When to use this calculator
Expected monetary value helps describe an uncertain payoff but does not capture the full risk or personal utility of the outcomes.
Explore the probability & distributions calculators for other questions in this topic. For a related calculation, use the Exponential Survival Probability Calculator: Find the probability of waiting longer than a chosen time in an exponential model.
PUTTING IT INTO PRACTICE
Expected Monetary Value: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Probability of first outcome (%) | 25 |
| First outcome amount | 100 |
| Second outcome amount | -20 |
| Result | 10 currency units |
- Check the input labels and enter the example values above.
- Apply the relationship: Expected value = probability × first outcome + (1 − probability) × second outcome.
- The result is 10 currency units, rounded for display.
How to interpret your result
The two outcomes must be exhaustive and mutually exclusive. An expectation is not a promise.
A distribution model is an assumption about the process, not a guarantee about outcomes. Independence, constant probability and fixed interval definitions matter. Exactly-k probabilities differ from cumulative probabilities.
Frequently asked questions
Does exactly two successes mean two or more?
No. Exactly two counts only outcomes with two successes. Two or more is a cumulative probability covering several counts.
When is the expected monetary value calculator useful?
Expected monetary value helps describe an uncertain payoff but does not capture the full risk or personal utility of the outcomes.
How do I use the expected monetary value calculator?
Enter probability of first outcome (%), first outcome amount, second outcome amount. The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Expected value = probability × first outcome + (1 − probability) × second outcome.
What should I check before using the result?
The two outcomes must be exhaustive and mutually exclusive. An expectation is not a promise.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
Further reading
For background on this topic, see NIST: probability distributions ↗. This is a topic reference, not an external review or endorsement of this tool.
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