Dice Roller
Simulate rolling dice with any number of sides. Roll multiple dice at once and see individual results, totals, and statistics. Perfect for board games, RPGs, and probability lessons.
Dice rolling has been a foundational randomization tool for thousands of years — used in games, divination, and now widely in tabletop role-playing games (RPGs) like Dungeons & Dragons, board games, and probability education. Modern gaming uses dice with various side counts: the standard 6-sided cube (D6), plus specialized RPG dice including D4 (tetrahedron), D8 (octahedron), D10, D12 (dodecahedron), D20 (icosahedron), and D100 (rolled with two D10s or a percentile die). Each provides different probability distributions and serves different game mechanics.
This calculator simulates rolling multiple dice with any number of sides, plus an optional modifier added to the total. Use it for: tabletop RPG play (especially when physical dice aren't handy), board game decisions, probability demonstrations, statistical learning, or any game requiring randomized outcomes. Notation convention from RPGs: "3d6+2" means roll 3 six-sided dice, sum the results, add 2. This calculator supports the standard format. For complex dice expressions (advantage/disadvantage in D&D 5e, exploding dice, drop-lowest), specialized dice calculators or RPG character sheet apps handle the additional logic.
Important context: physical dice have slight biases from manufacturing variations and wear; digital dice rollers use pseudorandom number generators producing mathematically uniform distributions. For casual play, physical dice are sufficient. For tournaments or precision-critical applications, digital rollers eliminate physical bias. Statistical patterns: rolling 2d6 produces a bell-shaped distribution (peak at 7, less common 2 and 12); rolling 1d20 is uniform (each result equally likely); rolling 4d6-drop-lowest skews higher (common D&D character generation). Understanding these distributions matters for game balance and strategic decisions.
Inputs
Added to total
Results
Notation
2d6
Total
3
Rolls
2, 1
Range
2 - 12
Individual Rolls
| Die # | Result |
|---|---|
| 1 | 2 |
| 2 | 1 |
Formula
How to use this calculator
- Enter number of dice (1-20).
- Enter sides per die (2-100; standard RPG dice are 4, 6, 8, 10, 12, 20, 100).
- Enter modifier to add or subtract from total (e.g., +3 for strength bonus in RPGs).
- Change "Roll Again" value to re-roll the dice.
- Review individual die results and total.
- For RPG play: roll attacks (1d20 + modifier vs. AC), damage (varies by weapon), ability checks (1d20 + skill modifier).
- For probability demonstration: roll many dice to show distribution patterns (2d6 bell curve, 1d20 uniform).
- For board games: replace physical dice when not available.
- For statistics teaching: compare 1d20 results (uniform) to 3d6 results (bell-shaped) to demonstrate Central Limit Theorem.
- For unfair-feeling streaks: realize that streaks of high/low rolls happen naturally in random sequences. Each individual roll independent.
- For complex mechanics (advantage, exploding dice, drop lowest): manually apply rules to results.
Worked examples
D&D attack roll
Player attacks with +5 attack bonus against enemy AC 16. Roll: 1d20 + 5 Random result example: 12 Total: 12 + 5 = 17 17 ≥ 16 → HIT Damage roll (longsword: 1d8 + 3 strength modifier): Roll: 1d8 + 3 Random result example: 6 Total: 6 + 3 = 9 damage Apply 9 damage to enemy. Critical hit (natural 20): typically rolls damage dice twice (e.g., 2d8 + 3 for longsword critical = 12+ average damage). Critical miss (natural 1): standard rule = miss regardless of modifier; some house rules add fumble effects.
Ability score generation
D&D character creation: roll 4d6, drop lowest, repeat 6 times for 6 ability scores. First score: Roll: 4d6 = 5, 3, 6, 2 Drop lowest (2): keep 5, 3, 6 Sum: 14 Repeat 6 times. Typical results: Strength: 14 Dexterity: 12 Constitution: 16 Intelligence: 10 Wisdom: 13 Charisma: 11 Average score in 4d6 drop lowest: ~12.24. Range theoretically 3-18 but extreme values rare. Comparison: 3d6 straight has average 10.5. 4d6-drop-lowest favors higher results, producing more "heroic" characters. Alternative methods: point buy (no dice, fixed point pool), standard array (predetermined scores), 4d6 (without drop), etc. Each produces different character power levels.
Probability demonstration
Roll 2d6 many times to observe bell-shaped distribution. After 100 rolls of 2d6, typical distribution approximates: Sum 2: 3 times (3%) Sum 3: 6 times (6%) Sum 4: 9 times (9%) Sum 5: 11 times (11%) Sum 6: 13 times (13%) Sum 7: 17 times (17%) Sum 8: 14 times (14%) Sum 9: 11 times (11%) Sum 10: 8 times (8%) Sum 11: 5 times (5%) Sum 12: 3 times (3%) Peak at 7 (most common sum). Sums of 2 and 12 rare. Bell-shaped distribution. Compare to 1d12 (single 12-sided die): each result 1-12 has ~8.3% probability — uniform distribution, NOT bell-shaped. Sum of multiple dice → approaches normal distribution (Central Limit Theorem). This is why "averages" of independent events look like bells.
When to use this calculator
Use this calculator for tabletop RPG play (D&D, Pathfinder, etc.), board game randomization, probability and statistics teaching, simulating dice mechanics, or replacing physical dice when unavailable.
Pair with random-number (general randomization) and coin-flip (binary random).
Important dice rolling considerations:
1. **Each roll is independent.** Past rolls don't affect future rolls. Don't fall for "I'm due for a critical hit" reasoning.
2. **Multiple dice produce bell distributions.** 2d6 has peak at 7; less common 2 or 12. 3d6 even more concentrated. Sum of independent uniform variables approaches normal.
3. **Single dice are uniform.** 1d20 every result equally likely. 1d6 every result equally likely. No bias toward middle.
4. **Modifier shifts distribution.** Adding +3 shifts entire range up 3 without changing shape.
5. **Advantage skews high.** Take higher of 2d20: mean 13.83 (vs. 10.5). Significant boost.
6. **Drop-lowest skews high.** 4d6-drop-lowest mean 12.24 (vs. 3d6 mean 10.5).
7. **Real dice have slight bias.** Manufacturing variations, wear over time. For casual play, irrelevant. For tournaments, machine-cut dice or digital rollers eliminate.
8. **Streaks are normal.** 10 rolls of 1d20 producing 3 consecutive 18+ rolls happens. Doesn't indicate bias.
9. **Variance matters in game design.** 2d6 (mean 7, σ=2.42) produces more consistent results than 1d12 (mean 6.5, σ=3.45). Game systems balance using different dice for different mechanics.
10. **Critical hit mechanics common.** Natural 20 usually special outcome. Critical fail (natural 1) varies by system.
11. **Use specialized tools for complex mechanics.** Advantage/disadvantage, exploding dice, reroll rules better handled by RPG character sheet apps or specialized dice rollers.
12. **Statistical equivalence.** Physical fair dice and digital pseudorandom dice produce statistically indistinguishable results for game purposes.
Common mistakes to avoid
- Believing streaks indicate bias. Random sequences naturally contain runs of high or low results.
- Treating multiple dice as uniform. 2d6 is bell-shaped (peak 7); not equal probability across 2-12.
- Forgetting modifier impact. +3 doesn't change distribution shape, just shifts up.
- Confusing advantage with rerolls. Advantage = take higher of two rolls; reroll = single replacement chance.
- Underestimating variance impact. 1d12 more swingy than 2d6 despite similar means.
- Applying physical dice intuition to digital. Both statistically equivalent for practical purposes.
Frequently Asked Questions
Sources & further reading
- Probability Theory Resources — U.S. Census Bureau
- Mathematics Education — National Council of Teachers of Mathematics
- Statistics Education Resources — American Statistical Association