🎲 EMV Calculator — Expected Monetary Value
Calculate expected value for decision making
Outcomes
Note: Probabilities must sum to 100%
How to Use This Calculator
Define Outcomes
For each possible outcome, enter the probability (as a percentage) and the monetary value (positive for gains, negative for losses).
Ensure Probabilities Sum to 100%
All probabilities must add up to exactly 100%. The calculator will verify this before calculating.
Add or Remove Outcomes
Use the "Add Outcome" button to add more possible outcomes, or "Remove" to delete outcomes you don't need.
Calculate and Review
Click calculate to see the Expected Monetary Value, which represents the average outcome you can expect.
Formula
Expected Monetary Value (EMV):
EMV = Σ (Probability × Monetary Value)
Sum of all (probability × value) for each outcome
Note: All probabilities must sum to 100% (1.0)
Example 1: Investment Decision
Outcome 1: 60% chance of $10,000 gain | Outcome 2: 40% chance of $5,000 loss
EMV: (0.60 × $10,000) + (0.40 × -$5,000) = $6,000 - $2,000 = $4,000
✅ Positive EMV indicates favorable expected outcome
Example 2: Project Risk Analysis
Outcome 1: 30% chance of $50,000 profit | Outcome 2: 50% chance of $20,000 profit | Outcome 3: 20% chance of $10,000 loss
EMV: (0.30 × $50,000) + (0.50 × $20,000) + (0.20 × -$10,000)
= $15,000 + $10,000 - $2,000 = $23,000
About EMV Calculator — Expected Monetary Value
The EMV (Expected Monetary Value) Calculator helps decision-makers evaluate decisions under uncertainty by calculating the weighted average of all possible monetary outcomes. This decision analysis tool combines probabilities and monetary values to provide a single number representing the expected outcome, helping you make informed decisions when facing risk and uncertainty.
When to Use This Calculator
- Investment Decisions: Evaluate investment opportunities with uncertain returns
- Risk Analysis: Assess risks and expected outcomes for business decisions
- Project Evaluation: Compare projects with different risk profiles
- Insurance Decisions: Evaluate insurance options and expected costs
- Strategic Planning: Make strategic decisions when outcomes are uncertain
- Contract Negotiation: Evaluate contract terms with uncertain outcomes
Why Use Our Calculator?
- ✅ Multiple Outcomes: Handle any number of possible outcomes
- ✅ Probability Weighting: Properly weights outcomes by their probabilities
- ✅ Clear Breakdown: Shows contribution of each outcome to total EMV
- ✅ Decision Support: Provides objective basis for decision making
- ✅ Free Tool: No cost for essential decision analysis
Common Applications
- Business Investment: Evaluate capital investment decisions
- Risk Management: Assess expected losses from risks
- Gaming and Gambling: Calculate expected value of bets
- Insurance Analysis: Evaluate insurance coverage decisions
Tips for Best Results
- Accurate Probabilities: Base probabilities on data, expert opinion, or historical patterns
- Complete Outcomes: Include all possible outcomes - probabilities must sum to 100%
- Realistic Values: Use realistic monetary values for each outcome
- Consider All Costs: Include both positive (gains) and negative (losses) values
- Regular Updates: Recalculate as probabilities or values change
Frequently Asked Questions
What does Expected Monetary Value mean?
EMV is the weighted average of all possible outcomes, where each outcome is multiplied by its probability. It represents the average outcome you can expect over many repetitions of the decision. A positive EMV is favorable, negative is unfavorable.
Do I need to use probabilities that sum to exactly 100%?
Yes. Probabilities must sum to exactly 100% because all possible outcomes must be accounted for. If you have uncertainty about probabilities, use your best estimates or run sensitivity analysis with different probability scenarios.
Can I use negative monetary values?
Yes! Negative values represent losses or costs. For example, if an outcome has a 30% chance of losing $10,000, enter -10000 as the value. The EMV will properly account for this loss.
How do I interpret a negative EMV?
A negative EMV means the expected outcome is a loss on average. This suggests the decision is unfavorable, but you may still choose it based on risk tolerance, strategic value, or other non-monetary factors.
Should I always choose the option with highest EMV?
Not necessarily. EMV is a useful guide, but also consider risk tolerance, worst-case scenarios, strategic value, and other factors. A higher EMV with high variance may be riskier than a lower EMV with lower variance.
How do I estimate probabilities accurately?
Use historical data, market research, expert opinions, or statistical models. For new situations, use conservative estimates or run sensitivity analysis. The key is being consistent and realistic in your probability estimates.