Expected Value Calculator
Works out the long-run average of something with uncertain outcomes.
Expected value
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Share sends a link that reopens these numbers. Copy details pastes the full breakdown as a list.
Values read in each list —
Variance —
Standard deviation —
Probabilities add up to —
Reading this —
The formula
E[X] = Σ x × P(x) Var[X] = Σ P(x)(x − E[X])²
Each outcome is weighted by its probability.
What to watch out for
The expected value need not be a possible result. Comparing options by this alone ignores risk, which is why the standard deviation is also shown.
Frequently Asked Questions
What is the expected value of a die?
3.5, a result you can never actually roll.
What is a worked example?
Outcomes 0, 10 and 100 at 0.9, 0.09 and 0.01 give 1.9.