Dice Average Calculator
Find the expected sum and standard deviation for identical independent fair dice.
Formula
E[S]=n(s+1)/2; SD(S)=√(n(s²−1)/12).
Mean of one die ≈ ((6)+1)÷2 · Expected sum ≈ (2)×(3.5) · Standard deviation of sum ≈ sqrt((2)×((6)^2-1)÷12)
How to use
- Enter the number of sides.
- Enter the number of independent dice.
- Read expected sum and standard deviation.
Examples
- Three fair d6 have expected sum 10.5.
Frequently asked questions
How are faces numbered?
Consecutively from 1 through the side count s.
Can I roll the average?
Not necessarily. An expectation may be fractional.
Does this support loaded dice?
No. Each face must have equal probability.
Sources
Updated: