DnD Dice Roller Calculator

Enter dice notation like 3d6+2 and get the exact minimum, maximum, average (expected value), and standard deviation of the roll total.

Quick Facts

Method
Exact NdX+M statistics: min = N+M, max = NX+M, mean = N(X+1)/2 + M
Standard deviation uses the uniform-die variance (X²−1)/12 per die.

Your Results

Calculated
Average total
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Expected value of the roll
Minimum
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Lowest possible total
Maximum
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Highest possible total
Standard deviation
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Typical spread of totals

Ready

Enter your dice and press Calculate.

Understanding the DnD Dice Roller

Tabletop games like Dungeons & Dragons describe every roll in "dice notation": NdX+M, where N is the number of dice, X is the number of sides on each die, and M is a flat modifier added to (or subtracted from) the total. So 3d6+2 means "roll three six-sided dice, add them together, then add 2." This calculator does not simulate a single random roll — it reports the exact statistics of the whole roll: the smallest and largest totals possible, the long-run average, and how much the total typically bounces around.

The formulas

A fair X-sided die is uniform over the values 1 through X. From that, every result on this page follows directly:

  • Minimum total: N + M — every die shows its lowest face (a 1), so the smallest sum is N, plus the modifier.
  • Maximum total: N·X + M — every die shows its highest face (X).
  • Average (expected value): N·(X+1)/2 + M. A single die averages (X+1)/2 — for a d6 that is 3.5 — and averages add across dice, then the modifier is added once.
  • Standard deviation: √( N·(X²−1)/12 ). Each fair die has variance (X²−1)/12; because the dice are independent, variances add, and the standard deviation is the square root of the total. The flat modifier shifts the average but never changes the spread.

Why this is useful

Knowing the average tells a designer or player whether a d10 (avg 5.5) versus 2d6 (avg 7) is the stronger damage die, and the standard deviation tells you how swingy it is. A single d12 (avg 6.5, SD ≈ 3.45) and 2d6 (avg 7, SD ≈ 2.42) are close in average but the 2d6 result is far more consistent — the more dice you roll, the tighter the total clusters around the mean. That trade-off between average and reliability is the core reason to compute these numbers instead of guessing.

Common reference points

  • d20: average 10.5, min 1, max 20, SD ≈ 5.77 — the classic attack/check die.
  • d6: average 3.5, SD ≈ 1.71.
  • 3d6: average 10.5, min 3, max 18, SD ≈ 2.96 — the traditional ability-score roll, tightly centered on 10–11.
  • 4d6 drop lowest: not computed by the simple formula above (it is not a plain sum), but averages about 12.24 — worth knowing because this page assumes you keep every die.

Frequently Asked Questions

What is the average of 3d6?
10.5. Each six-sided die averages (1+6)/2 = 3.5, and three of them give 3 × 3.5 = 10.5. Totals can range from 3 to 18, but because there are many ways to make a 10 or 11 and only one way each to make a 3 or 18, results cluster near the middle.
Does adding a modifier change how swingy the roll is?
No. A modifier like the "+2" in 3d6+2 shifts every possible total up by 2, so the minimum, maximum, and average all rise by 2, but the standard deviation is unchanged. Only the number and type of dice affect the spread.
Why does the calculator not handle "4d6 drop lowest"?
The min/max/mean/SD formulas here assume you sum every die. "Drop lowest," "keep highest," advantage, and exploding dice change the distribution and need a different calculation (the mean of 4d6-drop-lowest is about 12.24, not the plain 14 you would get from summing all four). Use this tool for straight NdX+M rolls.

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