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CALCPARK

Dice Roller

Roll d4, d6, d8, d10, d12, d20, d100 or custom dice, several at once with a modifier, keep-highest or drop-lowest rules, a roll history and the exact odds of each total.

Runs on your device
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How to use it

  1. Pick a die type, or choose Custom and type the number of sides. Set how many dice to roll and any modifier.
  2. For ability scores or advantage, choose a keep/drop rule and N – or type the whole thing as notation such as 4d6dl1.
  3. Press Roll. Each die is shown (dropped dice greyed out), the total is the headline, and the panel below gives the odds of that total.
  4. Roll again as often as you like; the last 20 rolls stay in the history. Copy the result line or the link to reuse the same dice.

Example

4d6dl1 for a character stat: the dice show 3, 6, 1, 6. The lowest die (1) is dropped, the kept dice sum to 15 and no modifier applies, so the total is 15. The odds panel says this combination averages 12.24, that 13 is the most likely total (13.3%) and that 15 or higher comes up 29.3% of the time. An attack roll with advantage, 2d20kh1+5, averages 18.8 and has a 9.75% chance of a natural 20.

How the rolls and odds are calculated

Each die is a uniform draw of a whole number from 1 to its number of sides, using the same crypto-backed randomIntas the random number generator (a 32-bit word from crypto.getRandomValues, rejected and redrawn when it would bias the top faces). Keep and drop rules sort the dice by value and mark the kept ones; ties are broken by position so the kept count is always exactly N.

total = Σ kept faces + modifier      P(sum of n dice = s) from the n-fold convolution of the uniform face distribution

For a plain sum the distribution is computed by convolution, which is exact for any size of roll (100d100 included). With a keep or drop rule the tool enumerates every outcome (6⁴ = 1,296 for 4d6) while there are at most one million; beyond that the odds panel is left out rather than approximated.

Limits. No exploding dice, rerolls, Fate/Fudge dice or success counting. The display shows the first 40 dice of a very large roll; the total always counts all of them.

Sources: Dice notation – overview of the d-notation conventions, Probability distribution of dice sums (AnyDice), MDN – Crypto.getRandomValues().

What are the odds of rolling a given number?

On a single fair die every face has probability 1 / sides: 16.7% on a d6, 5% on a d20, 1% on a d100. Sums of several dice are not uniform – middle totals are far more likely because more combinations produce them. Two six-sided dice total 7 in 6 of the 36 combinations (16.7%) but 2 or 12 in only one each (2.8%). The odds panel gives these figures for exactly the dice you chose, including keep and drop rules.

Questions

Does 4d6 drop lowest equal 4d6kh3?
Yes. Dropping the lowest one of four dice keeps the highest three, so 4d6dl1 and 4d6kh3 roll and score identically; the tool accepts both.
Are the rolls really fair?
Each face is drawn from the operating system’s entropy source through Web Crypto and mapped onto the die with rejection sampling, which removes the modulo bias that naive implementations have. Over many rolls each face appears equally often.
Can I roll a d3 or a d1000?
Choose Custom and enter any number of sides from 2 to 1,000. A d3 is a fair three-way pick; a d1000 behaves like a random number from 1 to 1,000.