Expected Value Calculator
Enter each possible outcome’s value and its probability (as a percent) to calculate the expected value, variance, and standard deviation of the distribution.
What is Expected Value?
Expected value (E(X)) is the long-run average outcome of a random process if it were repeated many times, weighted by how likely each outcome is. It is one of the most fundamental ideas in probability and shows up in games of chance, insurance pricing, and investment decisions.
The Formula
E(X) = Σ (value of outcome × probability of outcome). This calculator multiplies each outcome by its probability, adds the results together, and also reports the variance and standard deviation, which describe how spread out the possible outcomes are around the expected value.
- Enter probabilities as percentages (they don’t need to add to exactly 100% while you experiment, but should for a valid distribution).
- Leave unused outcome rows blank.
This tool is for general educational and planning purposes and is not financial or professional advice.