Dice Roller (roll d6, d20 or any dice online, with modifier & drop lowest)

Understanding the dice roller — concept and principle

This tool rolls any number of dice with any number of sides, such as 2d6 or 1d20, with an optional modifier and the option to drop the lowest or highest die. It shows every die, the total, the highest and lowest roll, the expected average and the possible range. Use it for board games, role-playing games and probability lessons.

Middle totals have more combinations, so 7 is most likely and 2 or 12 rarest.

How it is calculated

Each die is an independent, uniformly random whole number from 1 to the number of sides, drawn with the browser's cryptographic random generator and rejection sampling so no face is favoured.
Total = sum of the kept dice + modifier; a dropped die is shown in brackets.
Expected total of n dice with s sides = n(s + 1) ÷ 2 + modifier.
Dropping the lowest subtracts the expected minimum; dropping the highest subtracts the expected maximum (both found from E[X] = Σ P(X ≥ k)).
Range = n + modifier to n·s + modifier; notation such as 2d6 means two six-sided dice.

The principle

One fair die gives each face the same chance, so its average is the middle of 1 and s: (s + 1) ÷ 2, which is 3.5 for a d6. Adding dice adds their averages, but the totals are no longer equally likely: with 2d6 there are six ways to make 7 and only one way to make 2 or 12, which is why middle totals come up most. Dropping a die shifts the average: 4d6 drop lowest, a common way to roll role-playing ability scores, averages about 12.24 instead of 10.5 for 3d6.

Worked example

Default inputs: 2 dice with 6 sides, add all, modifier 0, roll number 1. The roll is random, so your screen may differ; when this page was checked it showed:

Dice rolled: 4, 6; highest 6, lowest 4.
Sum of kept dice = 4 + 6 = 10; total with modifier 0 = 10.
Expected total = 2 × (6 + 1) ÷ 2 = 7.
Possible range = 2 – 12; notation 2d6.

Each point is the calculator re-run with only “Roll number (change it to roll again)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Roll number (change it to roll again)	Total
0.25	5
0.5	6
0.75	3
1	8
1.25	7
1.5	6
2	5

How to read the result

A single roll tells you little; the expected total tells you what happens on average over many rolls. For 2d6, a 10 or more happens 6 times in 36, about 17 % of the time. Change the roll number to roll again with the same settings.

Common mistakes

Thinking a number is "due" after it has not appeared for a while.
Assuming all totals of 2d6 are equally likely.
Forgetting the modifier when comparing with a target number.
Confusing "drop lowest" with re-rolling the lowest die.

Keep in mind: For games and teaching only; not for gambling.

Frequently asked questions

What is the average roll of 2d6?

What does 3d6 mean?

Three six-sided dice added together, totals from 3 to 18.

What is the average of 4d6 drop lowest?

About 12.24.

Sources: W3C Web Cryptography API, crypto.getRandomValues · Expected value of a discrete uniform variable, standard probability theory

Checked 9 Nov 2026. Web Crypto API, crypto.getRandomValues (W3C Recommendation); unbiased bounded integers by rejection sampling; expected value of a discrete uniform die (s + 1)/2 and of the minimum/maximum of n dice via E[X] = Σ P(X ≥ k).

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