PMP Formulas Cheat Sheet: EVM, Critical Path & Calculation Shortcuts

Mastering Quantitative Questions on the PMP Exam

For project managers sitting the Project Management Professional (PMP)® exam in Singapore, mathematical calculations often trigger disproportionate stress. Whether managing tech implementations in One-North or capital projects in Jurong, candidates frequently worry about memorising dozens of equations. However, quantitative questions account for only roughly 5% to 10% of the 180 questions on the 230-minute Pearson VUE exam.

Crucially, the Project Management Institute (PMI)® rarely tests raw arithmetic anymore. Instead, the exam evaluates your situational diagnostic ability: understanding what the numbers tell you about project health and selecting the correct corrective action. This pmp formulas cheat sheet consolidates every essential equation across Earned Value Management (EVM), Critical Path Method (CPM), and project estimation into an actionable reference for your revision sprint.

Earned Value Management (EVM) Core Metrics

EVM measures project performance against scope, schedule, and cost baselines. Before memorising formulas, ground yourself in the three fundamental baseline variables:

• Planned Value ( ext{PV}): The authorized budget assigned to scheduled work.
• Earned Value ( ext{EV}): The measure of work performed expressed in terms of the budget authorized for that work.
• Actual Cost ( ext{AC}): The realized cost incurred for the work performed.
• Budget at Completion ( ext{BAC}): The total planned budget for the entire project.

Variance Formulas (Is the project ahead/behind?)

Variance metrics always subtract actuals or planned figures from the earned value ( ext{EV}):

Cost Variance:
\(CV = EV - AC\)
Interpretation: Positive (\(CV > 0\)) = Under budget; Negative (\(CV < 0\)) = Over budget; Neutral (\(CV = 0\)) = On budget.

Schedule Variance:
\(SV = EV - PV\)
Interpretation: Positive (\(SV > 0\)) = Ahead of schedule; Negative (\(SV < 0\)) = Behind schedule; Neutral (\(SV = 0\)) = On schedule.

Performance Indices (How efficiently are we utilizing resources?)

Index metrics divide earned value ( ext{EV}) by actual costs or planned values. Think of \(1.0\) as baseline parity:

Cost Performance Index:
\(CPI = \frac{EV}{AC}\)
Interpretation: \(CPI > 1.0\) means you are getting more than \(\$1.00\) worth of work for every dollar spent (cost efficient). \(CPI < 1.0\) indicates cost overruns.

Schedule Performance Index:
\(SPI = \frac{EV}{PV}\)
Interpretation: \(SPI > 1.0\) indicates project progression faster than planned. \(SPI < 1.0\) indicates schedule slippage.

EVM Forecasting Formulas (Where is the project heading?)

Forecasting questions on the PMP exam challenge you to determine the Estimate at Completion (\(EAC\)), Estimate to Complete (\(ETC\)), and Variance at Completion (\(VAC\)) based on specific assumptions.

1. Estimate at Completion (\(EAC\))

The calculation for \(EAC\) depends entirely on the situational scenario described in the question prompt:

• Scenario A: Current variances are typical and expected to continue at the same rate of efficiency.
  \(EAC = \frac{BAC}{CPI}\)
• Scenario B: Future work will be performed at the budgeted baseline rate (past variances were atypical).
  \(EAC = AC + (BAC - EV)\)
• Scenario C: Both cost and schedule performance indices influence remaining work.
  \(EAC = AC + \frac{BAC - EV}{CPI \cdot SPI}\)
• Scenario D: The original budget is fundamentally flawed and requires a ground-up re-estimate.
  \(EAC = AC + \text{Bottom-up } ETC\)

2. Estimate to Complete (\(ETC\)) & Variance at Completion (\(VAC\))

Estimate to Complete measures the expected cost required to finish all remaining work:
\(ETC = EAC - AC\)

Variance at Completion measures the expected budget surplus or deficit at project conclusion:
\(VAC = BAC - EAC\)
Interpretation: Positive (\(VAC > 0\)) = Anticipated surplus under original budget; Negative (\(VAC < 0\)) = Anticipated overrun.

3. To-Complete Performance Index (\(TCPI\))

\(TCPI\) calculates the cost performance efficiency required on remaining work to meet a specified management goal (either the original \(BAC\) or a revised \(EAC\)):

To achieve the original budget (\(BAC\)):
\(TCPI_{BAC} = \frac{BAC - EV}{BAC - AC}\)

To achieve the revised budget (\(EAC\)):
\(TCPI_{EAC} = \frac{BAC - EV}{EAC - AC}\)
Interpretation: \(TCPI > 1.0\) means the project team must perform with higher efficiency than baseline for the remaining duration; \(TCPI < 1.0\) means remaining work can be delivered with lower efficiency without breaching the target.

Critical Path Method (CPM) and Float Analysis

Critical Path analysis questions require you to understand activity dependencies, early/late dates, and schedule flexibility across a network diagram.

Float Calculations

• Total Float (Float): The amount of time an activity can be delayed without delaying the project completion date.
  \(TF = LS - ES\)  or  \(TF = LF - EF\)
• Free Float: The amount of time an activity can be delayed without delaying the Early Start (\(ES\)) of any immediate successor activity.
  \(FF = ES_{\text{successor}} - EF_{\text{current}} - \text{Lag}\)

Core CPM Rules for Exam Day:

• The Critical Path is the longest continuous sequence of activities in the network diagram and has the least total float (usually \(0\)).
• A project can have multiple critical paths, which increases overall project schedule risk.
• Negative total float (\(TF < 0\)) occurs when a fixed target completion date is earlier than the calculated early finish date.

Estimation and Communication Formulas

Three-Point Estimation (PERT)

When tasks carry uncertainty, PMI tests two types of weighted averages based on Optimistic (\(O\)), Most Likely (\(M\)), and Pessimistic (\(P\)) estimates:

• Beta (PERT) Distribution: Heavily weights the most likely scenario.
  \(\mu = \frac{O + 4M + P}{6}\)
  Standard Deviation: \(\sigma = \frac{P - O}{6}\)
• Triangular Distribution: Simple arithmetic average.
  \(E = \frac{O + M + P}{3}\)

Communication Channels

This formula measures the geometric expansion of potential communication lines as project team size changes:
\(\text{Channels} = \frac{n(n - 1)}{2}\)
Watch out for the exam trap: If the prompt says "The project manager adds 3 stakeholders to a team of 7," remember that \(n\) increases from \(8\) (including the PM) to \(11\). Always verify whether the project manager is included in the baseline count.

Expected Monetary Value (EMV)

Used in quantitative risk analysis and decision tree analysis:
\(EMV = \text{Probability} \times \text{Impact}\)
Positive \(EMV\) represents opportunities; negative \(EMV\) represents threat impacts.

Summary PMP Formula Reference Table

Review this quick-reference table during your final mock review cycles:

• \(CV = EV - AC\) → Positive = Good (Under Budget)
• \(SV = EV - PV\) → Positive = Good (Ahead of Schedule)
• \(CPI = \frac{EV}{AC}\) → \(> 1.0\) = Efficient Cost Utilization
• \(SPI = \frac{EV}{PV}\) → \(> 1.0\) = Efficient Schedule Progression
• \(EAC = \frac{BAC}{CPI}\) → Typical variance continuing forward
• \(ETC = EAC - AC\) → Cost to complete remaining scope
• \(VAC = BAC - EAC\) → Variance at project closeout
• \(TF = LS - ES = LF - EF\) → Schedule buffer before project end date moves
• \(\text{Beta Estimate} = \frac{O + 4M + P}{6}\) → Weighted 3-point estimate
• \(\text{Channels} = \frac{n(n - 1)}{2}\) → Number of communication lines

Situational Exam Strategies: How PMI Tests Formulas

In the modern 180-question format administered at Pearson VUE testing centres across Singapore (such as International Plaza or NTUC LearningHub), you will rarely need to perform long divisions on the digital calculator. Instead, you must diagnose multi-variable project health scenarios instantly.

Example Scenario:

"A project sponsor reviews a status report showing \(CPI = 0.82\) and \(SPI = 1.15\). The sponsor demands immediate corrective action. As the project manager, what is your primary assessment?"

Diagnostic logic:

• \(CPI = 0.82 < 1.0\) → The project is spending more money than budgeted for completed work (Over budget).
• \(SPI = 1.15 > 1.0\) → The project is completing work faster than the planned schedule baseline (Ahead of schedule).
• Correct response trajectory: The team is likely fast-tracking or utilizing overtime/expensive resources to beat the schedule, which is causing budget overruns. The project manager should review cost drivers and balance schedule acceleration against the budget baseline.

Optimising Your Calculation Preparation

Rather than memorizing equations in isolation, test your diagnostic reflexes against situational question banks. Explore more articles on professional exam preparation to build structured study routines tailored to full-time professionals.

Leverage the diagnostic tools on Thinka's AI-Powered Practice Platform to generate tailored EVM and critical path scenarios that mirror Pearson VUE question stems. You can also explore how Thinka uses AI-powered practice to prepare for exams, ensuring you build intuitive mastery over every formula before sitting your certification test.