme total is one outcome in 216; with four, one in 1,296 — each die added makes the edge six times harder to reach.

Worked example

Seven on two dice

Input: 2 dice, 6 faces, exactly 7

Output: 16.67 percent

Note: Six of the 36 outcomes make seven, against one for twelve. That six-to-one gap is why craps pays what it pays.

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Result

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