Roll any combination of dice for D&D, board games, and RPGs. Supports D4 through D100 with modifiers.
This tool simulates fair dice rolls using cryptographic randomness. Each face has exactly equal probability (1/6 for a standard d6). You can roll standard 6-sided dice or choose from common tabletop RPG dice: d4, d6, d8, d10, d12, d20, and d100 (percentile). Roll multiple dice simultaneously and see the total, individual results, and distribution over many rolls.
Select the type and number of dice, then click "Roll." The dice animate and show results. The tool tracks your roll history, calculates running averages, and shows the distribution of your results. For tabletop RPG players, you can roll complex combinations like "2d6 + 4" or "4d6 drop lowest" (for character stat generation). The Probability Calculator handles the underlying math.
A single six-sided die (d6) has uniform probability: each face has a 1/6 (16.67%) chance. When rolling two dice, the probabilities of sums are not uniform. The most likely sum is 7 (probability 6/36 = 16.67%) because there are six combinations that produce it (1+6, 2+5, 3+4, 4+3, 5+2, 6+1). The least likely sums are 2 and 12, each with only a 1/36 (2.78%) probability.
Tabletop RPGs use polyhedral dice sets including d4, d6, d8, d10, d12, and d20. The d20 is central to games like Dungeons and Dragons, where rolling a natural 20 is a critical success. The probability of rolling any specific number on a d20 is 5%. Rolling "with advantage" (rolling 2d20 and taking the higher) shifts the average from 10.5 to approximately 13.8, a significant mechanical boost.
Dice have been used for randomization for over 5,000 years. Mesopotamian archaeological sites have yielded cubic dice dating to 3000 BCE. Modern applications include statistical sampling, Monte Carlo simulations, and educational probability demonstrations. The Random Number Generator provides cryptographically random numbers for applications requiring true randomness beyond what physical dice offer.
Beyond tabletop RPGs, dice are fundamental to board game design. The probability distributions created by different dice mechanics (single die vs. multiple dice, exploding dice, dice pools) create distinct gameplay feels. Rolling 2d6 produces a bell curve centered on 7, making extreme results rare and creating consistency. Rolling 1d12 produces a flat distribution where every outcome is equally likely, creating more chaos and unpredictability. Game designers choose dice mechanics to match the narrative tone they want: consistent heroic action (2d6) vs. wild unpredictable adventure (1d20). Math educators use dice extensively to teach probability concepts because the physical act of rolling makes abstract statistics tangible.
Tabletop RPGs use a standard notation for dice rolls: NdX, where N is the number of dice and X is the number of sides. "1d8" means roll one 8-sided die. "2d6" means roll two 6-sided dice and sum the results. "1d20+5" means roll one 20-sided die and add 5 to the result (a modifier). This calculator supports all standard polyhedral dice used in Dungeons and Dragons, Pathfinder, and other tabletop systems: d4, d6, d8, d10, d12, and d20. You can roll any combination of dice types simultaneously.
d4 (tetrahedron): Used for small weapon damage (daggers), minor healing, and some spell effects in D&D. Range: 1-4, average: 2.5.
d6 (cube): The most common die. Used for ability score generation (4d6 drop lowest), fireball damage, sneak attack dice, and most board games. Range: 1-6, average: 3.5.
d8 (octahedron): Used for medium weapon damage (longsword, rapier), healing spells, and hit dice for several classes. Range: 1-8, average: 4.5.
d10 (pentagonal trapezohedron): Used for heavy weapon damage and percentile rolls (two d10s make a d100). Range: 1-10, average: 5.5.
d12 (dodecahedron): Used for greataxe damage and barbarian hit dice. Range: 1-12, average: 6.5.
d20 (icosahedron): The signature D&D die. Used for attack rolls, ability checks, and saving throws. A natural 20 is a critical hit, and a natural 1 is a critical failure. Range: 1-20, average: 10.5.
In D&D 5th Edition, rolling with advantage means rolling 2d20 and taking the higher result. Disadvantage means rolling 2d20 and taking the lower. Advantage shifts the average roll from 10.5 to approximately 13.8, while disadvantage shifts it to approximately 7.2. This mechanic replaces most situational modifiers from earlier editions of D&D, simplifying gameplay while maintaining meaningful differences in outcome probability. The Probability Calculator can model the exact probability distributions for any dice combination.
Understanding dice probability improves strategic decision-making in tabletop games. For a single die, every face has equal probability (1/n for an n-sided die). For multiple dice, the distribution follows a bell curve centered on the average. With 2d6, the most common result is 7 (probability 16.7%), while 2 and 12 each have only a 2.8% chance. The average roll for any die is (max + 1) / 2: 3.5 for d6, 10.5 for d20. For advantage/disadvantage in D&D 5e (rolling 2d20 and taking the higher/lower), the expected value shifts from 10.5 to approximately 13.8 (advantage) or 7.2 (disadvantage), equivalent to roughly a +3/-3 modifier.