Expected value calculator
Enter the possible outcomes and the probability of each in the same order to see the long run average of a decision, game or investment.
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How to use it
- Enter outcomes x, probabilities p (1/6 is accepted) and probability format.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
E(X) = Σ x × p. Variance = Σ x² × p - E(X)². Standard deviation = √variance. The probabilities must add up to 1 (or 100%).
Example
Inputs: Probability format = Decimals (sum to 1). Result: Expected value E(X): 23; Variance: 1,501; Standard deviation: 38.742741.
Limits and caveats
- Discrete variables only, with a finite list of outcomes.
- The expected value is a long run average, not what you will get on a single try.
Questions about this tool
What is the expected value of a die roll?
(1 + 2 + 3 + 4 + 5 + 6) ÷ 6 = 3.5, even though a single roll never shows 3.5.
How do I know a bet or offer loses money?
If the expected profit after the cost is negative, you lose on average every time you repeat it.
Can I enter probabilities like 1/3?
Yes, type the fraction as 1/3. A tiny rounding difference in the total is accepted.