PMP Formulas Cheat Sheet: Navigating Quantitative Scenarios

Quantitative questions on the Project Management Professional (PMP)® exam cause disproportionate anxiety for UK project professionals, especially those coming from non-engineering backgrounds. Yet, under the modern Project Management Institute (PMI)® Examination Content Outline (ECO), formula questions are far less about complex multi-step arithmetic and far more about quick, situational interpretation.

This PMP formulas cheat sheet breaks down every essential mathematical model tested under the Process domain. Rather than rote-memorising formulas in isolation, you will learn the core logic underpinning Earned Value Management (EVM), schedule float, communications, and forecasting permutations. This strategic approach ensures you can diagnose project health and select the correct remedial action in under 60 seconds.

The Core Earned Value Management (EVM) Foundations

Every EVM calculation builds upon three foundational inputs. In the exam vignette, PMI will either give you these figures directly or embed them in a narrative regarding project deliverables and spend:

1. Planned Value (PV): The authorised budget assigned to scheduled work: \(PV\).
2. Earned Value (EV): The measure of work performed expressed in terms of the budget authorised for that work: \(EV\). Think of \(EV\) as the anchor metric—it always comes first in variance calculations.
3. Actual Cost (AC): The realised cost incurred for the work performed: \(AC\).
4. Budget at Completion (BAC): The total planned baseline spend for the entire project: \(BAC\).

1. Variances (Cost & Schedule)

Variances measure the absolute difference between what you achieved and what you planned or spent. In British practice and globally, a positive variance is favourable, whereas a negative variance represents a problem:

\(CV = EV - AC\)

\(SV = EV - PV\)

Diagnostic Rule: If \(CV < 0\), you are over budget. If \(CV > 0\), you are under budget. If \(SV < 0\), you are behind schedule. If \(SV > 0\), you are ahead of schedule. When revising across our articles on professional exam preparation, you will notice that tracking the sign (positive vs negative) is often all the exam requires to rule out two of the four multiple-choice options immediately.

2. Performance Indices (CPI & SPI)

Indices represent efficiency ratios. Unlike variances, the benchmark is \(1.0\):

\(CPI = \frac{EV}{AC}\)

\(SPI = \frac{EV}{PV}\)

Diagnostic Rule: A ratio greater than \(1.0\) indicates efficiency (e.g., \(CPI = 1.25\) means you are getting £1.25 worth of work for every £1.00 spent). A ratio below \(1.0\) flags an operational shortfall. Many situational questions present a table showing \(CPI = 0.82\) and \(SPI = 1.15\) and ask what the project manager should do next. The answer is not to calculate, but to reallocate resources from the ahead-of-schedule path to correct the budget overrun.

EAC Variations: The Ultimate Decision Matrix

Estimate at Completion (\(EAC\)) questions represent the most challenging quantitative element on the exam. Candidates frequently get tangled in which \(EAC\) formula to employ. Use this structured decision tree to match the project scenario to the exact equation:

Condition 1: Variances are atypical (one-off event)

Use this when an anomalous event (e.g., a one-off supply chain interruption or regulatory permit delay) caused the variance, but future work is expected to proceed at the originally budgeted rate:

\(EAC = AC + (BAC - EV)\)

Condition 2: Variances are typical and will persist

Use this when past cost performance is expected to continue at the current rate of efficiency through to project completion:

\(EAC = \frac{BAC}{CPI}\)

Condition 3: Both cost and schedule performance influence future work

Use this when the project must adhere to a strict completion deadline, meaning schedule delays will force cost premiums (such as paying overtime or expediting vendor freight):

\(EAC = AC + \frac{BAC - EV}{CPI \cdot SPI}\)

Condition 4: The original baseline is fundamentally flawed

When initial project assumptions are completely invalid, you discard the original baseline and calculate a bottoms-up re-estimate from scratch:

\(EAC = AC + Bottom\text{-}Up\ ETC\)

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

To determine how much additional funding is required from this point forward, calculate \(ETC\):

\(ETC = EAC - AC\)

To evaluate whether the project will conclude within or over the authorised total budget, calculate \(VAC\):

\(VAC = BAC - EAC\)

A negative \(VAC\) confirms that the project will require an executive budget increase or a formal change request to increase the management reserves.

To-Complete Performance Index (TCPI)

The \(TCPI\) indicates the cost efficiency required for remaining work to meet a specified management goal. A \(TCPI > 1.0\) means the remaining work must be executed with higher efficiency than originally planned:

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

To achieve a revised budget target (\(EAC\)):
\(TCPI_{EAC} = \frac{BAC - EV}{EAC - AC}\)

Exam Trap: If the vignette states that the sponsor has officially approved a new budget forecast, you must switch your denominator from \(BAC - AC\) to \(EAC - AC\).

Beyond EVM: Critical Path, PERT & Communications

While EVM dominates quantitative questions, PMI regularly tests network diagrams, estimation models, and communication complexity.

1. PERT / Beta Three-Point Estimating

When assessing activity duration or cost under uncertainty, the standard weighted beta distribution gives four times the weight to the most likely scenario:

\(E = \frac{O + 4M + P}{6}\)

Standard Deviation (\(\sigma\)) of an activity:
\(\sigma = \frac{P - O}{6}\)

Variance of an activity:
\(Variance = \sigma^2 = \left(\frac{P - O}{6}\right)^2\)

Note: Triangular distribution gives equal weighting to all three estimates: \(E = \frac{O + M + P}{3}\). Only use triangular if the scenario explicitly specifies simple averaging.

2. Critical Path and Float Calculations

Float (or slack) defines how long an activity can be delayed without impacting subsequent tasks or the project delivery date:

\(Total\ Float = LS - ES = LF - EF\)

Exam Strategy: Any activity on the critical path possesses zero total float (\(Float = 0\)). If a question presents multiple parallel activity sequences, the sequence with the longest cumulative duration is your critical path. Activities with negative float indicate a project that is already running late against a hard deadline.

3. Communication Channels

As agile teams scale or new stakeholders join an infrastructure programme, potential communication pathways multiply exponentially:

\(Channels = \frac{n(n - 1)}{2}\)

Exam Trap: Watch out for the wording. If a project manager leads a team of 8 engineers and 3 new stakeholders join, \(n\) is not 3. The initial team size was \(n = 9\) (8 team members plus the project manager). The updated team size is \(n = 12\). If the question asks for the increase in channels, compute both totals and subtract the baseline from the updated figure.

Practical Question Strategy for the 230-Minute Exam

You have 230 minutes to tackle 180 questions, which breaks down to roughly 76 seconds per question. To protect your time buffer:

  • Do not reach for the on-screen calculator first: In over 60% of quantitative items, you can eliminate two distractors solely by observing whether the indices are above or below \(1.0\).
  • Identify the target metric in the final sentence: Project vignettes often provide extraneous details regarding team morale or procurement issues. Read the final question stem first to recognise whether the examiner wants \(CV\), \(CPI\), or an actionable management response.
  • Adopt active recall under time pressure: Memorising formulas passively from a document does not translate to high-speed recall during full-length mock exams. Leveraging intelligent spaced repetition on an interactive testing portal will train your brain to recognise EAC conditions and variance signs automatically.
  • Connect calculations to the ECO domains: When a calculation shows \(SPI = 0.75\), the next question will likely ask how to engage with the sponsor under the Business Environment domain, or how to lead a retrospective under the People domain. Math on the PMP is always a tool for strategic decision-making.

By treating each formula as an operational indicator rather than a mathematical hurdle, you can confidently secure every quantitative point available on exam day. Explore how Thinka uses AI-powered practice to diagnose weak formula topics, adapt question difficulty, and streamline your study hours.