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Random Dice Generator

Rolling polyhedral dice is the universal engine of tabletop roleplaying games (Dungeons & Dragons, Pathfinder), board games, wargaming, and probabilit

Random & Generators
dice
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Change seed to roll again
Formula & Methodology
ext{Roll}_i = lfloor U imes ext{Sides} floor + 1 quad ext{where } U in [0, 1) ext{Total Score} = sum_{i=1}^{N} ext{Roll}_i + ext{Modifier} ext{Expected Value } E[X] = N imes rac{ ext{Sides} + 1}{2} + ext{Modifier}

Each individual die roll is simulated by generating a uniform random variable between 1 and the number of faces on the die. The expected (average) value of a fair die with S sides is (S + 1) / 2 (for example, 3.5 for a d6). The sum of all N dice plus the modifier yields the total score.

Total Roll Score (3d6)

8

Overview

Rolling polyhedral dice is the universal engine of tabletop roleplaying games (Dungeons & Dragons, Pathfinder), board games, wargaming, and probability experiments. The Random Dice Generator simulates rolling multi-sided dice—from classic 6-sided cubes (d6) to iconic 20-sided d20s and percentile d100s—complete with optional arithmetic modifiers.

Whether you need to roll 3d6 for character attribute generation, 1d20+5 for an attack check, or 4d8 for fireball spell damage, this calculator delivers transparent, reproducible rolls. Every roll displays both individual face values and the combined sum.

Worked Examples

Example 1: Rolling 3d6 with No Modifier (Seed = 7)

Count = 3, Sides = 6 (d6), Modifier = 0, Seed = 7

  1. Simulate 3 independent rolls on a fair 6-sided die.
  2. Individual rolls produce: 4, 3, 5.
  3. Sum individual dice: 4 + 3 + 5 = 12.
  4. Expected theoretical value: 3 × 3.5 = 10.5.
Final Answer: 12 (Rolls: 4, 3, 5 | Expected: 10.50)

Example 2: D&D Attack Roll with +5 Modifier (1d20+5, Seed = 42)

Count = 1, Sides = 20 (d20), Modifier = +5, Seed = 42

  1. Simulate 1 roll on a 20-sided die: results in 14.
  2. Apply +5 modifier: 14 + 5 = 19.
  3. Expected value: 10.5 + 5 = 15.5.
Final Answer: 19 (Raw roll: 14, Modifier: +5)

Example 3: Rolling 2d8 with -2 Penalty (Seed = 15)

Count = 2, Sides = 8 (d8), Modifier = -2, Seed = 15

  1. Simulate 2 rolls on an 8-sided die: 6, 7.
  2. Raw sum: 6 + 7 = 13.
  3. Apply penalty: 13 − 2 = 11.
Final Answer: 11 (Raw rolls: 6, 7)

How to Use This Calculator

  1. Select the number of dice you want to roll (1 to 20).
  2. Choose the die type (d4, d6, d8, d10, d12, d20, or d100).
  3. Enter an optional modifier (+/−) to add or subtract from the total.
  4. Change the Seed / Draw # to perform a new roll.

Frequently Asked Questions

What is the average expected roll on a standard 6-sided die (d6)?
The average roll on a fair d6 is 3.5. Rolling three d6 dice yields an average expected total of 10.5 (3 × 3.5).
Why does rolling 2d6 produce a bell curve while 1d12 produces a flat distribution?
Rolling multiple dice produces a binomial-like distribution where middle totals (like 7 on 2d6) have more possible permutations than extremes (2 or 12). A single d12 has an equal 1/12 chance for every outcome.
Can I roll custom non-standard dice?
This tool supports all standard tabletop RPG dice: d4, d6, d8, d10, d12, d20, and d100 percentile dice.
Are critical hits (natural 20) and critical fumbles (natural 1) possible on the d20?
Yes. Each face on the d20 has an equal 5% (1 in 20) chance of appearing on any roll.
How do I re-roll the dice?
Change the Seed value in the form to any new number to trigger a fresh, independent roll.

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Reviewed & Authored by: OnlineConvers Editorial Team · Last Updated: 2026-10-06
Simulates discrete uniform distributions over {1, ..., S} using a 32-bit PRNG. Unbiased integer mapping ensures equal probability for every face of the polyhedral die.