Random Dice Calculator

Enter the number of dice and how many sides each die has to instantly see the possible range of outcomes and the statistically expected average roll. Works for all standard polyhedral dice — d4, d6, d8, d10, d12, d20 — as well as any custom die size you choose. Whether you are rolling for a tabletop RPG attack, resolving a board game movement, or running a probability experiment, this tool gives you the minimum possible total, maximum possible total, expected average, total number of distinct outcome combinations, and the spread between extremes. The expected average is the mathematically predicted result over many rolls, not a guarantee for any single roll. Because each die is independent, combining multiple dice narrows the effective probability distribution around the expected average — making extreme outcomes increasingly rare as the number of dice grows. This is why rolling 10d6 almost never produces all 1s or all 6s, even though those results remain theoretically possible.

For any fair die, each face is equally probable, so the expected value (average outcome) per die is the mean of all faces: (1 + sides) ÷ 2. For a standard d6 this is (1 + 6) ÷ 2 = 3.5. When rolling multiple dice, the expected total is simply the per-die average multiplied by the number of dice. The minimum possible total is always 1 per die (every die shows 1), and the maximum is the number of dice multiplied by the sides (every die shows the highest face). Total possible outcomes equals sides raised to the power of the number of dice, since each die outcome is independent.