statistics-and-probability calculator
Dice Average Calculator
Calculate a fair die's expected average or the average of recorded rolls.
Dice Average Calculator
Average per die
Choose a mode and enter dice information.
Expected value is a long-run average, not a prediction of one roll.
Formula version 1.0.0
How to use this calculator
- Choose expected or observed mode.
- Enter the number of sides on each fair die.
- For expected mode enter the dice count; for observed mode enter recorded rolls.
- Calculate and compare the mean with the expected total where applicable.
Symbols and units
| Symbol | Meaning | Unit or domain |
|---|---|---|
s | Sides per die | sides |
n | Number of dice or observations | count |
E[X] | Expected value per fair die | pips |
x̄ | Observed arithmetic mean | pips |
Checked examples
Two fair six-sided dice
Inputs: Expected mode, 2 dice, 6 sides
Calculation: E[X]=(1+6)÷2=3.5; total=2×3.5
Result: Average 3.5; expected total 7
This is a long-run expectation, not a guaranteed roll.
Check: dice-average.test.ts
Observed rolls
Inputs: 1, 3, 6, 4 on a six-sided die
Calculation: x̄=(1+3+6+4)÷4
Result: 3.5
The sample average happens to equal the fair-die expectation.
Check: dice-average.test.ts
Assumptions, rounding, and limits
- Expected mode assumes a fair die with faces 1 through s.
- Observed rolls are whole numbers within the die range.
- Rolls are treated as equally weighted observations.
- The tool does not test whether a die is fair.
Frequently asked questions
Does an expected total guarantee that roll?
No. Expected value is a long-run average over many repetitions.
Can I enter a custom-faced die?
No. Expected mode assumes consecutive labels from 1 to the side count.
Why can an observed mean differ?
Finite random samples naturally vary around the theoretical expectation.
Sources and review
- OpenStax: Expected Value — Expected value of a discrete random variable
- Formula version
- dice.average@1.0.0
- Formula review
- Equatara formula review
- Editorial review
- Equatara editorial review
- Last verified
- 2026-10-25
- Applicability
- Fair consecutive-faced dice or arithmetic mean of supplied valid rolls.
- Next review
- On material formula/source change, or by 2028-10-25.
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Found a problem?
Report a formula, result, example, source, or accessibility issue through the calculator correction process. Do not include sensitive input values.