Expected Value Calculator
Expected value of a discrete outcome list.
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ⓘ Live results
Results
- Expected value
- 25
- Variance
- 2325
- Standard deviation
- 48.2183
Quick answer
Expected value is the sum of each outcome multiplied by its probability of occurring.
E[X] = Σ x_i * p_i
How to use the Expected Value Calculator
- 1List each possible outcome value.
- 2List the matching probability for each outcome (they should add to 1).
- 3The expected value weights every outcome by how likely it is.
Worked example
Using the values the calculator loads with:
Inputs
- Outcome values (comma-separated)100,-20,50
- Probabilities (comma-separated, sum to 1)0.2,0.5,0.3
Results
- Expected value25
- Variance2325
- Standard deviation48.2183
Frequently asked questions
What if probabilities don't sum to 1?
Rescale them so they add up to 1, or double-check you haven't missed an outcome.
Can expected value be negative?
Yes — it just means the weighted average outcome is a loss, common in gambling analysis.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.