Project-management formulas help turn budget, schedule, risk and investment data into interpretable decisions. They can also appear in PMP preparation, but PMI does not promise a fixed number of mathematical questions. Its revised July 2026 PMP exam tests People (33%), Process (41%) and Business Environment (26%), with predictive, agile and hybrid scenarios throughout. Learn what each formula measures, when its assumptions hold and how to explain the result—not just the letters.
Use these symbols consistently in earned-value examples: BAC is the total baseline budget, PV is the budgeted value of work scheduled by the measurement date, EV is the budgeted value of work actually completed, and AC is its actual incurred cost. PV and EV are monetary quantities; they are not calendar dates. Earned-value calculations use an agreed measurement baseline, which might need revision under approved changes.
Communication channels and project complexity
The number of possible one-to-one communication channels among n participants is n(n − 1) / 2. With 8 stakeholders, there are 8 × 7 / 2 = 28 potential pairs. Adding two people creates 10 × 9 / 2 = 45 pairs—17 more than before. This arithmetic is useful for appreciating coordination complexity, but it does not imply that every pair will actually communicate.
A project manager can reduce avoidable confusion through clear roles, a shared decision register, regular targeted updates and one authoritative source for critical decisions. The formula illustrates possible connections, not the quality or frequency of communications.
Earned value: cost and schedule variance
Cost variance is CV = EV − AC. A negative result means the value of completed work is below the cost incurred, using the baseline valuation. Schedule variance is SV = EV − PV. A negative result means less budgeted work was completed than planned by the measurement point; it is measured in currency, not units of time.
Assume BAC = $120,000, EV = $60,000, PV = $70,000 and AC = $75,000. Then CV = $60,000 − $75,000 = −$15,000, while SV = $60,000 − $70,000 = −$10,000. These measures indicate cost overrun and lag against planned earned-value progress. They do not identify the root cause; investigate resource, scope, estimation and sequencing changes.
Cost performance index is CPI = EV / AC, giving 0.80 in the example. Schedule performance index is SPI = EV / PV, giving approximately 0.86. Values below 1 indicate underperformance against their respective baselines. Do not read SPI as proof of a specific number of calendar days of delay, especially near completion when earned-value schedule indicators can become less informative.
Estimate at completion, remaining cost and final variance
EAC forecasts the total final cost. When current CPI is expected to continue, a simple model is EAC = BAC / CPI. With $120,000 / 0.80, EAC is $150,000. That is a scenario forecast, not a guaranteed bill. If the remaining work is expected to proceed exactly at its original budgeted rate, another model is EAC = AC + (BAC − EV) = $75,000 + $60,000 = $135,000.
These models answer different questions. An analyst must choose an assumption justified by the work left and the reason the project has overrun. If a one-off supplier price increase will not recur, extrapolating poor CPI to every remaining task may be pessimistic. If an underlying productivity problem continues, assuming the rest will be delivered at the baseline rate may be unrealistic.
Estimate to complete is ETC = EAC − AC. Under the continuing-CPI forecast, the project requires $75,000 beyond what has already been spent. Variance at completion is VAC = BAC − EAC, or −$30,000, indicating a projected budget overrun. These quantities help leaders decide whether to revise funding, reduce scope through authorized change control, or improve execution.
To-complete performance index and target feasibility
TCPI measures the future cost efficiency needed to meet a specified target. To meet the original BAC, TCPI = (BAC − EV) / (BAC − AC). In the example that equals $60,000 / $45,000, about 1.33. The remaining work would have to earn $1.33 of budgeted value for each dollar spent, much better than the current CPI of 0.80.
That gap is a management warning. It does not prove that recovery is mathematically impossible, but it shows the original budget would demand a substantial change in performance. When the agreed target changes to an authorized EAC, the denominator can instead use EAC − AC. Always state which target is being evaluated.
PERT, estimate spread and expected monetary value
A three-point PERT estimate uses optimistic O, most likely M and pessimistic P outcomes: expected duration = (O + 4M + P) / 6. If a task might take 4, 7 or 16 days, the weighted mean is (4 + 28 + 16) / 6 = 8 days. The conventional PERT standard-deviation estimate is (P − O) / 6, giving 2 days for those estimates.
PERT does not eliminate risk or guarantee a normal duration distribution. It makes uncertainty visible, but assumptions about independent tasks and the shape of outcomes matter. For a critical-path or delivery commitment, consider dependencies and correlation as well as individual activity estimates.
Expected monetary value is probability multiplied by financial impact. A risk with a 20% chance of a $50,000 loss has an EMV of −$10,000. An opportunity with a 30% chance of a $20,000 gain has an EMV of +$6,000. Adding EMVs can help compare alternatives, but severe low-probability losses may still require special treatment beyond their average expected cost.
Return on investment, present value and selection
A simple return on investment calculation is ROI = (gain from investment − investment cost) / investment cost. For a project costing $100,000 and producing $125,000 in gross measurable financial benefits, the net gain is $25,000 and ROI is ($125,000 − $100,000) / $100,000 = 25%. Define the time horizon and whether the benefit number is gross or net; otherwise two teams can report different results using the same acronym.
Present value discounts future cash flows into today’s terms: PV = FV / (1 + r)^n for one amount, using discount rate r and n periods. Net present value sums discounted cash flows, including the initial outlay. With consistent assumptions, a positive NPV suggests a proposal adds value relative to the chosen discount rate. Internal rate of return is the rate that makes NPV zero, but it can mislead for unusual cash-flow patterns or comparisons of different project scales.
A benefit-cost ratio compares discounted benefits with discounted costs, subject to an agreed definition. The payback period describes how quickly an initial outlay is recovered, but often ignores later cash flows and the time value of money. Compare several measures and business constraints rather than allowing a single ratio to override strategic or legal needs.
Apply each formula to a decision
Start each question by identifying its quantities and what the decision maker wants to know: current performance, the final-cost forecast, future required efficiency, risk exposure or investment selection. Check units and sign conventions, write the formula, calculate, then explain what would make the assumption invalid.
Earned-value calculations can help interpret project cost and schedule performance, but their indicators depend on trustworthy baselines and reporting. Project risk management also evaluates uncertainty and responses that no single formula can select. Quantitative results should inform—not replace—professional judgment.
Under PMI’s current approach, candidates must recognize the business and people consequences of project decisions as well as numerical indicators. Correct arithmetic is useful, but an effective project manager also asks why performance diverged and what action is authorized.