PMP Exam Formulas Cheat Sheet: EVM, PERT, and Critical Path Guide

Mastering PMP Exam Formulas for the Modern Test-Taker

Preparing for the Project Management Professional (PMP)® certification in Singapore often means balancing demanding project deliverables across tech hubs like one-north or the Central Business District (CBD) with rigorous evening revision. Under the current PMI Examination Content Outline (ECO), the 180-question exam is structured across three core domains: 50% Process, 42% People, and 8% Business Environment. While agile and hybrid frameworks dominate modern discussions, quantitative mastery remains an indispensable anchor within the Process domain.

Today's exam rarely presents raw arithmetic questions in isolation. Instead, PMI tests your ability to interpret variance metrics, evaluate cost and schedule health on hybrid projects, and select corrective actions. Whether you are sitting your exam at an authorized Pearson VUE test center in Bras Basah or taking it via online proctoring at home, this authoritative cheat sheet breaks down every essential mathematical formula, complete with calculation steps and situational decision frameworks.

1. Earned Value Management (EVM) Metrics and Variances

Earned Value Management represents the most frequently tested quantitative framework on the exam. To interpret EVM correctly, always remember that EV comes first in variance and index calculations.

Core EVM Parameters

Before computing variances, understand the three fundamental baseline values:
- Planned Value (PV): The authorized budget assigned to scheduled work: $PV$.
- Earned Value (EV): The measure of work performed expressed in terms of the authorized budget: $EV$.
- Actual Cost (AC): The realized cost incurred for the work executed: $AC$.
- Budget at Completion (BAC): The total planned budget for the entire project: $BAC$.

Variance Calculations

Variances measure the difference between performance and expectations in monetary terms. A positive variance indicates favorable performance, whereas a negative variance signals trouble.

Cost Variance (CV):
$CV = EV - AC$
- If $CV > 0$: Under budget (favorable)
- If $CV = 0$: Exactly on budget
- If $CV < 0$: Over budget (unfavorable)

Schedule Variance (SV):
$SV = EV - PV$
- If $SV > 0$: Ahead of schedule (favorable)
- If $SV = 0$: On schedule
- If $SV < 0$: Behind schedule (unfavorable)

Performance Indices

Indices reflect cost and schedule efficiency as ratios. A benchmark of $1.0$ represents baseline performance.

Cost Performance Index (CPI):
$CPI = \frac{EV}{AC}$
- $CPI > 1.0$: Getting more than \$1.00 of value for every dollar spent.
- $CPI < 1.0$: Cost overrun; project is burning cash faster than value is delivered.

Schedule Performance Index (SPI):
$SPI = \frac{EV}{PV}$
- $SPI > 1.0$: Work is progressing faster than planned.
- $SPI < 1.0$: Work is progressing slower than planned.

Situational EVM Decision Framework

PMI scenario questions frequently present contrasting index pairs to test your management instincts:
- $CPI < 1.0$ and $SPI > 1.0$: The project is ahead of schedule but over budget (common when fast-tracking or using paid overtime). Corrective action: assess cost controls and eliminate non-critical overtime.
- $CPI > 1.0$ and $SPI < 1.0$: The project is behind schedule but under budget. Corrective action: consider crashing the schedule by deploying surplus budget to add resources to critical path activities.

2. Forecasting and Completion Metrics

When current performance diverges from the baseline, project managers must forecast final outcomes.

Estimate at Completion (EAC)

The forecasted total cost of the project upon completion depends on whether current cost variances are expected to continue.

Standard formula (variances are typical and expected to continue):
$EAC = \frac{BAC}{CPI}$

When future work will be performed at the budgeted rate (atypical past variances):
$EAC = AC + (BAC - EV)$

When both cost and schedule performance influence future work:
$EAC = AC + \frac{BAC - EV}{CPI \times SPI}$

Estimate to Complete (ETC) and Variance at Completion (VAC)

Estimate to Complete (remaining cost required):
$ETC = EAC - AC$

Variance at Completion (forecasted budget surplus or deficit):
$VAC = BAC - EAC$
- Positive $VAC$ means finishing under initial budget; negative $VAC$ forecasts an overrun.

To-Complete Performance Index (TCPI)

$TCPI$ calculates the cost efficiency required on remaining work to meet a specified target.

To achieve original $BAC$:
$TCPI = \frac{BAC - EV}{BAC - AC}$

To achieve revised $EAC$:
$TCPI = \frac{BAC - EV}{EAC - AC}$
- A $TCPI > 1.0$ indicates that the team must perform with higher cost efficiency for the remainder of the project to meet the goal.

3. Three-Point Estimating and PERT Calculations

Program Evaluation and Review Technique (PERT) accounts for uncertainty by weighting Optimistic ($O$), Most Likely ($M$), and Pessimistic ($P$) estimates.

Beta (PERT) Distribution

The standard PERT Beta distribution places greater weight on the most likely outcome:
$E = \frac{O + 4M + P}{6}$

Triangular Distribution

When historical data is scarce, simple average weighting is applied:
$E = \frac{O + M + P}{3}$

Activity Standard Deviation and Variance

Standard deviation measures the risk and dispersion of an individual activity duration:
$\sigma = \frac{P - O}{6}$
$Variance = \sigma^2 = \left(\frac{P - O}{6}\right)^2$

4. Critical Path Method and Float Calculations

Network diagram calculations establish the shortest possible project duration and identify schedule flexibility across non-critical paths.

Total Float vs. Free Float

Total Float (TF): The amount of time an activity can be delayed without delaying the project finish date.
$Total\ Float = LS - ES = LF - EF$
Where $LS$ is Late Start, $ES$ is Early Start, $LF$ is Late Finish, and $EF$ is Early Finish.

Free Float (FF): The amount of time an activity can be delayed without delaying the early start of any immediate successor.
$Free\ Float = ES_{(successor)} - EF_{(current activity)}$

Critical Path Rule: Activities on the critical path have a Total Float of zero (or negative if the project is behind an enforced deadline). Any delay on a critical path activity directly delays the project completion date.

5. Communication Channels Formula

As agile teams scale or organizational stakeholders expand, the complexity of communication channels increases exponentially.

Potential Communication Channels:
$Channels = \frac{n(n - 1)}{2}$
Where $n$ represents the total number of stakeholders (including the project manager).

Example: If a project team expands from 6 members to 10 members, initial channels were $\frac{6(5)}{2} = 15$, and new channels become $\frac{10(9)}{2} = 45$. The net increase is $45 - 15 = 30$ additional lines of communication.

How to Practice and Retain Formulas for Exam Day

Memorizing formulas is only half the battle. Success under the 230-minute exam time constraint requires rapid recall and situational interpretation. Follow this strategy:

Daily Formula Brain Dumps: Practice writing down the core EVM and PERT formulas in under three minutes at the start of your study sessions.
Drill Hybrid and Agile Scenarios: Recognize how EVM concepts translate into agile settings (e.g., using burndown and burnup velocity metrics alongside EV trends). Discover more articles on professional exam preparation to refine your study roadmap.
Active Retrieval Practice: Instead of passively re-reading flashcards, use intelligent question banks. You can explore how Thinka leverages AI-powered learning to diagnose your weak formula areas and generate custom calculation scenarios.
Simulated Timed Drills: Ensure you can complete full mathematical evaluations within 60 to 75 seconds per question on the AI-powered practice platform before testing in real exam conditions.

Key Formula Summary Cheat Sheet

- Cost Variance: $CV = EV - AC$
- Schedule Variance: $SV = EV - PV$
- Cost Performance Index: $CPI = \frac{EV}{AC}$
- Schedule Performance Index: $SPI = \frac{EV}{PV}$
- Estimate at Completion: $EAC = \frac{BAC}{CPI}$
- Estimate to Complete: $ETC = EAC - AC$
- To-Complete Performance Index: $TCPI = \frac{BAC - EV}{BAC - AC}$
- PERT Expected Duration: $E = \frac{O + 4M + P}{6}$
- PERT Standard Deviation: $\sigma = \frac{P - O}{6}$
- Total Float: $TF = LS - ES = LF - EF$
- Communication Channels: $Channels = \frac{n(n - 1)}{2}$