What is expected value?

Expected value (EV) is the long-run average result of a random process. It is calculated as the sum of each outcome multiplied by its probability: EV = sum(x * P(x)).

Do probabilities need to sum to 1?

Yes, for a valid probability distribution all probabilities must sum to exactly 1 (or 100%). The calculator shows a warning if they do not, but still computes the weighted sum so you can spot the imbalance.

Can I enter probabilities as percentages?

Yes. The calculator automatically detects values greater than 1 and treats them as percentages, dividing by 100 before computing. So 25 and 0.25 are treated identically.

Can outcomes be negative?

Yes. Losses, costs, or penalties should be entered as negative numbers. The calculator handles negative outcomes correctly.

What does each outcome's contribution mean?

Each row's contribution is outcome × probability. The expected value is the sum of all contributions. The contribution bar shows how much each outcome pulls the EV up or down relative to the total.

How many outcomes can I add?

There is no hard limit — you can add as many rows as needed. For readability the table scrolls when rows exceed the visible area.

Expected Value Calculator

Enter outcomes and their probabilities to instantly compute the expected value of any discrete distribution.

Outcomes & Probabilities

Enter each outcome and its probability. Probabilities can be decimals (0.25) or percentages (25).

#	Outcome (x)	Probability P(x)

Expected Value

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Outcomes

Prob. Sum

Variance

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Contribution Breakdown

Add at least one outcome to see the breakdown.

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Summary

The expected value (EV) is the probability-weighted average of all possible outcomes of a random variable. It answers the question: "On average, what result should I expect?" This calculator lets you enter any number of outcome–probability pairs and computes the expected value, probability sum, and a visual breakdown of each outcome's contribution.

How it works

Enter a numeric outcome value in the "Outcome" field.
Enter its probability as a decimal (e.g. 0.25 for 25%) or a percentage (e.g. 25%).
Click "Add Row" to add more outcome–probability pairs.
The expected value updates live as you type.
Click "Reset" to clear all rows and start over.

Use cases

Evaluate the expected return of a lottery or gambling scenario.
Compare investment options by their probability-weighted payoffs.
Compute the expected score on a multiple-choice test with guessing.
Model expected project costs across optimistic, likely, and pessimistic scenarios.
Verify probability distribution homework problems.
Analyze expected profit/loss for business decisions with uncertain outcomes.

Frequently Asked Questions

Last updated: 2026-06-04 · Reviewed by Nham Vu