Dice Probability Calculator
Exact counts, not a normal approximation that fails at the tails.
Work out Dice Probability. Exact counts, not a normal approximation that fails at the tails. States the assumption instead of hiding it.
Chance of rolling exactly 7
16.667%
6 of 36 possible rolls
These are exact counts, not approximations. The number of ways to make each total is built up die by die, so the tails are right — which matters, because the normal approximation people reach for is visibly wrong at exactly the extremes anyone is asking about. The distribution of a dice sum is not flat. On two six-sided dice there are six ways to make 7 and one to make 12, which is the whole basis of every dice game ever designed. The average total is always the number of dice times the average face value — 3.5 on a d6 — and it sits at the peak of the distribution when the dice are identical.
How the Dice Probability Calculator works
The exact probability of rolling a given total on any number of dice, with cumulative figures for at least and at most. The counts are built up die by die, so the tails — where everyone is actually asking — come out right.
Also known as: chance of rolling a 7 · 2d6 probability chart · odds of rolling snake eyes · probability of dice total
Frequently asked questions
What is the probability of rolling a 7 with two dice?
One in six, or 16.67%. There are six ways to make 7 out of 36 possible rolls, more than any other total, which is the basis of every dice game ever designed.
Why is 7 more likely than 12?
Because there are six combinations that sum to 7 and only one that sums to 12. Totals in the middle can be made more ways, so the distribution peaks at the centre rather than being flat.
How do I calculate probability for more than two dice?
By counting combinations, which grows impractical by hand — three dice have 216 outcomes and six have 46,656. This builds the count up one die at a time, which stays exact at any number of dice.
Is the distribution of dice sums normal?
It approaches normal as dice are added, but it is not normal, and the approximation is worst at the extremes. Since the extremes are what people ask about, exact counts are used here instead.
What is the average roll on a die?
Half of the sides plus one — 3.5 on a d6, 10.5 on a d20. For several dice, multiply by the number of dice, which also lands exactly on the peak of the distribution.
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