PMP Formulas That Still Matter

PMP preparation still includes quantitative reasoning, but the purpose of formulas is not to turn project management into a mathematics exam. The July 2026 PMP refresh places greater emphasis on value, business impact, stakeholder engagement, adaptive delivery, AI, and sustainability. At the same time, project professionals still need to interpret cost, schedule, uncertainty, estimates, and financial choices. Formulas are useful because they turn project data into decisions.

The calculations below are therefore best learned with interpretation. For each one, know what the variables mean, what assumption the formula makes, and what decision the result should influence. Memorizing a ratio without understanding its implication is fragile preparation.

For broader context, PMP certification now tests a balance of People, Process, and Business Environment, with the Business Environment domain carrying substantially more weight than it did before July 2026.

Earned value foundations

Earned Value Management (EVM) compares planned work, completed work, and actual cost on a common budget basis. The three foundational measures are Planned Value (PV), Earned Value (EV), and Actual Cost (AC).

1. Planned Value (PV). PV is the approved budget for work scheduled to be complete by the status date. It answers: how much budgeted work should have been completed?

2. Earned Value (EV). EV is the approved budget value of work actually completed. It answers: how much budgeted value have we earned through completed work?

3. Actual Cost (AC). AC is what the completed work actually cost. It is an input measure rather than a derived formula, but it is essential to every cost-performance calculation.

4. Percent complete by earned value = EV ÷ BAC × 100. When earned value is appropriate to the project, this expresses completed budgeted work as a percentage of Budget at Completion (BAC). It should not be confused with subjective “we feel 80% done” reporting.

Earned value management only produces useful metrics when the project has a credible performance baseline; otherwise the arithmetic can be precise while the underlying plan is not.

Cost and schedule variance formulas

5. Cost Variance (CV) = EV − AC. Positive CV means the project has earned more budgeted value than the cost incurred; negative CV means it is over budget for the amount of work completed.

6. Schedule Variance (SV) = EV − PV. Positive SV means more budgeted work has been completed than planned by the status date; negative SV means less has been completed.

7. Cost Performance Index (CPI) = EV ÷ AC. CPI above 1.0 indicates favorable cost efficiency. CPI below 1.0 indicates that each unit of actual cost is producing less than one unit of budgeted value.

8. Schedule Performance Index (SPI) = EV ÷ PV. SPI above 1.0 is ahead of the planned earned-value position; below 1.0 is behind.

9. Cost Variance Percentage = CV ÷ EV × 100. This expresses the cost variance relative to the value of completed work. It can make differences easier to compare across projects of different sizes.

10. Schedule Variance Percentage = SV ÷ PV × 100. This normalizes the schedule variance against planned value at the measurement point.

These indicators should trigger investigation rather than automatic conclusions. A CPI of 0.90 tells you there is cost inefficiency; it does not tell you why. The cause might be estimation, productivity, procurement, rework, scope interpretation, or another factor.

Estimate-at-completion formulas

EAC formulas differ because they make different assumptions about future performance. Picking the formula is a judgment call.

11. EAC = BAC ÷ CPI. Use this when current cost efficiency is expected to continue through the remaining work. If CPI is consistently poor and the underlying cause remains, this can provide a realistic forecast.

12. EAC = AC + (BAC − EV). Use this when past variance is treated as atypical and the remaining work is expected to perform according to the original budget rate.

13. EAC = AC + (BAC − EV) ÷ (CPI × SPI). This incorporates both cost and schedule efficiency into the remaining-work forecast when both are expected to influence completion cost.

14. Bottom-up EAC = AC + new ETC. If the original estimating assumptions are no longer credible, re-estimate the remaining work and add it to actual cost. This can be more defensible than forcing a historical performance index onto a fundamentally changed project.

15. Estimate to Complete (ETC) = EAC − AC. Once the total EAC is known, ETC is the expected cost still required from the status date forward.

16. Variance at Completion (VAC) = BAC − EAC. Positive VAC indicates the forecast is under budget; negative VAC indicates an expected overrun.

To-complete performance formulas

TCPI asks a different question from CPI. CPI describes performance so far; TCPI describes the efficiency required on the remaining work to hit a target.

17. TCPI based on BAC = (BAC − EV) ÷ (BAC − AC). Use this when the goal is still to complete within the original Budget at Completion.

18. TCPI based on EAC = (BAC − EV) ÷ (EAC − AC). Use this when management has accepted a revised Estimate at Completion and wants to know the remaining efficiency needed to meet it.

A very high TCPI can be a warning that the original target is no longer realistic. The calculation should lead to a management conversation about scope, resources, productivity, or forecast credibility rather than pressure the team to “work harder” without changing the underlying system.

Three-point estimation and uncertainty

Three-point estimates use optimistic (O), most likely (M), and pessimistic (P) estimates to make uncertainty explicit.

19. PERT expected estimate = (O + 4M + P) ÷ 6. This weighted formula gives the most likely estimate greater influence while still incorporating the range.

20. Triangular estimate = (O + M + P) ÷ 3. This simple average gives all three estimates equal weight.

21. PERT standard deviation = (P − O) ÷ 6. A larger range between optimistic and pessimistic values produces a larger standard deviation.

22. PERT variance = [(P − O) ÷ 6]². Variance is the square of the standard deviation and can be used when combining independent uncertainty estimates.

Do not treat three-point estimates as magic accuracy. Their value is that they force a conversation about range and uncertainty instead of hiding every estimate behind one deterministic number.

Schedule-network calculations

23. Total Float = LS − ES. Late Start minus Early Start gives one way to calculate total float.

24. Total Float = LF − EF. Late Finish minus Early Finish should produce the same result when the network calculations are consistent.

25. Critical-path duration = sum of activity durations along the longest path. The critical path is the path that currently determines the earliest project completion date. It is not necessarily the path with the most activities.

26. Free Float = earliest start of successor − earliest finish of activity. This expresses how much an activity can slip without delaying the early start of its immediate successor under a simple finish-to-start relationship.

Network calculations are useful because they reveal which activities actually constrain the finish date. A schedule with hundreds of tasks can still be driven by a relatively small number of critical or near-critical paths.

Communication and risk calculations

27. Communication channels = n(n − 1) ÷ 2. If everyone in a group can communicate directly with everyone else, the number of potential pairwise channels grows quickly as team size increases. The formula is a reminder that coordination complexity does not grow linearly.

28. Expected Monetary Value (EMV) = probability × financial impact. For a threat, impact is often modeled as a negative value; for an opportunity, it can be positive.

29. Expected value of a decision branch = sum of probability × outcome for the possible branches. Decision-tree analysis uses this logic to compare choices under uncertainty.

Quantitative risk analysis does not replace judgment. A probability estimate can be weak, an impact can ignore nonfinancial consequences, and a low-EMV risk can still be unacceptable because of regulation, safety, reputation, or strategic importance.

Business-case and investment formulas

The 2026 PMP exam gives the Business Environment much greater weight, so candidates should be comfortable connecting project decisions with value and financial logic.

30. Return on Investment (ROI) = (benefit − cost) ÷ cost × 100. ROI expresses return relative to the investment, but the definition of benefit and the time horizon must be consistent.

31. Benefit-Cost Ratio (BCR) = benefits ÷ costs. A result above 1 indicates quantified benefits exceed quantified costs under the assumptions used.

32. Net Present Value (NPV) = Σ[CF_t ÷ (1 + r)^t] − initial investment. NPV discounts future cash flows because money received later is worth less than money received today at a positive discount rate. When comparing projects under consistent assumptions, higher positive NPV is generally more attractive financially.

33. Payback period for even annual cash flows = initial investment ÷ annual net cash inflow. This simple form applies only when cash inflows are relatively even. Irregular cash flows require cumulative calculation by period.

Financial formulas should never be treated as the only project-selection criteria. Regulation, safety, strategy, capacity, social value, and risk can all justify work that does not win a simple ROI comparison.

Suppose BAC is $500,000, EV is $200,000, AC is $250,000, and PV is $225,000. CV equals −$50,000 and CPI equals 0.80, so the project is cost-inefficient at the status date. SV equals −$25,000 and SPI is about 0.89, so the earned-value position is also behind plan. If current cost efficiency is expected to continue, EAC using BAC ÷ CPI would be $625,000.

The important response is not “the project is bad.” Ask what is driving the variance. If a one-time procurement event caused the cost problem and future work is expected to return to plan, BAC ÷ CPI may be too pessimistic. If the project has persistent rework and productivity problems, the forecast may be realistic or even optimistic.

For a three-point example, assume an activity has O = 6 days, M = 9 days, and P = 18 days. The PERT expected duration is (6 + 4×9 + 18) ÷ 6 = 10 days. The standard deviation is (18 − 6) ÷ 6 = 2 days. The calculation makes uncertainty visible; it does not guarantee the task will take exactly ten days.

For communication channels, a core team of 8 people has 8×7÷2 = 28 potential pairwise channels. Increasing the group to 12 creates 66. The formula illustrates why adding people can increase coordination overhead even when it also adds capacity.

Keep units visible while calculating. EV, PV, AC, BAC, EAC, ETC, CV, SV, and VAC are monetary or budget-value measures; CPI, SPI, and TCPI are unitless indices; float is time; probabilities are proportions. Unit awareness catches many mistakes before the arithmetic is finished.

Also remember that schedule variance in classic EVM is expressed in budget-value units, not days. It describes whether earned progress is ahead of or behind the planned-value position at the status date. Network schedule calculations are still needed when the management question is specifically “how many days can this activity move?”

How to study formulas for the current PMP exam

Start by learning the variables: EV, PV, AC, BAC, EAC, ETC, CPI, SPI, and TCPI. Then work small scenarios where you explain the result in words. If CPI is 0.82, what does that say about cost efficiency? If TCPI based on BAC is 1.25, what would have to change for the original budget to remain credible?

Do the same with schedule networks and three-point estimates. The objective is not only to reach the correct number but to identify the assumption behind the calculation and the management action that follows.

Finally, keep the formulas in proportion. The current PMP exam is 180 questions over 240 minutes and is designed around real project situations, not a spreadsheet contest. The strongest preparation combines quantitative fluency with the leadership, delivery, and business judgment expected across the current exam domains. If you are still confirming eligibility or scheduling, review the updated PMP application process before building the final study timeline.