Calculates the long-run average outcome of a random variable, weighting each possible result by how likely it is.
How it works
Each outcome is multiplied by its probability, and those products are summed.
What this does not include
This page supports up to three outcomes — a distribution with more possible outcomes needs every one accounted for, which this simplified form doesn’t handle.
How to use this calculator
- Enter each possible outcome and its probability (all probabilities must sum to 1).
A worked example
Two outcomes: +10 at 50% probability, −5 at 50% probability → expected value = (10 × 0.5) + (−5 × 0.5) = 2.5.
Three outcomes: 5 (20%), 10 (30%), 20 (50%) → expected value = (5×0.2) + (10×0.3) + (20×0.5) = 14.
What the variables mean
| Variable | Meaning |
|---|---|
| Outcome value | A possible result |
| Probability | Chance of that specific outcome occurring |
Edge cases worth knowing
Probabilities that don’t sum to exactly 1 signal a missing or double-counted outcome — the full set of listed outcomes must cover every possibility for the calculation to mean anything.
A negative expected value means a net loss on average over many repetitions — common in gambling scenarios deliberately designed to favor the house, even though any single play could still win.
Frequently asked questions
What does a negative expected value mean?
On average, over many repetitions, the outcome tends to be a net loss rather than a gain — common in gambling scenarios designed to favor the house.
Does expected value predict any single outcome?
No — it’s a long-run average across many repetitions, not a prediction of what happens on any one trial.
Why must the probabilities sum to exactly 1?
Because the outcomes listed must cover every possibility — probabilities that don’t sum to 1 mean some outcome is missing or double-counted.
