Expected Utility Calculator

How the Expected Utility Calculator works and its utility

The Expected Utility Calculator computes the expected value of different scenarios by combining probabilities and associated monetary values. It converts percentage probabilities into decimal probabilities, multiplies each decimal probability by its monetary value to get weighted values, and sums those weighted values to produce the expected utility. This approach is rooted in expected utility theory and is useful for evaluating choices under uncertainty.

This calculator helps decision makers estimate the average outcome of risky options before committing resources. It is particularly useful for investors, risk managers and financial professionals who need a quick quantitative assessment of tradeoffs between probability and monetary outcomes. Using the calculator can clarify whether an option has a positive expected return, identify dominant alternatives, and support risk-aware comparisons between projects or investments.

Key outputs produced by the calculator

• Weighted Value Event 1: probability of event 1 (decimal) multiplied by monetary value of event 1
• Weighted Value Event 2: probability of event 2 (decimal) multiplied by monetary value of event 2
• Total Probability: sum of input probabilities, as a check that probabilities add up sensibly
• Expected Utility: sum of all weighted values; represents the expected monetary outcome

How to use the calculator (step by step)

1. Enter Probability of Event 1 (%) in the field labeled "Probability of Event 1 (%)". Example format: 30 for thirty percent. This value should be between 0 and 100.
2. Enter the Monetary Value of Event 1 in the field labeled "Monetary Value of Event 1". Use the same currency or unit across all events.
3. Enter Probability of Event 2 (%) in the field labeled "Probability of Event 2 (%)". Again, use a percentage value between 0 and 100.
4. Enter the Monetary Value of Event 2 in the field labeled "Monetary Value of Event 2".
5. Click Calculate. The calculator will:
   • Convert each percentage probability to decimal form by dividing by 100.
   • Compute weighted values: decimal probability multiplied by the corresponding monetary value for each event.
   • Sum the weighted values to produce the Expected Utility result.
   • Report the Total Probability by summing the input percentages to help you spot input errors.
6. If you need to start over, click Reset to clear the inputs and outputs.

Formula used

For two events, the calculator uses the following formula:

Expected Utility = (Probability of Event 1 as decimal) × (Monetary Value of Event 1) + (Probability of Event 2 as decimal) × (Monetary Value of Event 2)

Example notation: Expected Utility = p1 × v1 + p2 × v2

Practical examples of use

The examples below demonstrate how to apply the calculator to common decision situations.

Example 1: Investment choice with positive expected return

Scenario: A small investment can yield either a gain of 1,000 or a loss of 200. You estimate a 70% chance of gain and a 30% chance of loss.

• Probability of Event 1 = 70% → p1 = 0.70
• Monetary Value of Event 1 = 1000 → v1 = 1000
• Probability of Event 2 = 30% → p2 = 0.30
• Monetary Value of Event 2 = -200 → v2 = -200

Weighted Value Event 1 = 0.70 × 1000 = 700

Weighted Value Event 2 = 0.30 × -200 = -60

Expected Utility = 700 + (-60) = 640

Interpretation: On average, this investment yields 640 per trial. The positive expected utility suggests the tradeoff is favorable under these assumptions.

Example 2: Business project with uneven probabilities

Scenario: A project either succeeds, producing 50,000 in profit, or fails, producing a loss of 10,000. You estimate a 20% chance of success and an 80% chance of failure.

• Probability of Event 1 = 20% → p1 = 0.20
• Monetary Value of Event 1 = 50,000 → v1 = 50,000
• Probability of Event 2 = 80% → p2 = 0.80
• Monetary Value of Event 2 = -10,000 → v2 = -10,000

Weighted Value Event 1 = 0.20 × 50,000 = 10,000

Weighted Value Event 2 = 0.80 × -10,000 = -8,000

Expected Utility = 10,000 + (-8,000) = 2,000

Interpretation: The expected utility is 2,000. Even with a low chance of success, the high payoff makes the project marginally attractive by expected value. Consider risk tolerance and capital constraints before proceeding.

Practical tips when using the calculator

• Ensure Total Probability is meaningful: for mutually exclusive outcomes the probabilities should sum to 100%. If they do not, normalize or revisit your inputs.
• Use consistent monetary units: mix of currencies or units will make results meaningless.
• Consider using a utility transformation for large stakes: monetary value can be transformed by a utility function if risk preferences matter (for example, diminishing marginal utility of money).
• Round intermediate values sensibly when presenting results, but keep full precision for internal calculations.

Expected Utility Applications

• Investment Analysis: Evaluate different investment options considering expected returns and associated risks.
• Risk Management: Quantify risks in business projects and strategic decisions.
• Decision Making: Compare alternatives with different success probabilities and associated values.

Important Note

This calculator assumes mutually exclusive events and independent probabilities. In practice, consider correlations between events and adjust probabilities as needed for your specific scenario.

Conclusion

The Expected Utility Calculator is a straightforward, quantitative tool for comparing uncertain options using probabilities and monetary outcomes. It helps reveal the average expected outcome, supports objective comparisons between alternatives, and highlights whether an option is favorable on expectation. Key benefits include faster decision making, clearer communication of tradeoffs, and a simple method to screen investment or project choices before applying deeper analysis. Use it as a first-step risk assessment, and complement its results with sensitivity checks, correlation analysis, and considerations of risk preferences when stakes are high.