Dice Probability Calculator | Visualize NdM Roll Distributions
Type in how many dice you roll and how many sides each has, and see the odds for every possible total on a bar chart. From classic 2d6 to 3d8 or 4d20, the full NdM distribution appears at a glance.
💡 About this tool
If you play tabletop RPGs or design board games, you constantly ask "how likely is this roll, really?" Knowing that 7 comes up most often on 2d6 is one thing — knowing it lands exactly 16.67% of the time, and seeing how the curve flattens or sharpens as you add dice, is what actually informs balance decisions. Counting combinations by hand gets hopeless fast: the number of outcomes grows as sides raised to the power of dice.
This calculator takes a dice count (1–20) and side count (2–100), then instantly reports the minimum, maximum, mean and total number of combinations, and draws a bar chart of every sum's probability. For 2d6 it works through all 36 combinations and highlights 7 at 16.67% as the tallest bar. Add more dice and watch the distribution pull toward the center into a familiar bell shape.
🧐 Frequently asked questions
What is the most likely total on 2d6? Seven. It can be made six ways — (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) — out of 36 total combinations, which is 6/36 = 16.67%. The extremes 2 and 12 each occur just once, at 2.78%.
How does the shape change as I add dice? A single die is flat — every face is equally likely. Two dice form a triangle, and by about four dice the shape is already close to a bell curve. By the central limit theorem, the more dice you sum, the more the distribution resembles a normal curve.
How is the average calculated? A single M-sided die averages (M+1)/2. For N dice the mean is N × (M+1)/2. So 3d6 averages 3 × 3.5 = 10.5.
Does it handle d20 or large dice? Yes — set sides to 20, or anything from 2 to 100, with 1 to 20 dice. Inputs that would produce an extremely large number of combinations are capped to keep the chart responsive.
📚 Reading the bell curve in dice notation
The "d" in 2d6 stands for dice, and the NdM format — count, then sides — is the shared shorthand across RPG systems worldwide. Modifiers like 2d6+3 simply shift the whole distribution up; the shape stays the same, which is why this tool charts the raw sum first. Designers favor multiple dice over a single one precisely because the bell shape clusters results near the average and makes wild extremes rare, giving more predictable, "swingy-but-fair" outcomes than a flat single-die roll.