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Dice Roller - Roll Dice Online Free

Roll virtual dice online. Choose from D4, D6, D8, D10, D12, D20 and custom sides. Roll multiple dice at once with instant results and roll history.

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Formula

Roll = Random(1 to Sides) for each die, then sum + modifier

Each die generates a random integer from 1 to its maximum face value. Multiple dice are summed together, then any modifier is added to produce the final result.

Worked Examples

Example 1: D&D Attack Roll

Problem: A fighter with +7 to hit attacks an enemy with 15 AC. What does he need to roll?

Solution: Attack Roll = d20 + attack modifier\n\nTo hit AC 15 with +7 modifier:\nNeed: d20 + 7 โ‰ฅ 15\nd20 โ‰ฅ 15 - 7 = 8\n\nMust roll 8 or higher on d20\nProbability: 13/20 = 65% chance to hit\n\nNatural 20 always hits (critical!)\nNatural 1 always misses

Result: Need to roll 8+ on d20 (65% chance)

Example 2: Character Stat Generation

Problem: Generate ability scores using 4d6 drop lowest method.

Solution: Roll 4d6, remove lowest die, sum remaining 3.\n\nExample rolls: 4, 2, 6, 5\nDrop lowest (2): 4 + 6 + 5 = 15\n\nStatistical properties:\n- Minimum: 3 (all 1s after drop)\n- Maximum: 18 (all 6s)\n- Average: ~12.24\n- Mode: 13\n\nRepeat 6 times for all abilities.\nThis method produces higher than average scores.

Result: Typical set: 15, 14, 13, 12, 10, 8

Example 3: Damage Calculation

Problem: A rogue with 4d6 sneak attack hits with a shortsword (1d6+4). Calculate damage.

Solution: Weapon damage: 1d6 + 4 (Dex modifier)\nSneak attack: 4d6\n\nTotal: 5d6 + 4\n\nMinimum: 5 + 4 = 9 damage\nMaximum: 30 + 4 = 34 damage\nAverage: 5 ร— 3.5 + 4 = 21.5 damage\n\nOn a critical hit, roll all dice twice:\n10d6 + 4 = average 39 damage!

Result: Average 21.5 damage (9-34 range)

Frequently Asked Questions

What dice are used in Dungeons & Dragons?

D&D uses a standard 7-dice set: D4 (small weapon damage), D6 (fireball, sneak attack), D8 (longsword damage), D10 (heavy crossbow), D12 (greataxe), D20 (attack rolls, saving throws, ability checks - the most important die), and D100/percentile (random tables). The D20 is central to the d20 system - you roll it for almost every action and add modifiers.

How do I roll with advantage or disadvantage?

In D&D 5e, advantage means rolling 2d20 and taking the HIGHER result. Disadvantage means rolling 2d20 and taking the LOWER result. Advantage comes from favorable conditions, ally help, or certain abilities. Disadvantage comes from bad conditions, difficult situations, or penalties. They cancel each other out - any amount of advantage with any disadvantage means normal roll.

How does dice notation work (like 2d6+3)?

Dice notation follows the pattern: [number of dice]d[sides]+[modifier]. Examples: 2d6 = roll two six-sided dice and add them. 1d20+5 = roll one d20, add 5 to the result. 4d6 drop lowest = roll four d6, remove the lowest, sum the rest (common for character stat generation). 2d10ร—10 = roll 2d10 and multiply by 10. This notation is universal across most tabletop RPGs.

Is online dice rolling truly random?

Online dice rollers use pseudo-random number generators (PRNGs), which are deterministic algorithms that produce sequences appearing random. For gaming purposes, they're more than fair enough - the sequences pass statistical randomness tests. Physical dice can actually be LESS random due to manufacturing imperfections, worn edges, or rolling technique. For cryptographic security, specialized hardware random number generators are used.

What are percentile dice (D100)?

Percentile dice generate numbers 1-100. You can roll an actual d100 (100-sided die), or use two d10s: one for tens digit (0-9 representing 00-90) and one for ones digit (0-9). Rolling 00 and 0 equals 100, not 0. Used for percentage-based tables: 'Roll d100, on 01-15 you find treasure.' Some systems like Call of Cthulhu use percentile dice as the core mechanic.

How do different dice affect game feel?

Dice choice significantly affects gameplay feel. D20: High variance, swingy results - a peasant can sometimes beat a master. D100: Granular probabilities, skills matter more incrementally. 2d6 or 3d6: Bell curve means average results are common, extremes rare - more predictable. Dice pools (multiple dice, count successes): Scale smoothly with ability, success is probability-based. Game designers choose dice systems to create specific dramatic effects.

Background & Theory

The Dice Roller - Virtual D&D Dice & RPG Dice applies the following established principles and formulas. Probability theory provides the mathematical foundation for analysing all games of chance. The fundamental measure assigns a probability between 0 and 1 to each outcome by dividing the count of favourable outcomes by the count of equally likely total outcomes. Rolling a standard six-sided die produces a 1/6 probability for each face; the probability that a fair coin lands heads exactly three times in five tosses follows the binomial distribution with parameters n=5 and p=0.5. Expected value (EV) is the probability-weighted average outcome of a random variable: EV equals the sum of each outcome multiplied by its probability. A fair coin flip paying $1 for heads and costing $1 for tails has EV of zero. Casino games are designed with negative expected value for the player; the house edge is the casino's average percentage profit per bet. European roulette with a single zero has a house edge of 2.7 percent, while American roulette's double zero raises it to 5.26 percent. Poker hand probabilities derive from combinatorics. From a 52-card deck, the number of distinct 5-card hands is C(52,5) = 2,598,960. A royal flush can occur in only 4 ways, giving it a probability of approximately 0.000154 percent. Blackjack basic strategy tables, derived from computer simulation of millions of hands, reduce the house edge from roughly 2 percent to below 0.5 percent by specifying the optimal hit, stand, double, or split decision for every player hand against every dealer up-card. Sports betting implied probability converts decimal odds to a probability estimate: implied probability equals 1 divided by decimal odds. Odds of 2.5 imply a 40 percent probability. The Kelly Criterion provides the theoretically optimal bet fraction: f equals (bp minus q) divided by b, where b is the net odds received, p is the probability of winning, and q is the probability of losing. This formula maximises the long-run geometric growth rate of a bankroll.

History

The history behind the Dice Roller - Virtual D&D Dice & RPG Dice traces back through the following developments. Physical evidence of dice play dates to around 2500 BCE at the Indus Valley city of Mohenjo-daro, where excavators found carved cubic astragali remarkably similar to modern dice. Ancient Egyptian, Greek, and Roman cultures all incorporated dice games into both leisure and religious ritual, suggesting gambling emerged independently across early civilisations as a universal human impulse. The first systematic attempt to mathematically analyse games of chance came from Gerolamo Cardano, the Italian polymath who wrote "Liber de Ludo Aleae" (Book on Games of Chance) around 1564. Cardano derived correct probabilities for dice combinations and introduced the concept of sample space, though his work remained unpublished until 1663. The field transformed into a rigorous discipline through correspondence in 1654 between Blaise Pascal and Pierre de Fermat prompted by a gambling problem posed by the Chevalier de Mere. Their exchange established the rules of probability, including the concept of expected value. Jacob Bernoulli's "Ars Conjectandi" (1713) formalised the law of large numbers, proving that sample frequencies converge to true probabilities as trials increase. The 20th century brought two pivotal developments. Stanislaw Ulam and John von Neumann devised Monte Carlo simulation methods in 1947 while working at Los Alamos, showing that complex probabilistic systems could be analysed by random sampling. Game theory and poker strategy developed in parallel, with John von Neumann's minimax theorem providing early foundations and later work by game theorists formalisingrational play under incomplete information. Online gambling launched in the mid-1990s following the passage of the Free Trade and Processing Act in Antigua in 1994, which issued the first online casino licences. The Unlawful Internet Gambling Enforcement Act of 2006 disrupted US online gambling markets. Esports betting and video game loot box mechanics brought probability and expected value calculations to younger audiences in the 2010s, prompting regulatory scrutiny of randomised virtual reward systems across multiple jurisdictions.

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