What This Calculator Does
This calculator finds the expected (average) total when rolling one or more dice with any number of sides, based on probability theory rather than simulation.
The Formula
For a single fair die with s sides numbered 1 through s, the expected value of one roll is:
- Average per die = (s + 1) / 2
- Expected total for n dice = n × (s + 1) / 2
- Variance per die = (s² − 1) / 12, and total variance scales as n × variance per die
This is the long-run average you’d see if you rolled the dice many, many times and averaged the results — any single roll will vary around this number, with the standard deviation showing how much typical rolls swing away from the average. For general educational and gaming-reference use.
Last reviewed August 2026