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Expected value calculator

Add each outcome and its probability to calculate Σxᵢpᵢ without silently normalizing the probabilities.

Values and probabilities

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Values may be negative, zero, or positive.

Use decimals from 0 to 1. All entered probabilities must total 1.

Expected value result

Enter at least one complete value–probability pair.

How to calculate expected value

Expected value is a probability-weighted long-run average for a fully specified discrete distribution. It is not a prediction of the next outcome.

How to use

  1. Enter one possible numeric value in each used row.
  2. Enter its probability as a decimal from 0 to 1; a probability of 0 is allowed.
  3. Leave unused rows completely blank and make the entered probabilities total 1.
  4. Calculate and inspect each xᵢ×pᵢ contribution before using the total.

Formula and probability check

For outcomes x₁…xₙ with probabilities p₁…pₙ, E(X)=Σxᵢpᵢ. The contribution list exposes every term in that sum.

The probability sum must be within 0.000000001 of 1 to allow ordinary decimal entry. The calculator reports a mismatch and does not rescale the values.

Worked examples

Three outcomes

For −2 with 0.25, 1 with 0.50, and 4 with 0.25, E(X)=−0.5+0.5+1=1.

Zero-probability outcome

Adding 999 with probability 0 contributes 0 and does not change the expected value.

Negative expected value

For −10 with probability 0.25 and 2 with probability 0.75, E(X)=−2.5+1.5=−1.

Limits and interpretation

  • This page accepts up to six discrete outcomes. It does not accept probability densities or continuous distributions.
  • Rows must be complete and probabilities must lie from 0 to 1. Blank lists, Infinity, NaN, and values beyond ±1 trillion are rejected.
  • Expected value is not the ordinary mean of the typed values unless their probabilities are equal.
  • The result does not guarantee a future outcome and is not gambling, investment, or risk advice.

Frequently asked questions

Why must probabilities total 1?

The rows should describe all mutually exclusive outcomes of one distribution.

Can expected value be negative?

Yes. Negative outcomes can outweigh positive contributions.

Why can the answer be impossible as one outcome?

Expected value is a weighted long-run average; it need not itself be an attainable outcome.

Is this a weighted-average calculator?

The arithmetic is similar, but these weights must be probabilities forming a complete distribution.