Expected Utility Calculator

Expected Utility Calculator

Free online expected utility calculator to estimate expected utility from possible outcomes and their probabilities. This calculator is useful for economics students, finance students, risk analysts, investors, decision-makers, researchers, and anyone comparing uncertain choices where utility matters more than raw money alone. Expected utility is a core idea in economics and decision theory because people do not always evaluate choices only by expected money value. Instead, they may care about satisfaction, preference, risk tolerance, or overall usefulness. This page gives a simple way to turn those utility judgments into one expected value for comparison.

The calculator works with two outcomes and their probability percentages. Outcome 1 utility means the utility score assigned to the first scenario. Outcome 2 utility means the utility score assigned to the second scenario. Each outcome has its own probability. Once those values are entered, the calculator shows the weighted utility of each outcome, the total expected utility, and the combined probability total. This makes the page useful for comparing risky choices, checking classroom examples, testing basic decision models, and understanding how probabilities and preferences work together in one result.

The formula of expected utility

Weighted utility 1 = Outcome 1 utility x Outcome 1 probability

Weighted utility 2 = Outcome 2 utility x Outcome 2 probability

Expected utility = Weighted utility 1 + Weighted utility 2

Probability total = Outcome 1 probability + Outcome 2 probability

Here utility means the satisfaction, preference score, or usefulness assigned to an outcome, and probability means the chance of that outcome occurring. Expected utility means the average utility you would expect when probabilities and utility values are combined. Unlike expected monetary value, the utility scores do not need to be currency values. They can be any consistent preference scale that reflects how desirable each outcome feels to the decision-maker.

Solved Example

Example 1: Find the expected utility if Outcome 1 utility is 90 with a 60% probability, and Outcome 2 utility is 40 with a 40% probability.

Solve: Weighted utility 1 = 90 x 0.60 = 54

Weighted utility 2 = 40 x 0.40 = 16

Expected utility = 54 + 16 = 70

Probability total = 60% + 40% = 100%

Example 2: Find the result if Outcome 1 utility is 120 with a 35% probability, and Outcome 2 utility is 30 with a 65% probability.

Solve: Weighted utility 1 = 120 x 0.35 = 42

Weighted utility 2 = 30 x 0.65 = 19.50

Expected utility = 42 + 19.50 = 61.50

Example 3: Find the result if Outcome 1 utility is 70 with a 25% probability, and Outcome 2 utility is 10 with a 75% probability.

Solve: Weighted utility 1 = 70 x 0.25 = 17.50

Weighted utility 2 = 10 x 0.75 = 7.50

Expected utility = 17.50 + 7.50 = 25.00

Table of expected utility calculator

How to use this expected utility calculator

Enter the first outcome utility in the proper input field. After that, enter the probability percentage for that outcome. Then enter the second outcome utility and its probability percentage. Finally, click the calculate button. The calculator will show the weighted utility of each outcome, the expected utility, and the combined probability total in the result box. Make sure the two utility scores belong to the same decision and use the same preference scale.

This calculator is useful when money alone is not enough to describe the quality of a decision. In many choices, a person or business may prefer a safer option with lower expected money if it delivers higher expected utility because of lower risk, more certainty, or better alignment with preferences. That is why expected utility is such an important idea in economics and behavioral decision-making. It helps compare alternatives when satisfaction or usefulness matters as much as, or more than, the monetary outcome itself.

When using the result, remember that expected utility depends heavily on how utility scores are assigned. Different people can assign different utility values to the same outcomes because they have different preferences, risk tolerance, goals, or constraints. The calculator also uses only two outcomes in this version, so more complex decisions may need additional modeling. Even so, expected utility remains one of the clearest entry points into decision theory. This calculator gives a fast numerical view that supports classroom learning, simple risk analysis, preference modeling, and clearer comparison of uncertain choices.