Expected value is used in betting, insurance, investing and decision analysis.
How to use the Expected Value Calculator
- Outcomes
- Probabilities (same order) — As decimals or percentages; they are normalised.
Results update as you type, and every field accepts the units shown in its menu.
How it works
Multiply each outcome by its probability and add. Probabilities should sum to 1 (or 100).
Inputs explained
| Field | What to enter |
|---|---|
| Outcomes | A list of numbers separated by commas, spaces or new lines |
| Probabilities (same order) | A list of numbers separated by commas, spaces or new lines. As decimals or percentages; they are normalised. |
What each result means
- Expected value = wavg([Outcomes], [Probabilities (same order)])
- Sum of probabilities = sum([Probabilities (same order)])
Formula
E[X] = Σ xᵢ pᵢWorked example
Inputs — Outcomes: 100, 20, 0, -10; Probabilities (same order): 0.05, 0.25, 0.4, 0.3.
Results — Expected value = 7; Sum of probabilities = 1.
Frequently asked questions
Do probabilities have to add to 1?
They should; the calculator normalises them if they do not.
Is a positive expected value a guaranteed profit?
Only in the long run over many repetitions.
What formula does the Expected Value Calculator use?
E[X] = Σ xᵢ pᵢ.