Dice probability calculator
Choose the number of dice, sides and target sum. The calculator computes the exact distribution and compares it with a reproducible roll simulation.
Theoretical and simulated distribution
The line is the exact probability and the bars show the simulation for the same dice.
Sum distribution
| Sum | Probability | Simulated frequency |
|---|---|---|
| Fill in the fields above — the result is computed on this page. | ||
How do I use this page?
- Choose exact, at most or at least.
- Enter the dice and side counts.
- Enter a possible target sum.
What this page does not do: The model assumes fair dice with equal numbers of sides and independent rolls.
Further reading
Theory — why aren't all dice sums equally likely?
The calculator lets you set the number of dice, the number of sides and a target sum, then computes the exact probability distribution and compares it with a simulated series of rolls. Every ordered outcome of d independent dice has the same probability of 1/sᵈ, but different sums arise from different numbers of such ordered outcomes, which is why they are not equally likely. The simulation shows the natural random error of a single run, and more trials bring the result closer to the theoretical distribution.
Frequently asked questions
Why are sums not equally likely?
Does it work for d20 dice?
See also
A/B test calculator
Compare two proportions in an A/B test. Calculate conversion rates, difference, uplift, z score, p value and c
A/B test planning — sample size, MDE and duration
Plan a two-proportion experiment, estimate detectable effect and traffic duration.
ACF and PACF autocorrelation calculator
Calculate ACF and PACF across time-series lags. Review the chart, reference bounds and coefficient table.