1. Enter possible outcomes
Use positive numbers for gains, negative numbers for losses, and zero for break-even outcomes.
Probability and decision analysis
Expected Value Calculator
Calculate the probability-weighted average of possible outcomes, measure variance and standard deviation, review gain and loss probabilities, and project the expected total across repeated trials.
Dynamic outcome rows
Weighted contributions
Risk and variability
Expected value
$28.00
Std. deviation
$66.45
Gain probability
70%
Calculate expected value from multiple outcomes
Enter each outcome and probability. Probabilities must total 100% or 1.00.
Expected value is a long-run probability-weighted average. It does
not guarantee the result of one trial and should be considered with
downside risk, variability, assumptions, and probability quality.
How the Expected Value Calculator works
Each outcome is multiplied by its probability. The weighted contributions are added to calculate expected value, while variance and standard deviation measure how widely possible outcomes are spread around that average.
2. Assign probabilities
Enter percentages totalling 100% or decimals totalling 1.00.
3. Review expected return and risk
Compare expected value with standard deviation, outcome range, and gain or loss probability.
Expected Value
E(X) = Σ [Outcome × Probability]
Variance
Var(X) = Σ [Probability × (Outcome − E(X))²]
Repeated-Trial Expected Total
Expected Total = E(X) × Number of Trials
Signal
Meaning
What to review
Positive expected value
Favourable long-run average
Review downside size, liquidity, time horizon, variability, and the reliability of the probability estimates.
Negative expected value
Unfavourable long-run average
Repeated participation is expected to lose value unless missing benefits or outcomes materially change the model.
High standard deviation
Wide uncertainty
Results may differ greatly from the expected value. Review rare outcomes, risk limits, and diversification.
Incomplete probability total
Missing or overlapping scenarios
Confirm that outcomes are mutually exclusive and collectively exhaustive, then correct rounding or omissions.
Frequently asked questions
Important details for calculating and interpreting expected value.
What is expected value?
Expected value is the probability-weighted average of all possible outcomes. It represents the long-run average result across many repetitions.
How is expected value calculated?
Multiply every outcome by its probability, then add all weighted contributions.
Must probabilities total 100%?
Yes. They should total 100% in percentage format or 1.00 in decimal format.
Can expected value be negative?
Yes. A negative result means the probability-weighted average outcome is below zero.
Does positive expected value guarantee profit?
No. It describes a long-run average, not the guaranteed result of one attempt.
Why calculate variance and standard deviation?
They describe variability and help distinguish decisions with similar expected values but different risk.
What does expected value over repeated trials mean?
It is the single-trial expected value multiplied by the number of comparable repetitions.
Where is expected value used?
It is used in probability, finance, insurance, games, forecasting, investing, business analysis, and risk management.