The average result you’d expect from rolling one or more fair dice, over many rolls.
How it works
For a fair die, every face is equally likely, so averaging the minimum and maximum face gives the expected value per die; multiplying by the number of dice gives the total expected value.
What this does not include
This does not include the probability of any specific roll outcome — for that, use this site’s coin flip or binomial probability calculators for similar probability questions.
How to use this calculator
- Enter the number of sides per die and how many dice you’re rolling.
A worked example
A single 6-sided die: expected value = 3.5 — the average of 1 through 6, even though 3.5 itself can never actually be rolled.
Two 6-sided dice: expected value = 7 — exactly double a single die’s average, since expected values add across independent dice.
What the variables mean
| Variable | Meaning |
|---|---|
| Sides | Number of sides on each die |
| Number of dice | How many dice are being rolled together |
Edge cases worth knowing
The expected value of a single die is never a number you can actually roll. 3.5 is the long-run average across many rolls, not a possible single outcome — a common point of confusion for expected value in general.
A die with zero sides has no meaningful average, so the calculator declines to show a result for that input.
Frequently asked questions
Why is a standard die’s average 3.5, not a whole number?
Because the average of 1 through 6 is 3.5 — no single face shows that value, but it’s the long-run average across many rolls.
Does the expected value change with more dice?
Yes — it scales directly with the number of dice, since each die independently contributes its own expected value to the total.
Is this the same as the most likely roll?
Not necessarily — for multiple dice, the most common single outcome (the mode) can differ from the mathematical average, especially as more dice are added.
