Dice Expected Value Calculator

Calculate the expected sum and statistics for rolling dice.

Fill in the fields below to calculate

Number of Dice

Die Type

Enter your values above to see the result.

Your Results

Expected Total

Variance

Std. Deviation

Minimum Roll

Maximum Roll

Formulas

Single Die Expected Value:

E = (n + 1) / 2

Single Die Variance:

Var = (n² - 1) / 12

Multiple Dice (N dice):

E_total = N × E

Var_total = N × Var

where n = number of sides per die

Pro Tips

Results update as you type — change any field to see the effect immediately.

Check that every value uses the same unit before comparing results.

Use the copy button to paste the dice expected value figures into a note or spreadsheet.

Nothing is sent to a server, so you can use this with private figures.