Dice probability calculator
Enter a dice expression such as “2d6” and the total you want to investigate to calculate the probability of rolling exactly that total, at least that total or at most that total. View the distribution of totals and the mean, for estimating TRPG checks or learning dice probabilities.
What you can do
Check probabilities for three conditions
Compare the probabilities of a total being exactly, at least, or at most the specified value.
Read the distribution for each total
View totals and probabilities in a table and compare their likelihoods by bar length. The mean and standard deviation are also displayed.
Take all the results with you
Copy the calculation results and entire distribution, or save them as a text file.
How to use
Enter a dice expression
2d6 is the sum of two 6-sided dice. Enter 2d6+3 to add 3 to the sum, or 2d6-1 to subtract 1.
Enter the total to investigate
For example, entering 7 lets you investigate three probabilities: exactly 7, at least 7, and at most 7.
Calculate and review the distribution
Review probabilities by condition and the distribution for each total. If you change the input, calculate again.
Useful when
Estimate TRPG checks
For a check using multiple dice with the same number of sides, check the probability of reaching at least the target total.
Learn how likely each total is
Compare how likely central and extreme totals are for two 6-sided dice.
How to read dice notation and probabilities
Dice count, sides, and modifier
NdS+M means adding M to the sum of N dice with S sides. This screen handles dice that all have the same number of sides.
Why 7 is more likely with 2d6
There are 36 possible outcomes for two dice. Of these, 6 give a total of 7, while totals of 2 and 12 each have 1 outcome. Even when all sides are equally likely, totals are not equally likely.
This does not predict actual rolls
The calculation assumes independent dice with all sides equally likely. The mean is a long-term reference, and the standard deviation measures how much totals vary. These values do not guarantee the result of the next roll.
Frequently asked questions
What does 2d6 mean?
The sum of two 6-sided dice. With 2d6+3, 3 is added to that sum. Include the number of dice and sides in your input.
Does this feature actually roll dice?
No. It calculates theoretical probabilities from all combinations of outcomes. To roll dice, use the related “Dice” tool.
Can I use different numbers of sides or reroll rules?
This screen supports NdS expressions with an integer modifier added or subtracted. It does not support expressions mixing different numbers of sides, rerolls, or special rules that exclude some outcomes.
What happens if I specify a total outside the range?
For an impossible total, the probability of exactly that total is 0%. The probabilities of being at least or at most the specified value are also calculated according to that value and the possible range.
How are long distributions and small probabilities displayed?
The distribution is displayed in groups of 50 entries. Numbers on screen are rounded, and small probabilities use scientific notation. Copying and saving include the entire distribution.
Input and results
- Input
- A dice expression NdS±M and the total to investigate. Dice count: 1–100; sides: 2–100; modifier: −1,000,000–1,000,000.
- Output
- Probabilities by condition, minimum, maximum, mean, standard deviation, number of combinations, and distribution. Copy all entries or save them as text.
- Assumptions
- All sides are equally likely and dice are independent. Changing the input clears the previous results; recalculate with the new settings.