Expected Value Calculator
Enter discrete outcomes and their probabilities to calculate expected value, net expectation after a fixed cost and outcome spread.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Multiply every outcome by its probability and add the contributions. Subtract a fixed participation cost for net expectation. Variance weights squared differences from the mean; its square root is the standard deviation.
E[X]=ΣxP(x); net expectation=E[X]−cost; Var(X)=Σ(x−E[X])²P(x)
Worked example
Outcomes0,10,20 with probabilities50%,30%,20% have expected value7. With fixed cost5, net expectation is2 per trial. A single trial need not return7.
Assumptions and input details
Use1–20 rows, with signed outcome values and nonnegative probabilities that sum to exactly100%. Values, probabilities and cost accept fractions or six-place decimals within±1e6 and reduced denominators≤1e6. Cost must be nonnegative and share the same unit or currency as outcomes. No currency conversion, tax or predictive probabilities are supplied. Exact fractions determine expectation and variance; standard deviation is approximate.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Entered probabilities, expectation and variance use exact fraction arithmetic. Standard deviation and the probability chart are approximate.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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