Science & Engineering

Dice Average Calculator (NdS + Modifier)

Enter a dice expression like NdS with a modifier and it returns the expected average, the minimum, the maximum, and the standard deviation. It works with d4 through d20 and custom-sided dice.

How to use

Set the number of dice and the number of sides.
Add a modifier if your roll has one, like 2d6+3.

Dice count

Faces per die

Flat modifier

Roll

Expected average

10.5

3d6 · rolls land between 3 and 18

Min – Max

3 – 18

Std deviation σ

2.958

Variance

8.75

Single-die avg

3.5

For study and estimation. Verify against authoritative data before relying on a result.

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Worked examples

Roll	Min	Max	Average
1d6	1	6	3.5
2d6	2	12	7
1d20	1	20	10.5
3d6	3	18	10.5
2d6+3	5	15	10

Common questions

What's the average roll of 2d6?

Seven. Each die averages 3.5, and two dice add up to 7, which is why 7 is the most common total in craps.

What's the average of a single d20?

10.5. For any fair die the average is (sides + 1) divided by 2.