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Calculation Machine

Expected Value Calculator

Expected value of a discrete outcome list.

Reviewed by the Calculation Machine team · How we check our maths

Your values

ⓘ Live results

Results
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.

The formula

E[X] = Σ x_i * p_i

Worked example

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

Result

  • Expected value25
  • Variance2325
  • Standard deviation48.2183

How to use the Expected Value Calculator

  1. 1List each possible outcome value.
  2. 2List the matching probability for each outcome (they should add to 1).
  3. 3The expected value weights every outcome by how likely it is.

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.

About this calculator