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Dice Probability Calculator
Wonder how likely you are to roll a 7? Roll two dice. Designing a tabletop game and want to know the real odds behind a skill check? This dice probability calculator will tell you the exact odds of any dice throw.
The probability of a particular sum, a range of sums, or a certain number of dice that show a chosen face.
Enter the number of dice, select the sides on each die (d4 to d100, or a custom number) and receive your answer as a percentage, a simplified fraction and odds — plus the full probability distribution so you can see how all the possible outcomes stack up.
Whether you're working out the odds of rolling snake eyes, calculating craps probability, balancing a homebrew RPG mechanic, or just settling an argument about how "lucky" a roll really was, the numbers below are calculated exactly -- not estimated by simulation.
How to Use Dice Probability Calculator
- Choose the number of dice you are rolling ( 1 to 50 ) .
- Choose how many sides each die has (standard d4, d6, d8, d10, d12, d20, d100 or type in a custom value)
- Choose what you want to know:
- Sum Probability — the likelihood that the sum of all the dice is greater than, less than, or between certain numbers.
- Face Value Probability - the chance that a certain number of dice will land on a particular face
4. Click Calculate to see the probability as a percentage, fraction and odds, plus a full breakdown of every possible total.
How to Calculate Probabilities of Dice
Dice probability is all about comparing the number of successful outcomes to the number of possible outcomes.
Single die: The probability of rolling a particular number on a fair die with s sides is:
P = 1/s
For any one face , on a normal 6 sided die , that 's 1/6 = 16.67 % .
Total outcomes for multiple dice If you roll n dice, each of s sides, then the total number of possible outcomes is:
Total outcomes = s^n
The number of possible outcomes for two six sided dice is 6^2=36 , for three dice it is 6^3=216 and so on .
Probability of a sum:
As the die rolls are independent events, the number of ways to get a certain sum is determined by convolving the outcomes of each die together.
This calculator does not estimate the full probability distribution, but instead builds it directly, so sums in the middle of the range (like 7 on 2d6) are more likely than sums at the extreme ends (like 2 or 12), the classic dice “bell curve.”
Probability of a face value on multiple dice For questions like "what's the probability that at least 2 of 5 dice show a 6", the calculator uses the binomial probability formula:
P(k successes) = C(n,k) . p^k . (1-p)^(n-k)
where n is the number of dice, k is the number of dice that should show the target , p is 1/s (the chance of that face on one die), and C(n, k) is the number of combinations of n dice taken k at a time.
Common Dice Probability Examples
| Scenario | Probability |
|---|---|
| Rolling a 7 with two six-sided dice | 16.67% (6 in 36) |
| Rolling doubles with two six-sided dice | 16.67% (6 in 36) |
| Rolling a sum of 2 (snake eyes) with 2d6 | 2.78% (1 in 36) |
| Rolling a sum of 12 (boxcars) with 2d6 | 2.78% (1 in 36) |
| Sum of 10 or higher with 2d6 | 16.67% |
| At least one 6 with two six-sided dice | 30.56% |
| Rolling a natural 20 on a d20 | 5% (1 in 20) |
| Sum between 8 and 10 with three six-sided dice | roughly 44% |
Why Some Sums of Dice Are More Probable Than Others
For one die all the faces are equally probable. But with a second die, totals are no longer equally likely. Because there are more combinations of the dice that add up to middle values than to extreme values. If you roll two 6 sided dice , there is only one way to get 2 ( 1+1 ) , but there are six ways to get 7 ( 1+6 , 2+5 , 3+4 , 4+3 , 5+2 , 6+1 ) , so 7 is the most likely outcome .
This is the same principle as in games like craps, where different point numbers have different payouts.
That is why the probability of dice sums has a triangular or bell-shaped distribution, and not a flat one.
Dice Probability Calculator
Frequently Asked Questions (FAQs)
What is the probability of rolling a specific number on a die?
For a fair die with s sides, the probability of any single number is 1/s. On a standard six-sided die, that's 1/6, or about 16.67%.
What are the odds of rolling a 7 with two dice?
Rolling a 7 with two standard six-sided dice has a probability of 6/36, or 16.67% so the highest probability of any sum on 2d6.
How do you calculate the probability of a dice sum?
First of all add up the number of dice combinations that produce that sum, now divide by the total number of possible combinations .
What's the difference between "at least" and "exactly" in dice probability?
"Exactly" asks for one specific results (e.g., exactly 3 dice showing a 6). "At least" includes that the outcome and every outcome above it (e.g., 3, 4, or 5 dice showing a 6).
"At least" probabilities are always have equal to or higher than the matching "exactly" probability.
Does the number of sides change how the probability is calculated?
Yes. The formulas stay the same for this but every 1/s term will use the actual number of sides. So a d20's odds will look very different from a d6's, even if the question are of same type.
Is this calculator can calculater the accurate for unusual dice, like d100 or 50 dice at once?
Yes. Our Dice Probability Calculator can calculate the full probability distribution mathematically for any given number of dice and any given number of sides you enter, rather than relying on simulation or rounding.
