By El Mehdi Bouchti, PMP, PMI-ACP · Updated October 20, 2026

PMP Formulas Cheat Sheet: Every Formula With Worked Examples

The PMP formulas worth knowing fall into eight groups: earned value management (EVM), three-point estimating, schedule float, communication channels, risk, procurement incentive contracts, agile forecasting, and project selection finance. Each table below gives the formula, the question it answers and how to read the result, followed by worked examples with real numbers.

An honest note before you memorize anything: the current exam, built on the July 2026 Examination Content Outline, has fewer pure calculation questions than older formats. Expect some calculations, mostly EVM, and a lot of interpretation. Many questions hand you a CPI or SPI that is already calculated and ask what it means or what the project manager should do next. Knowing how to read a result matters more than computing it quickly.

Earned value management: the core terms

Every EVM formula uses four inputs. Get these definitions straight first.

• PV (planned value): the budgeted value of the work scheduled to be done by now.
• EV (earned value): the budgeted value of the work actually completed by now.
• AC (actual cost): what the completed work has actually cost.
• BAC (budget at completion): the total approved budget for the work.

Two memory aids cover most of the section. Variances and indices always start with EV. For variances (subtract), negative is bad. For indices (divide), below 1.0 is bad.

Performance: variances and indices

Forecasting: EAC, ETC, VAC and TCPI

Which EAC formula should you pick?

Exam questions signal the right EAC through the story, not the numbers. Read for these cues:

• "Current performance is expected to continue" or no reason to expect change: use BAC / CPI.
• "A one-time problem," "an unusual event," "will not recur": use AC + (BAC - EV).
• "The original estimate was fundamentally flawed" or assumptions changed: use AC + bottom-up ETC.
• A fixed deadline or a note that schedule performance will also affect cost: use AC + (BAC - EV) / (CPI × SPI).

For the interactive version, with a calculator that shows every metric as you change PV, EV, AC and BAC, use the EVM study guide and calculator.

Worked example 1: a project over budget and behind schedule

BAC is $200,000. At the month 4 status review, PV is $80,000, EV is $70,000 and AC is $87,500.

• CV = 70,000 - 87,500 = -$17,500 (over budget).
• SV = 70,000 - 80,000 = -$10,000 (behind schedule).
• CPI = 70,000 / 87,500 = 0.80: the project earns 80 cents of work per dollar spent.
• SPI = 70,000 / 80,000 = 0.875: work is progressing at 87.5% of the planned rate.
• EAC (typical) = 200,000 / 0.80 = $250,000; ETC = 250,000 - 87,500 = $162,500; VAC = 200,000 - 250,000 = -$50,000.
• EAC (atypical) = 87,500 + (200,000 - 70,000) = $217,500.
• EAC (CPI × SPI) = 87,500 + 130,000 / 0.70 = about $273,214.
• TCPI to BAC = 130,000 / 112,500 = about 1.16. The team must improve from 0.80 to 1.16, which is unlikely without a change.
• TCPI to the typical EAC = 130,000 / 162,500 = 0.80, which matches the current CPI.

The interpretation is what the exam rewards: the three EACs range from $217,500 to about $273,214 depending on the assumption, and hitting the original budget would need performance the team has not shown. The project manager should analyze the root cause, discuss options with the sponsor and route any budget or baseline change through integrated change control.

One more SPI subtlety: SV and SPI are measured in money. On a predictive project, EV eventually equals PV and BAC once all work is done, so SPI drifts back toward 1.0 near the end even if the project finishes late. Late in a project, check the schedule itself rather than relying on SPI.

Estimating: PERT, triangular and standard deviation

Worked example 2: a three-point estimate

An activity has an optimistic estimate of 4 days, a most likely estimate of 7 days and a pessimistic estimate of 16 days.

• PERT mean = (4 + 4 × 7 + 16) / 6 = 48 / 6 = 8 days.
• Triangular = (4 + 7 + 16) / 3 = 27 / 3 = 9 days.
• Standard deviation = (16 - 4) / 6 = 2 days, so one standard deviation either side of the PERT mean is 6 to 10 days.

The pessimistic tail pulls both averages above the most likely value. The triangular result is higher because it gives the 16-day pessimistic case the same weight as the most likely case.

Schedule: total float and free float

Example: an activity has ES 5, EF 9, LS 8 and LF 12. Total float is 8 - 5 = 3 days. Its only successor has an ES of 11, so free float is 11 - 9 = 2 days. Some textbooks start networks at day 0 and others at day 1; a question will use one convention consistently, so follow it rather than switching. The critical path is the longest path through the network, and the exam cares more about what you do when a critical activity slips (for example crashing or fast tracking, with their cost and risk trade-offs) than about drawing the network. The schedule management guide covers those responses.

Communication channels and risk

Worked example 3: channels, EMV and a decision tree

Channels. A team of 8 people (including you) has 8 × 7 / 2 = 28 channels. Adding 4 people gives 12 × 11 / 2 = 66 channels, an increase of 38. That growth is why larger teams need a deliberate communications management plan.

EMV. A threat has a 30% probability of a $40,000 penalty: EMV = 0.30 × -40,000 = -$12,000. An opportunity has a 20% probability of saving $25,000: EMV = +$5,000. Combined EMV is -$7,000.

Decision tree. Option A costs $120,000 and returns $300,000 if demand is high (60%) or $150,000 if demand is low (40%). Its expected return is 0.6 × 300,000 + 0.4 × 150,000 = $240,000, so its net value is $120,000. Option B costs $50,000 and returns $180,000 (60%) or $130,000 (40%): expected return $160,000, net value $110,000. Choose Option A, because $120,000 is higher than $110,000. The logic is always the same: calculate the EMV of each branch, subtract the cost of the decision, then pick the best net value (highest for gains, lowest for costs). See the risk management guide for how EMV feeds contingency reserves.

Procurement: point of total assumption (PTA)

PTA applies to fixed price incentive fee (FPIF) contracts. The terms matter more than the arithmetic:

• Target cost and target fee add up to the target price.
• Ceiling price is the most the buyer will pay.
• Share ratio (buyer/seller, for example 70/30) says how cost overruns and underruns are split. The buyer's share is the first number.

PTA = ((ceiling price - target price) / buyer's share ratio) + target cost. It is the actual cost at which the seller starts to absorb every additional dollar, because the buyer's payment has reached the ceiling.

Example: target cost $100,000, target fee $10,000 (target price $110,000), ceiling price $120,000, share ratio 70/30. PTA = (10,000 / 0.70) + 100,000 = about $114,286. Check: at that cost the overrun is about $14,286, the seller absorbs 30% of it (about $4,286), the fee falls to about $5,714, and cost plus fee equals the $120,000 ceiling. Above $114,286, the seller pays 100% of further overruns. The procurement guide explains how contract type shifts risk between buyer and seller.

Agile forecasting: velocity

Sprints remaining = remaining story points / velocity, rounded up to whole sprints. With 240 points left and an average velocity of 30 points, the team needs 8 sprints; with two-week sprints that is about 16 weeks. Use a recent average or a range (best and worst recent sprints) rather than a single sprint. Velocity belongs to one team and its own estimating scale, so never use it to compare teams or as a productivity target. Scenario questions on this topic are in the agile and hybrid guide.

Business and finance concepts for project selection

These mostly appear at concept level: you need to know which number to prefer, not how to build a discounted cash flow model.

Example: $121,000 received in two years at a 10% discount rate is worth 121,000 / 1.21 = $100,000 today. Two related ideas show up in selection questions: sunk costs (money already spent) should not influence the decision, and opportunity cost is the value of the best option you did not choose.

Worked example 4: reading results, not computing them

A typical modern question reads: "Midway through the project, CPI is 1.05 and SPI is 0.82. What should the project manager do first?" No arithmetic is needed. The project is under budget but behind schedule, so the useful response is to analyze why work is behind (resource availability, dependencies, scope growth) and then consider options such as fast tracking or adding resources, weighing their cost and risk, before changing any baseline through change control. The trap answers usually celebrate the cost result or jump straight to a baseline change.

Common formula mistakes

• Starting a variance or index with AC or PV instead of EV.
• Using BAC / CPI when the question says the variance was a one-time event.
• Reading a negative VAC as savings. Negative VAC means a forecast overrun.
• Forgetting to count yourself in n for communication channels.
• Using PERT when the question asks for a triangular (simple) average, or the reverse.
• Using the seller's share instead of the buyer's share in the PTA formula.
• Comparing velocity across teams, or treating it as a commitment.
• Choosing projects by payback period when NPV or IRR is given; NPV is the stronger measure.

How to practice formulas efficiently

Learn each formula together with the decision it supports. Write the cheat sheet from memory once a week, then spend most of your time on scenario questions where the numbers are already given. The cost management guide covers reserves and budgets, and the PMP glossary defines the terms used in this sheet.

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