EMV = Probability × Impact, summed across outcomes
Expected monetary value turns a risk, or a choice with uncertain outcomes, into one dollar figure you can compare. Use the risk list for threats and opportunities, or the decision tree to compare two options, then read how the exam tests it below.
Click Calculate to see the EMV of each risk and the net.
Updated October 2026.
PMBOK 8's glossary defines expected monetary value as “the estimated value of an outcome expressed in monetary terms.” In plain English: for one risk, multiply the probability by the impact, and when there are several possible outcomes, do that for each one and add them up. The guide doesn't print a standalone EMV = probability × impact formula. The probability-weighted math appears inside its example decision tree, Figure 5-5 in Section 5.
A threat costs you money, so its EMV is negative. An opportunity earns you money, so its EMV is positive. A 30 percent chance of a $40,000 loss is −$12,000. A 40 percent chance of a $10,000 saving is +$4,000. Add the signed values across a risk list and you get the net EMV. A negative net means the threats outweigh the opportunities on average.
PMBOK 8 describes decision tree analysis as a diagramming and calculation technique for evaluating a chain of options under uncertainty, used to select the best of several alternatives. The branches carry costs and individual risks, both threats and opportunities, and the tree is evaluated by calculating the EMV of each branch so the optimal path can be selected. It's listed as a data analysis technique of Perform Risk Analysis (Section 2.7.2.3, Figure 2-50), in the Risk performance domain.
Two node types matter. A decision node (a square) is where you choose. A chance node (a circle) is where the outcome is left to probability, and the probabilities on one chance node have to total 100 percent. To evaluate an option, multiply each chance outcome by its probability, add them up, then subtract the investment cost of that option. Pick the option with the higher EMV. If you have the guide, Figure 5-5 shows a worked tree. The example below uses our own numbers.
The calculator above is prefilled with these numbers. Click Calculate on each tab to see them.
Risk list.
Decision tree, “Build in-house or buy?”
Buy has the bigger payoff and the safer odds, and it still loses once you subtract what it costs. That's the trap the exam is built around.
PMBOK 8 (Section 2.7.2.3) describes qualitative analysis as assessing individual risks by probability and impact throughout the project. Quantitative analysis may not always be required, and when it is, it numerically analyzes the combined effect of risks and uncertainty on project objectives. EMV and decision trees are quantitative tools.
PMI doesn't publish a formula list, so no one can promise you an EMV question. What's documented: PMBOK 8 lists decision tree analysis as a data analysis technique of Perform Risk Analysis, which sits in the Risk performance domain, and risk work falls in the Process domain, 41 percent of the exam. Recent passers report very little calculation on the new exam, so expect EMV as a reading question: which option, which risk to address first, is the reserve enough. Know the math well enough to check an answer choice in ten seconds.
One related point. PMBOK 8 says contingency reserves are budget within the cost baseline for identified risks, and may be developed using quantitative analysis methods. A common way to size a contingency reserve is to add up the EMVs of the identified threats. That's common practice, not something the guide prints.
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Start Free →For one risk, EMV is probability times impact: a 30 percent chance of a $40,000 loss is an EMV of -$12,000. Across several outcomes, multiply each by its probability and add them up. Threats are negative, opportunities positive. PMBOK 8 defines EMV as the estimated value of an outcome expressed in monetary terms and shows the weighted calculation in its example decision tree.
For each option, multiply every chance outcome by its probability, add them up, then subtract that option's investment cost. The option with the higher EMV wins. If the tree is built in costs, the lowest expected cost wins. The probabilities on each chance branch must total 100 percent.
PMI does not publish a formula list. PMBOK 8 lists decision tree analysis as a data analysis technique of Perform Risk Analysis, which sits in the Risk performance domain, and risk work falls in the Process domain, 41 percent of the exam. Recent passers report very few calculations, so expect EMV inside a scenario where you pick an option or a risk response.
Quantitative. Qualitative analysis ranks individual risks by probability and impact. Quantitative analysis puts numbers on the combined effect of risks, and PMBOK 8 notes it isn't always required. EMV and decision trees are quantitative tools.