standarddeviationcalculator.net

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Statistics

Dice roller

Roll any set of dice. Type notation like 2d6+3, or set the number of dice, sides and modifier, then press Roll to see each die and the total.

Fill this in to override the three boxes: 2d6+3, d20, 4d6−1.

d4, d6, d8, d10, d12, d20, d100 or any number.

What a roll should look like

Every roll here is random, so there is no fixed answer to show. What is fixed is the pattern the totals follow over many rolls. For N dice with S sides and a modifier M:

average total = N × (S + 1) ÷ 2 + M SD = √(N × (S² − 1) ÷ 12)

The roller shows this average next to each result, so you can see whether a roll was high or low for its dice.

A worked example

The default rolls 2d6. The average total is 2 × 3.5 = 7 and the standard deviation is √(2 × 35 ÷ 12) = 2.42. Suppose the dice come up 5 and 6. The total of 11 is 4 above average, about 1.7 standard deviations. Rolls of 11 or 12 happen 3 times in 36, one roll in twelve, so you will see one every so often.

Now type 3d8+2 and roll. The dice add to somewhere from 3 to 24, the modifier adds 2, and the average total is 3 × 4.5 + 2 = 15.5. Roll it a few times and the history table under the dice fills up, most totals landing within 4 or so of 15.5.

How the dice are rolled

Each die takes a random number from crypto.getRandomValues, scales it to the range 1 to S and rounds down, so each face has exactly the same chance. The dice are independent of each other and of earlier rolls. Physical dice are rarely this fair: cheap dice with drilled pips are slightly lighter on the high faces, and a hand-rolled d20 can favour a side if it is not tumbled well.

Reading a single roll

One roll tells you almost nothing about whether dice are fair. To test a physical die, roll it many times, at least 30 rolls per face, and compare the counts with a chi-square goodness-of-fit test. The virtual dice here pass that test easily. For a single roll, the useful comparison is with the average and standard deviation shown beside the result: a total more than two standard deviations from the average happens roughly one roll in twenty.

Common mistakes

  • Rolling 1d12 when a rule says 2d6. Both reach 12, but 2d6 averages 7 and rarely gives extremes, while 1d12 is flat and starts at 1.
  • Adding the modifier to each die. In 3d8+2 the +2 is added once to the total. For a per-die bonus, roll the dice and add N × bonus.
  • Expecting a low roll to be followed by a high one. The dice have no memory.

To know the odds of a total before you roll, use the dice probability calculator.

Dice roller: the worked example on this page, with its result and chart
Dice roller: the worked example above, at a glance.

Common questions

How do I roll something like 2d6+3?

Type it into the dice notation box and press Roll. The notation is number of dice, “d”, number of sides, then an optional + or − modifier: d20, 3d8+2, 4d6-1. Leave the box empty to use the three separate fields instead.

Are the rolls fair?

Yes. Each die uses the browser's cryptographic random generator, and each face has probability exactly 1/s. The dice are independent, so a run of low rolls says nothing about the next one. The page's own tests roll 60,000 d6 and check each face turns up close to 10,000 times.

Which dice can it roll?

Any die with 2 or more sides: the standard d4, d6, d8, d10, d12, d20 and d100, and odd ones such as d3 or d7. Six-sided dice are drawn with pips; the others show the number.

Is the history saved?

Only while the page is open. The last ten rolls are listed under the dice, and they disappear when you close or reload the page. Nothing is sent anywhere.

How do I roll with advantage or drop the lowest die?

Roll the extra die and ignore the one you drop: 2d20 for advantage, keeping the higher, or 4d6 for an ability score, dropping the lowest. The highest and lowest die are listed under each roll. The dice average calculator gives the average of those rolls.

Written and reviewed by our editorial team. Last updated . Method and sources: how these numbers are computed.