# Expected Value Calculator

URL: https://speedycalculator.com/calculators/statistics/expected-value/
Last updated: 2026-10-25

> The expected value calculator finds the long-run average outcome of a random variable from its possible values and their probabilities, plus the variance and standard deviation.

## Inputs

- Outcomes
- Probabilities (same order) — As decimals or percentages; they are normalised.

## Results

- Expected value
- Sum of probabilities

## Formula

```
E[X] = Σ xᵢ pᵢ
```

## Explanation

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

FieldWhat to enterOutcomesA list of numbers separated by commas, spaces or new linesProbabilities (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)])

## Worked 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.

## FAQ

**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.