EMV Calculator – Expected Monetary Value

Weigh a decision's possible outcomes by their probability. Enter the payoff and likelihood of the optimistic, most-likely, and pessimistic cases to get the Expected Monetary Value (EMV), the risk spread, and the outcome range.

Quick Facts

Formula
EMV = Σ (probability × payoff)
Each outcome's payoff is weighted by its probability, then the weighted values are summed.
Rule
Probabilities must total 100%
The three outcomes must be mutually exclusive and cover every possibility for a valid expected value.

Your Results

Calculated
Expected Monetary Value
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Probability-weighted average payoff
Standard deviation
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Spread of outcomes around the EMV
Outcome range
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Optimistic minus pessimistic value
Relative risk (CV)
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Standard deviation as a share of EMV

Ready

Enter each outcome's value and probability (must total 100%), then press Calculate.

How the EMV Calculator works

Expected Monetary Value (EMV) is a standard decision-analysis technique used in project risk management, capital budgeting, and general decision trees. It converts a set of uncertain outcomes into a single probability-weighted average, so options with different risk profiles can be compared on the same scale.

The formula

For a decision with outcomes that are mutually exclusive and together cover every possibility, Expected Monetary Value is:

EMV = Σ (Probability of outcome × Value of outcome)

This calculator uses three outcomes — optimistic, most likely, and pessimistic — so the formula expands to EMV = (P1 × V1) + (P2 × V2) + (P3 × V3), where P1, P2, and P3 are expressed as decimals and must sum to 1 (100%). Because the probabilities must add up to 100%, EMV is a true weighted average, not just a sum of possibilities.

Worked example

Suppose a project has a 20% chance of a $50,000 payoff, a 55% chance of a $15,000 payoff, and a 25% chance of an $8,000 loss. The EMV is (0.20 × $50,000) + (0.55 × $15,000) + (0.25 × −$8,000) = $10,000 + $8,250 − $2,000 = $16,250. That figure is the average outcome you would expect if the same decision were repeated many times — no single trial actually lands on $16,250.

Reading the risk measures

  • Standard deviation measures how far the individual outcomes typically sit from the EMV. A small standard deviation means the outcomes cluster near the expected value; a large one means the decision could swing far in either direction even though the average looks fine.
  • Outcome range is simply the optimistic value minus the pessimistic value — the full width of what could happen, ignoring probability.
  • Coefficient of variation (CV) expresses the standard deviation as a percentage of the EMV, which makes it easier to compare risk across decisions with very different dollar scales.

What EMV does not tell you

EMV is a planning input, not a guarantee. It assumes the probabilities are estimated well, it treats gains and losses of equal size as equally important (no adjustment for risk aversion), and it says nothing about what happens if the pessimistic case actually occurs and the loss cannot be absorbed. In project risk management, EMV of individual risks is commonly summed to size a contingency reserve — but the reserve still needs judgment about which risks can happen at the same time.

Frequently Asked Questions

What is the formula for Expected Monetary Value?
EMV = sum of (probability of each outcome × monetary value of that outcome). This calculator uses three outcomes — optimistic, most likely, and pessimistic — so EMV = (P1 × V1) + (P2 × V2) + (P3 × V3), where P1+P2+P3 = 100%. The result is the probability-weighted average payoff of the decision.
Why do the probabilities have to add up to 100%?
EMV assumes the outcomes listed are mutually exclusive and cover every possibility for that decision. If the probabilities do not sum to 100%, the weighted average is not a true expected value — either an outcome is missing or one is double-counted, so the calculator flags the input as invalid until it sums correctly.
Can EMV be negative?
Yes. A negative EMV means the probability-weighted losses outweigh the probability-weighted gains, so on average the decision is expected to lose money over many repetitions. Enter losses as negative values in the outcome fields (for example -8000) to capture that in the calculation.
Does a higher EMV always mean the better choice?
EMV identifies the option with the best average payoff if the same decision were repeated many times, but it does not account for risk tolerance. A choice with a lower EMV but a much smaller standard deviation may be preferable when a single bad outcome cannot be absorbed, which is why this calculator also reports the standard deviation and range alongside the EMV.

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