This dice average calculator reports the expected total, range, variance, and standard deviation for identical independent fair dice.
Statistics
Dice Average Calculator
Calculate the expected total, range, variance, and standard deviation for identical fair dice.
Calculator
About this calculator
Formula notes
one-die mean = (faces + 1) / 2; total mean = dice × one-die mean; total variance = dice × (faces^2 - 1) / 12; standard deviation = square root of variance.
Worked examples
- Example: two fair six-sided dice have expected total 7, range 2 to 12, variance 35/6, and standard deviation about 2.415.
- Five fair eight-sided dice have expected total 22.5, minimum 5, maximum 40, variance 26.25, and standard deviation about 5.1235.
How to use it
- Choose the number of faces on each die.
- Enter the number of identical dice.
- Use the expectation for long-run averages, not as a promised roll.
Frequently asked questions
Does an expected total of 7 mean I will roll 7?
No. Expectation is a long-run average across repeated independent rolls, not a prediction of one outcome.
Can this model loaded or mixed dice?
No. Every die is assumed fair, independent, and to have the same supported number of faces.
Limits and interpretation
- The closed-form moments require identical independent fair dice; loaded dice, rerolls, exploding dice, keep-highest rules, or mixed face counts need a different probability model.
- Mean and standard deviation do not provide the full discrete probability distribution, tail probabilities, or the chance of hitting a particular target total.