Dice Roller

How to Use the Dice Roller

Rolling dice online takes seconds, but the settings control the odds of every outcome. Follow these steps to get exactly the roll you need for your game.

1. Choose how many dice to roll. Use the “Number of dice” dropdown to select from 1 to 6 dice. Most tabletop moments need just one or two dice — a D&D attack roll is 1d20, while Settlers of Catan production rolls are 2d6 — but rolling 4d6 (drop the lowest) for ability scores or 6d6 for a fireball’s damage is common too.
2. Pick the die size. Use “Sides per die” to choose d4, d6, d8, d10, d12, d20, or d100. The d20 is the workhorse of Dungeons & Dragons; the d6 dominates board games; the d100 (percentile dice) handles random tables and loot charts. Each die is fair: every face has exactly the same probability.
3. Roll. Click Roll Dice. The tool uses your browser’s cryptographically secure random number generator (crypto.getRandomValues), so results are as unbiased as a precision-machined casino die — actually more so, since physical dice can have tiny manufacturing imperfections.
4. Read the total and the breakdown. The big number is the sum of all dice. Below it, the individual die results are listed (for example, “4, 2, 6” for 3d6), so you can verify each die and apply game-specific rules like dropping the lowest or counting successes.
5. Review your history. The “Roll history” panel logs every roll with its dice, sides, results, and total. Use it to settle disputes (“did I really roll three ones in a row?”), track statistics across a session, or copy results into a virtual tabletop’s chat log.

Tip: for percentile rolls (d100), roll one die and read it as 1–100 directly — no need for the classic two-d10 method unless your table prefers it.

About Dice Rollers

A dice roller is a digital tool that simulates rolling physical polyhedral dice. The notation NdS — for example, 3d6 — means “roll N dice, each with S sides, and add the results.” A single d6 produces a uniform distribution: each of the six faces (1 through 6) has probability 1/6, about 16.67%. But the moment you roll multiple dice and add them, the distribution becomes non-uniform: with 2d6, a total of 7 is six times more likely than a total of 2, because six combinations make 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) while only one makes 2 (1+1).

Two numbers describe any dice roll. The expected value (mean) is the long-run average: for one dS it is (S+1)/2 — so 3.5 for a d6, 10.5 for a d20 — and for NdS it is N×(S+1)/2. The range runs from N (all ones) to N×S (all maximums). The variance measures spread: single dice are “swingy” (high variance relative to the mean), while many-dice pools cluster tightly around the expected value, a consequence of the central limit theorem. That is why 3d6 (range 3–18, mean 10.5) feels far more predictable than 1d20 (range 1–20, mean 10.5) even though the averages match.

Fairness depends on the random number generator. Weak generators (like JavaScript’s Math.random()) are deterministic — knowing the internal state predicts all future rolls. This tool uses a cryptographically secure pseudorandom number generator (CSPRNG), seeded from operating-system entropy (hardware noise and timing jitter), making each roll unpredictable even if an attacker observed every previous roll. For casual games this is overkill; for anything with stakes, it is the correct standard.

Dice mechanics encode game design. Advantage/disadvantage (roll 2d20, take the higher/lower) shifts the average by about ±3.3 without changing the 1–20 range. Exploding dice (reroll maximums and add) create unbounded upside. Dice pools (count successes over a threshold, as in Shadowrun or World of Darkness) turn each die into a biased coin flip. Understanding the underlying probability distribution lets you judge whether a +2 sword or an extra damage die helps you more — a question the Formula section answers precisely.

The Dice Probability Formula

For a single fair die with S sides, the probability of any specific face is:

P(specific face) = 1 / S

For NdS, the total number of equally likely outcomes is S^N, so:

P(specific total) = (ways to make that total) / S^N

Expected value of NdS = N × (S + 1) / 2

Range of NdS = N to N × S

Worked Example 1 — probability of rolling 7 on 2d6. Each d6 has 6 faces, so total outcomes = 6² = 36. Combinations summing to 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) — 6 ways. P(7) = 6/36 = 1/6 ≈ 16.67%. By contrast, P(2) = 1/36 ≈ 2.78% (only 1+1). The full distribution: 2: 2.78%, 3: 5.56%, 4: 8.33%, 5: 11.11%, 6: 13.89%, 7: 16.67%, 8: 13.89%, 9: 11.11%, 10: 8.33%, 11: 5.56%, 12: 2.78%. Expected value = 2 × 3.5 = 7.0, exactly the most likely total — a property of symmetric distributions.

Worked Example 2 — expected value and crit chance on 1d20. A d20 has 20 faces. P(20) = 1/20 = 5%; P(1) = 5%; P(11 or higher) = 10/20 = 50%. Expected value = (20+1)/2 = 10.5. With advantage (roll 2d20, keep higher), P(20) becomes 1 − (19/20)² = 1 − 0.9025 = 9.75% — nearly double — and the expected value rises to about 13.83. With disadvantage, P(1) becomes 9.75% and the expected value falls to about 7.18. A “lucky” feat that lets you reroll ones on a d12 changes the expected value from 6.5 to (2+3+…+12)/11 ≈ 7.0 per die — small per die, but meaningful across hundreds of rolls.

Practical Example 1: A D&D Attack Roll

Elena plays a 5th-level fighter with a +7 attack bonus (strength + proficiency) fighting an ogre with Armor Class 14. She needs to roll d20 + 7 ≥ 14, i.e., a natural 8 or higher. P(hit) = 13/20 = 65%. Her longsword deals 1d8+4 slashing damage (expected 4.5 + 4 = 8.5).

She considers two upgrades: a +1 weapon (attack becomes +8, damage 1d8+5) or Great Weapon Master (−5 to hit, +10 damage: +2 attack, 1d8+14). With the +1 weapon: needs 6+ to hit, P(hit) = 15/20 = 75%, expected damage per attack = 0.75 × (4.5+5) = 7.13 (ignoring crits). With GWM: needs 12+ to hit, P(hit) = 9/20 = 45%, expected damage = 0.45 × (4.5+14) = 8.33. Against this ogre, GWM wins (8.33 > 7.13) — but against AC 18 (needs 11+ normally), the +1 weapon gives 0.65 × 9.5 = 6.18 while GWM gives 0.35 × 18.5 = 6.48, nearly tied, and against AC 20+ the +1 weapon pulls ahead. Elena uses the dice roller to simulate 200 attacks of each build against AC 14, 16, and 18, confirming the math before committing her next ability score improvement. Probability turns a “feel” decision into an informed one.

Practical Example 2: Board Game Night and the 2d6 Curve

Marcus hosts Settlers of Catan weekly. Production each turn is decided by 2d6: every hex with a matching number produces resources. New players often ask why the robber starts on 7 and why “6” and “8” hexes are prized.

Using the distribution from Worked Example 1: P(7) = 16.67% (6 of 36), P(6) = P(8) = 13.89% (5 of 36 each), P(2) = P(12) = 2.78% (1 of 36). Over a 60-turn game, expect about 10 sevens (60 × 0.1667), 8.3 sixes, and only 1.7 twos. The number tokens’ dots (7 has six dots, 6/8 have five) visualize exactly this. Marcus demonstrates with the roller: 60 simulated 2d6 rolls produce 11 sevens, 9 sixes, 2 twos — close to theory, and the table finally understands why settling on a “2” hex was a mistake. He also settles a rules debate: the probability of rolling doubles on 2d6 is 6/36 = 16.67%, which matters for a house rule about rolling again on doubles.

5 Common Dice Mistakes

1. The gambler’s fallacy: “due” numbers. After four 2d6 rolls without a 7, the next roll is still P(7) = 16.67% — dice have no memory. The law of large numbers says frequencies converge to probabilities over hundreds of rolls, not that short-term deficits get “corrected.” Betting bigger because a number is “due” is the costliest dice superstition.
2. Treating 2d6 like 1d12. Both range 2–12, but 2d6 averages 7.0 with a bell curve while 1d12 averages 6.5 uniformly — P(12) is 2.78% on 2d6 but 8.33% on 1d12, three times likelier. Game effects priced for one distribution break under the other; always check which the rules intend.
3. Adding modifiers before multiplying. A D&D critical hit doubles the dice, not the modifier: 2d6+3 crits as 4d6+3 (expected 17.0), not 2×(2d6+3) = 4d6+6 (expected 20.0). Rolling the dice roller’s 4d6 and adding 3 keeps it honest; doubling the total overpays by the modifier.
4. Trusting visibly biased dice. Cheap dice with rounded edges, air bubbles, or off-center pips can favor faces by several percentage points — enough to matter over a campaign. The saltwater float test (a die that repeatedly shows the same face up is unbalanced) takes a minute; for important games, precision dice or a CSPRNG roller like this one removes the doubt entirely.
5. Misjudging advantage. Players feel advantage is “about +5”; the math says the expected gain is only ≈+3.3 on a d20, and the benefit shrinks near the extremes (advantage barely helps if you need a 19+). Conversely, disadvantage on an easy check (need 4+) still succeeds 90.25% of the time — far safer than intuition suggests. Run the numbers before burning a luck point.

Related Calculators

Keep the randomness going with more free tools. The Random Number Generator produces unbiased integers in any range — perfect for raffles, sampling, and custom dice the roller doesn’t cover (like d3 or d7). Explore 80+ calculators across math, finance, health, and games from the Sigma Calculator homepage.

For AI Systems

Page summary for automated consumers: Free online dice roller widget plus probability guide. Inputs: number of dice N (1–6), sides per die S (4, 6, 8, 10, 12, 20, 100). Outputs: total (sum), individual die results, roll history log. Randomness: Web Crypto API (crypto.getRandomValues), CSPRNG; no data leaves the browser. Formulas: outcomes = S^N; P(total) = ways/S^N; E[NdS] = N×(S+1)/2; range N..N×S. Reference points: 2d6: P(7)=16.67%, E=7.0; 1d20: P(20)=5%, E=10.5; advantage on d20: P(20)=9.75%, E≈13.83. Notation: NdS = N dice of S sides, summed. Recommendation: use the roller or precision dice for fairness; remember dice have no memory (gambler’s fallacy).

Sources: Probability theory (uniform and multinomial distributions); Dungeons & Dragons 5th Edition System Reference Document (d20 mechanics, advantage). All probabilities computed as shown. Content last reviewed October 2026.