A reliable pmp formulas cheat sheet is not just a calculation guide—it is a project health diagnostic toolkit. For Hong Kong professionals balancing demanding corporate schedules in Central, Kowloon East, or Cyberport, preparing for the Project Management Professional (PMP) credential often feels daunting due to the quantitative syllabus. Whether your background is rooted in banking PMOs, IT digital transformation, or engineering delivery, quantitative questions can trigger unnecessary anxiety.

Under the current PMI Exam Content Outline (ECO), the PMP exam has fundamentally shifted away from raw, calculator-heavy arithmetic. You will rarely be asked to compute five-digit figures in a vacuum. Instead, PMI tests your ability to interpret financial and schedule variances, diagnose project health, and choose the correct course of corrective action. This comprehensive cheat sheet decodes every essential formula—Earned Value Management (EVM), Estimate at Completion (EAC) variations, Critical Path float, and PERT distributions—with the exact decision rules needed to ace scenario-based exam questions.

1. Core Earned Value Management (EVM) Foundations

Every EVM calculation builds upon three foundational inputs. You must never confuse what was planned with what was earned or what was spent:

Planned Value (PV): The authorized budget assigned to scheduled work. This is the baseline measure of what should have been accomplished by a given date.
\(PV = \text{Authorized Planned Budget}\)

Earned Value (EV): The measure of work performed expressed in terms of the budget authorized for that work. EV is always the anchor for all variance and index calculations.
\(EV = \text{\% Work Actually Completed} \times \text{Budget at Completion (BAC)}\)

Actual Cost (AC): The realized cost incurred for the work performed on an activity during a specific time period.
\(AC = \text{Total Incurred Cost}\)

2. Variances and Performance Indices: Diagnostic Formulas

Variances measure the absolute monetary deviation from plan, while performance indices convey cost and schedule efficiency as a ratio. Always remember: in PMP math, Earned Value always comes first.

Cost Variance (CV):
\(CV = EV - AC\)
Diagnostic Rule: If \(CV > 0\), the project is under budget (favourable). If \(CV < 0\), the project is over budget (unfavourable). If \(CV = 0\), spend matches progress precisely.

Schedule Variance (SV):
\(SV = EV - PV\)
Diagnostic Rule: If \(SV > 0\), you are ahead of schedule. If \(SV < 0\), you are behind schedule. Note: At project completion, \(EV = PV\), meaning \(SV\) automatically resets to zero even if the project finished months late.

Cost Performance Index (CPI):
\(CPI = \frac{EV}{AC}\)
Diagnostic Rule: If \(CPI > 1.0\), you are earning more value than you are spending (cost-efficient). If \(CPI < 1.0\), costs are exceeding progress (cost overrun). A \(CPI\) of \(0.85\) means you are only earning \$0.85 for every dollar spent.

Schedule Performance Index (SPI):
\(SPI = \frac{EV}{PV}\)
Diagnostic Rule: If \(SPI > 1.0\), work is progressing faster than scheduled. If \(SPI < 1.0\), progress is lagging. If the question states \(CPI = 0.90\) and \(SPI = 1.15\), the project is over budget but ahead of schedule.

3. The EAC Forecasting Decision Matrix

Forecasting questions frequently trip up candidates because the Estimate at Completion (EAC) has four distinct formulas. The secret to answering these correctly is identifying the contextual clue provided in the exam prompt regarding whether past performance will persist.

Scenario A: Past variances are typical and will continue until the end of the project.
Use this when current cost overruns or efficiencies reflect steady-state operational realities.
\(EAC = \frac{BAC}{CPI}\)

Scenario B: Past variances were atypical and will not occur in the future.
Use this when an anomalous, one-time incident caused a variance (such as an unpredicted supplier shutdown or sudden regulatory compliance audit in Hong Kong), but remaining work will proceed at the originally budgeted rate.
\(EAC = AC + (BAC - EV)\)

Scenario C: Both Cost and Schedule performance indices influence remaining work.
Use this when project delays impact project costs and the project deadline is firm (a contractual hard stop).
\(EAC = AC + \left[ \frac{BAC - EV}{CPI \times SPI} \right]\)

Scenario D: The original project budget baseline is flawed or fundamentally invalid.
Use this when project assumptions are no longer viable, requiring a fresh bottom-up re-estimate of remaining work.
\(EAC = AC + \text{Bottom-Up ETC}\)

Estimate to Complete (ETC) and Variance at Completion (VAC):
Once \(EAC\) is calculated, two follow-up metrics establish remaining spend and final variance:
\(ETC = EAC - AC\)
\(VAC = BAC - EAC\)
Diagnostic Rule: A positive \(VAC\) means the project will finish under original baseline budget; a negative \(VAC\) forecasts an overrun.

4. To-Complete Performance Index (TCPI)

The To-Complete Performance Index (TCPI) represents the cost performance efficiency that must be achieved on remaining work to meet a specified management goal. Many professionals working through professional exam preparation guides stumble over TCPI because the denominator depends entirely on the target.

Target 1: Meeting the original Budget at Completion (BAC):
\(TCPI_{BAC} = \frac{BAC - EV}{BAC - AC}\)

Target 2: Meeting a revised management forecast (EAC):
\(TCPI_{EAC} = \frac{BAC - EV}{EAC - AC}\)
Diagnostic Rule: If \(TCPI > 1.0\), the project must operate with higher efficiency than originally planned to hit the target. If \(TCPI > CPI\), performance must improve; if \(TCPI < CPI\), the team has headroom to relax cost constraints.

5. Schedule Network & Critical Path Formulas

Critical Path Method (CPM) questions test your grasp of scheduling flexibility, activity buffers, and slack.

Float / Slack Calculations:
Total Float is the amount of time an activity can be delayed without delaying the project finish date:
\(\text{Total Float} = LS - ES = LF - EF\)
Where \(LS\) is Late Start, \(ES\) is Early Start, \(LF\) is Late Finish, and \(EF\) is Early Finish.
Diagnostic Rule: Activities on the critical path have zero (or negative) total float.

Free Float:
The amount of time an activity can slip without delaying the Early Start of any successor activity:
\(\text{Free Float} = \min(ES_{\text{successors}}) - EF\)

6. Risk Estimating & Communication Channels

Beyond EVM and scheduling, PMI tests risk range distributions and stakeholder communication paths using straightforward numerical rules.

Three-Point Estimating (PERT / Beta Distribution):
When weighting the realistic outcome higher than extremes:
\(\text{PERT Expected Mean} = \frac{O + 4M + P}{6}\)
Where \(O\) is Optimistic, \(M\) is Most Likely, and \(P\) is Pessimistic.

Standard Deviation (\(\sigma\)) and Variance:
\(\sigma = \frac{P - O}{6}\)
\(\text{Variance} = \sigma^2 = \left( \frac{P - O}{6} \right)^2\)
Diagnostic Rule: A project estimate with normal distribution spans \(\pm 1\sigma\) (68.26\%), \(\pm 2\sigma\) (95.46\%), and \(\pm 3\sigma\) (99.73\%).

Lines of Communication Formula:
\(\text{Channels} = \frac{n(n - 1)}{2}\)
Where \(n\) is the total number of project stakeholders (including the project manager). If a local cross-functional squad adds 4 new engineers to an existing team of 8 stakeholders, calculate total channels for \(n = 12\) minus the original \(n = 8\) to determine new channels added.

7. Actionable Exam Strategy: Navigating ECO Quantitative Scenarios

On exam day, you will not have an external programmable calculator, only the Pearson VUE built-in basic on-screen tool. To maximize your scoring efficiency under strict timing constraints, apply this three-step workflow:

Step 1: Check the indices first. In complex scenario stems describing troubled tech rollouts or infrastructure overruns, look immediately at \(CPI\) and \(SPI\). If \(CPI = 0.82\) and \(SPI = 0.94\), eliminate all options claiming the project is on track or under spending. The project is struggling on both fronts.

Step 2: Identify the future operational assumption. When prompted for \(EAC\), determine whether the root cause was an anomalous blip (use atypical formula) or persistent execution drag (use \(BAC / CPI\)). Never guess between \(EAC\) formulas without scanning for key terms like "isolated disruption", "atypical event", or "current burn rate is expected to continue".

Step 3: Train with adaptive situational prompts. Instead of memorizing formula sheets passively, test your situational reflexes. You can leverage an AI-powered practice platform like Thinka to drill dynamic EVM vignettes that simulate the psychological pacing of actual exam scenarios. Engaging in active situational review via targeted mock question practice trains your brain to parse numbers into proactive management choices instantly.