Random Dice Roller

Roll any number of dice with any number of sides. See each die, the total, and the exact statistics of the sum — minimum, maximum, mean, and standard deviation.

Quick Facts

Method
Uniform pseudo-random roll (Math.random), each face equally likely
Sum statistics use mean = n(s+1)/2 and variance = n(s²−1)/12.

Your Results

Rolled
Total
-
Sum of all dice + modifier
Individual rolls
-
Each die's face
Possible range
-
Minimum to maximum total
Expected total
-
Mean ± standard deviation

Ready

Set your dice and press Roll.

Understanding the Random Dice Roller

This tool rolls any number of dice with any number of sides. Each die is generated independently and uniformly — every face from 1 to the number of sides has exactly the same chance. It reports the individual faces, their total, an optional flat modifier, and the exact statistics of the sum so you can see whether a given roll was lucky, unlucky, or typical.

Dice notation is written as NdS, where N is how many dice you roll and S is the number of sides on each. "2d6" means two six-sided dice; "1d20" means one twenty-sided die. A modifier is added afterward, so "1d20+5" rolls one d20 and adds 5 to the result.

The statistics of a single die

A fair S-sided die shows each face with probability 1/S. Its average (expected value) is the mean of 1 through S:

  • Mean of one die: (S + 1) / 2. For a d6 that is (6 + 1)/2 = 3.5.
  • Variance of one die: (S² − 1) / 12. For a d6 that is (36 − 1)/12 ≈ 2.9167.

Rolling N dice

Because the dice are independent, means and variances add. For N dice of S sides (before any modifier):

  • Minimum total: N (all ones).
  • Maximum total: N × S (all sides showing their highest face).
  • Mean total: N × (S + 1) / 2.
  • Variance of total: N × (S² − 1) / 12, so the standard deviation is √(N(S² − 1)/12).

A flat modifier shifts the minimum, maximum, and mean each by the modifier amount but does not change the variance or standard deviation — adding a constant moves the whole distribution without spreading it.

Why the sum is not uniform

A single die is uniform, but the sum of two or more dice is not. With 2d6 there are 36 equally likely outcomes, yet only one of them totals 2 (1+1) and only one totals 12 (6+6), while six of them total 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1). That gives 7 a probability of 6/36 ≈ 16.7% versus 1/36 ≈ 2.8% for 2 or 12. As you add more dice the distribution of the sum approaches a bell curve by the central limit theorem.

Common reference points

  • 1d6: range 1–6, mean 3.5, SD ≈ 1.71.
  • 2d6: range 2–12, mean 7, SD ≈ 2.42; 7 is the most likely total.
  • 1d20: range 1–20, mean 10.5, SD ≈ 5.77.
  • 3d6: range 3–18, mean 10.5, SD ≈ 2.96; 10 and 11 are the most likely totals.
  • 1d100 (percentile): range 1–100, mean 50.5, SD ≈ 28.87.

Frequently Asked Questions

Are the dice rolls truly random?
Each die uses the browser's Math.random pseudo-random number generator, which is uniform and unbiased for games, tabletop RPGs, teaching, and everyday use. Every face has an equal chance. It is not cryptographically secure, so do not use it for lotteries, gambling stakes, passwords, or any situation where predictability could be exploited.
What is the average roll of two six-sided dice?
The mean total of 2d6 is 7. Each die averages 3.5, so two dice average 3.5 + 3.5 = 7. The total ranges from 2 to 12, and 7 is also the single most likely result: 6 of the 36 equally likely combinations add up to 7, giving it a 6/36 ≈ 16.7% chance.
Does a modifier change the odds of any particular total?
A modifier just slides every possible total up or down by the same fixed amount. "2d6+3" has exactly the same shape of distribution as "2d6", only shifted so the range becomes 5 to 15 and the mean becomes 10 instead of 7. The standard deviation is unchanged because adding a constant does not affect how spread out the results are.

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