Expected Value Calculator
Expected value of a discrete outcome list.
Enter your values
Enter the outcome values (comma-separated) you are working with.
Enter the probabilities (comma-separated, sum to 1) you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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
At a glance
| What it does | Expected value of a discrete outcome list. |
|---|---|
| Category | Statistics |
| Inputs needed | Outcome values (comma-separated), Probabilities (comma-separated, sum to 1) |
| Main output | Expected value |
| Formula | E[X] = Σ x_i * p_i |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Outcome values (comma-separated)
- Enter the outcome values (comma-separated) you are working with.
- Probabilities (comma-separated, sum to 1)
- Enter the probabilities (comma-separated, sum to 1) you are working with.
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.
What do I need to enter into the Expected Value Calculator?
Just 2 values: outcome values (comma-separated), probabilities (comma-separated, sum to 1). Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Expected Value Calculator work out the answer?
Expected value is the sum of each outcome multiplied by its probability of occurring. It applies the formula E[X] = Σ x_i * p_i and shows the working so you can check each step by hand.
Is the Expected Value Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.