PMP formulas cheat sheet: every formula with a worked example
Earned value, PERT, float, expected monetary value and communication channels, each with the formula, one worked example and what the answer tells a project manager. The examples share one project so you can check every number.
Before the formulas: how the exam uses math
PMI's Examination Content Outline does not list formulas. It lists tasks such as Plan and manage finance, Plan and manage schedule, Evaluate project status and Plan and manage risk, and the math lives inside them. Most PMP questions are situational, so a formula is usually a step toward a decision: the CPI tells you whether to act on cost, the float tells you whether a delay matters, the EMV tells you which option to pick.
Learn each formula, then practice reading the result. A number below 1, a negative variance or a path with zero float should trigger the same instinct every time: analyze the cause, then act through the agreed process.
Earned value management (EVM)
The example project: budget at completion (BAC) 100,000. At the status date, planned value (PV) is 50,000, earned value (EV) is 40,000 and actual cost (AC) is 45,000.
| Metric | Formula | Worked example | How to read it |
|---|---|---|---|
| Planned value (PV) | Budgeted cost of work scheduled to date | 50,000 | What you planned to have done by now |
| Earned value (EV) | % complete × BAC | 40% × 100,000 = 40,000 | The budgeted value of the work actually done |
| Actual cost (AC) | What the work done has really cost | 45,000 | Money spent to earn the EV |
| Cost variance (CV) | EV − AC | 40,000 − 45,000 = −5,000 | Negative: over budget |
| Schedule variance (SV) | EV − PV | 40,000 − 50,000 = −10,000 | Negative: behind schedule |
| Cost performance index (CPI) | EV ÷ AC | 40,000 ÷ 45,000 = 0.89 | Below 1: about 89 cents of value per dollar spent |
| Schedule performance index (SPI) | EV ÷ PV | 40,000 ÷ 50,000 = 0.80 | Below 1: progressing at 80% of the planned rate |
Forecasting: EAC, ETC and VAC
Same project. The estimate at completion (EAC) depends on what you expect the rest of the work to look like, so the scenario wording decides the formula.
| Situation in the question | EAC formula | Worked example |
|---|---|---|
| Current cost performance will continue (typical variance) | BAC ÷ CPI | 100,000 ÷ 0.889 = 112,500 |
| The overrun was a one-time event; the rest goes to plan (atypical) | AC + (BAC − EV) | 45,000 + 60,000 = 105,000 |
| Both cost and schedule performance will drive the remaining work | AC + (BAC − EV) ÷ (CPI × SPI) | 45,000 + 60,000 ÷ 0.711 = 129,375 |
| The original estimate is no longer valid | AC + bottom-up ETC | 45,000 + new estimate of 58,000 = 103,000 |
| Metric | Formula | Worked example (typical EAC) | How to read it |
|---|---|---|---|
| Estimate to complete (ETC) | EAC − AC | 112,500 − 45,000 = 67,500 | Money still needed to finish |
| Variance at completion (VAC) | BAC − EAC | 100,000 − 112,500 = −12,500 | Negative: expected to finish over budget |
| TCPI to meet BAC | (BAC − EV) ÷ (BAC − AC) | 60,000 ÷ 55,000 = 1.09 | Every remaining dollar must earn 1.09 of value to land on budget |
| TCPI to meet EAC | (BAC − EV) ÷ (EAC − AC) | 60,000 ÷ 67,500 = 0.89 | Matches the current CPI, as it should for a typical EAC |
Estimating: PERT and standard deviation
Three-point estimates use an optimistic (O), most likely (M) and pessimistic (P) duration or cost. The example activity: O = 4 days, M = 6 days, P = 14 days.
| Estimate | Formula | Worked example |
|---|---|---|
| Triangular (simple average) | (O + M + P) ÷ 3 | (4 + 6 + 14) ÷ 3 = 8 days |
| Beta / PERT (weighted average) | (O + 4M + P) ÷ 6 | (4 + 24 + 14) ÷ 6 = 7 days |
| Standard deviation (beta) | (P − O) ÷ 6 | (14 − 4) ÷ 6 = 1.67 days |
| Variance | SD squared | 1.67 × 1.67 = 2.78 |
With a beta estimate of 7 days and a standard deviation of 1.67, a one-standard-deviation range is 5.33 to 8.67 days, which covers roughly 68% of outcomes under a normal distribution; two standard deviations (3.67 to 10.33 days) cover roughly 95%. A larger standard deviation means a less certain estimate.
Schedule: critical path and float
Example network: activity A (3 days) comes first, then B (5 days) and C (2 days) run in parallel, and D (4 days) starts when both B and C finish. Path A-B-D is 12 days; path A-C-D is 9 days.
| Activity | Duration | ES | EF | LS | LF | Total float |
|---|---|---|---|---|---|---|
| A | 3 | 0 | 3 | 0 | 3 | 0 |
| B | 5 | 3 | 8 | 3 | 8 | 0 |
| C | 2 | 3 | 5 | 6 | 8 | 3 |
| D | 4 | 8 | 12 | 8 | 12 | 0 |
These numbers use the convention where the first activity starts at day 0 and a successor's early start equals its predecessor's early finish. Some references start at day 1 and add 1 to each start; the float values come out the same either way.
Risk: expected monetary value (EMV)
Formula: EMV = probability × impact. Threats carry a negative impact, opportunities a positive one, and you add them up for the overall exposure.
Worked example: a threat has a 20% chance of costing 50,000, so its EMV is 0.20 × −50,000 = −10,000. An opportunity has a 30% chance of saving 20,000, so its EMV is 0.30 × 20,000 = +6,000. The combined EMV is −4,000, a reasonable starting point for a contingency reserve for these two risks.
Decision tree example: Vendor X costs 100,000 with a 25% chance of 40,000 in rework, an expected cost of 100,000 + 10,000 = 110,000. Vendor Y costs 105,000 with a 10% chance of 20,000 in rework, an expected cost of 105,000 + 2,000 = 107,000. Vendor Y has the lower expected cost even though its price is higher.
Communication channels
Formula: channels = n(n − 1) ÷ 2, where n is the number of people, including the project manager.
Worked example: a team of 8 has 8 × 7 ÷ 2 = 28 channels. If 4 more people join, 12 × 11 ÷ 2 = 66 channels, so the change adds 66 − 28 = 38 channels. Questions often ask for the increase, not the new total, so read the last sentence carefully.
Agile forecasting: velocity
Velocity is the amount of work, often in story points, that a team completes per iteration. Worked example: the last three sprints delivered 30, 34 and 26 points, an average of 30. With 240 points left in the backlog, the forecast is 240 ÷ 30 = 8 more sprints. Velocity is for the team's own planning; comparing velocity between teams is a classic wrong answer, because each team sizes stories differently.
Five rules that catch wrong answers
Want the context for these numbers? Read what changed in the 2026 PMP exam, then schedule your practice with the PMP study plan.
Drill the math inside real scenarios
Six full-length PMP mock exams with earned value, PERT, float and EMV worked out under every calculation question.
PMP formulas FAQ
How many formulas do I need for the PMP exam?
PMI does not publish a formula list. In practice, earned value (CV, SV, CPI, SPI, EAC, ETC, VAC, TCPI), PERT estimates, float, expected monetary value and communication channels cover the math most candidates report.
Is there a calculator on the PMP exam?
Yes. The computer-based exam has a built-in calculator, and the PMI Certification Handbook says you can request a handheld one at the test center.
Which EAC formula should I use?
Read the scenario. If the current cost performance is expected to continue, use BAC / CPI. If the variance was a one-time event, use AC + (BAC − EV). If both cost and schedule performance will drive the rest of the work, use AC + (BAC − EV) / (CPI × SPI). If the original estimate is no longer valid, use AC + a new bottom-up ETC.
Is a CPI above 1 good or bad?
Good. A CPI above 1 means you get more than one dollar of planned value for each dollar spent, so the project is under budget. Below 1 means over budget. SPI works the same way for schedule.
How much of the PMP exam is math?
PMI does not publish a number. The exam is mostly situational judgment, so the math matters most when it helps you interpret status, such as reading a CPI of 0.85 as a cost problem that needs action.
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