Expected Utility (EU) Calculator
Enter probabilities (in %) and utility scores for up to four outcomes. The tool computes expected utility using decision theory: EU = Σ(p × u).
What Is an EU Calculator?
An EU calculator is a practical tool for decision analysis. EU stands for Expected Utility, a framework used in economics, finance, psychology, and management to compare uncertain choices. Instead of asking only, “What is the average outcome?”, expected utility asks, “How valuable is each possible outcome to me, and how likely is it?”
That distinction matters when risk preferences are involved. Two choices can have the same average payoff but feel very different if one has higher downside risk. Utility lets you map outcomes to personal value, so your final score better reflects how you actually decide.
How the Formula Works
Core Equation
EU = Σ (Probability of outcome × Utility of outcome)
If there are four possible outcomes, you multiply each probability by its utility and add all contributions together. In this calculator, probabilities are entered in percent, then converted into weights.
Normalization Rule
If your probabilities do not sum to exactly 100%, this calculator automatically normalizes them so they still represent a full distribution. This is helpful for rough estimates and quick scenario testing.
How to Use This EU Calculator
- Enter a probability and utility for each outcome you want to include.
- Leave unused outcomes at zero.
- Optionally enter a certainty equivalent (or risk-free utility) to compare with your EU.
- Click Calculate EU to generate the result and contribution breakdown.
Worked Example: Choosing Between Two Career Paths
Suppose you are evaluating a startup role. You define these outcomes:
- 50% chance of moderate success, utility = 70
- 30% chance of strong success, utility = 95
- 15% chance of stagnation, utility = 25
- 5% chance of failure, utility = -40
The EU combines all four outcomes into one score. You can then compare that score to a stable corporate role with a known utility (for example, 55). If startup EU is above 55, your own utility assumptions suggest the startup is preferred.
Interpreting Your Result
Higher EU Means Better (Given Your Inputs)
Expected utility is comparative. A value of 42 is not universally “good” or “bad.” It becomes meaningful when compared to alternative decisions computed on the same utility scale.
Utility Scale Consistency Matters
If you use a 0–100 utility scale for one option, keep the same scale for the alternatives. Inconsistent scales create misleading comparisons.
Common Mistakes to Avoid
- Confusing payoff with utility: money, time, stress, and meaning may all influence utility.
- Ignoring downside outcomes: small-probability losses can strongly affect expected utility.
- Using random probabilities: estimates should be thoughtful and evidence-based when possible.
- Comparing scores from different scales: always standardize your utility method first.
When an EU Calculator Is Most Useful
This expected utility calculator is especially useful for:
- Investment and portfolio decisions
- Business strategy under uncertainty
- Career planning and life tradeoffs
- Policy choices where outcomes have different social values
- Any decision that has multiple possible futures
Final Thoughts
A good EU calculator does not replace judgment; it structures it. By explicitly setting probabilities and utility values, you make your assumptions visible, testable, and easier to improve. If your assumptions change, update the inputs and re-run the model. Over time, this creates sharper decisions and a clearer understanding of your risk preferences.