Expected Value Calculator

Calculate expected value, variance and standard deviation from a discrete probability distribution

Your result will appear here.

About the Expected Value Calculator

Expected Value Calculator finds the probability-weighted average outcome of a random process. It is useful for games, insurance, decisions and probability models where several outcomes have different chances.

Expected value is a long-run average, not a prediction of what must happen in the next trial. A process can have a positive expected value even though most individual outcomes are losses.

How to Use the Expected Value Calculator

  1. Enter each possible outcome value.
  2. Enter the probability associated with each outcome.
  3. Confirm probabilities sum to 1, or 100%, when the list is complete.
  4. Calculate the expected value and interpret it over repeated comparable trials.

How the Calculation Works

Expected value E[X] = Σ xi pi, where xi is an outcome and pi is its probability.

For a complete discrete distribution, probabilities should sum to 1. The weighted products are added to obtain the long-run average outcome.

Worked example

Expected Value Calculator Worked Example

50% chance of $10 and 50% chance of $0

Expected value = 10×0.5 + 0×0.5 = $5.

Result guide

Understanding Your Expected Value Calculator Result

An expected value of $5 does not mean one play will pay $5. It means the average result approaches $5 per trial over many repetitions under the same probabilities. Expected value is additive, which makes it useful for portfolios of repeated risks or rewards. Even so, a positive long-run average may be unsuitable when a single loss could exceed available cash or acceptable risk.

Before you rely on the answer

Assumptions and Limitations

  • Outcome values and probabilities are paired correctly.
  • Probabilities are valid and complete for the modeled distribution.
  • Repeated trials are comparable when using the long-run interpretation.

Practical tip

Using This Result in Practice

For decisions, compare expected value with risk and cash-flow constraints. Two choices can have the same expected value but very different downside exposure.

Related calculations

Useful Calculations to Continue With

If you need to calculate the underlying event probabilities first, use the Probability Calculator.

If outcomes come from repeated identical success/failure trials, use the Binomial Probability Calculator.

Common questions

Expected Value Calculator FAQ

What is expected value?

The probability-weighted average of all possible outcomes.

Does expected value predict the next outcome?

No. It describes the long-run average under repeated comparable trials.

Can expected value be negative?

Yes. Negative outcomes with enough probability or magnitude can make the weighted average negative.