The Definitive PMP Formulas Cheat Sheet for Quantitative Confidence

Quantitative questions typically make up 5% to 10% of the 180 questions on the Project Management Professional (PMP)® exam. While calculations represent a relatively modest fraction of the 230-minute Pearson VUE testing sitting, they generate disproportionate anxiety for project practitioners. Modern PMP assessments rarely demand tedious manual arithmetic; instead, the Project Management Institute (PMI)® tests your ability to diagnose project health, interpret variances, and select corrective interventions under real-world delivery constraints.

This PMP formulas cheat sheet consolidates every mathematical equation you need for the exam—spanning Earned Value Management (EVM), Critical Path Method (CPM) schedule analysis, three-point estimating, and communication channels. By pairing formula definitions with diagnostic rules of thumb, you can eliminate rote memorisation and solve numerical scenario questions rapidly.

Earned Value Management (EVM) Core Metrics

Earned Value Management is the cornerstone of PMP quantitative testing. Every EVM calculation builds upon three foundational inputs:

1. Planned Value (PV): The authorised budget assigned to scheduled work: \( \text{PV} = \text{Planned \% Complete} \times \text{BAC} \)
2. Earned Value (EV): The measure of work performed expressed in terms of the authorised budget: \( \text{EV} = \text{Actual \% Complete} \times \text{BAC} \)
3. Actual Cost (AC): The realised cost incurred for work performed on an activity during a specific time period.
4. Budget at Completion (BAC): The total planned budget for the entire project.

Variances & Performance Indices

When calculating variances, always start with \( \text{EV} \). A positive variance indicates favourable performance, whereas a negative variance signals trouble:

Cost Variance (CV): \( \text{CV} = \text{EV} - \text{AC} \)
Interpretation: \( \text{CV} > 0 \) (under budget), \( \text{CV} = 0 \) (on budget), \( \text{CV} < 0 \) (over budget).

Schedule Variance (SV): \( \text{SV} = \text{EV} - \text{PV} \)
Interpretation: \( \text{SV} > 0 \) (ahead of schedule), \( \text{SV} = 0 \) (on schedule), \( \text{SV} < 0 \) (behind schedule).

Cost Performance Index (CPI): \( \text{CPI} = \frac{\text{EV}}{\text{AC}} \)
Interpretation: \( \text{CPI} > 1.0 \) (spending less than planned for work completed), \( \text{CPI} = 1.0 \) (on budget), \( \text{CPI} < 1.0 \) (cost overrun).

Schedule Performance Index (SPI): \( \text{SPI} = \frac{\text{EV}}{\text{PV}} \)
Interpretation: \( \text{SPI} > 1.0 \) (progressing faster than planned), \( \text{SPI} = 1.0 \) (on schedule), \( \text{SPI} < 1.0 \) (schedule slippage).

EVM Scenario Diagnostic Table

Exam scenarios often provide indices without asking for raw arithmetic. Use this reference to diagnose project status instantaneously:

\( \text{CPI} > 1.0 \) & \( \text{SPI} > 1.0 \): Under budget and ahead of schedule (ideal performance).
\( \text{CPI} > 1.0 \) & \( \text{SPI} < 1.0 \): Under budget but behind schedule (work is progressing slowly, but costs are contained).
\( \text{CPI} < 1.0 \) & \( \text{SPI} > 1.0 \): Over budget but ahead of schedule (likely crashing the schedule or using expensive overtime).
\( \text{CPI} < 1.0 \) & \( \text{SPI} < 1.0 \): Over budget and behind schedule (critical distress requiring immediate corrective action).

Forecasting Formulas: EAC, ETC, VAC, and TCPI

Forecasting formulas determine what the project will cost upon completion based on current performance trends.

Estimate at Completion (EAC)

The method you choose for calculating \( \text{EAC} \) depends entirely on future performance assumptions stated in the scenario:

1. Current cost trends will continue:
\( \text{EAC} = \frac{\text{BAC}}{\text{CPI}} \)

2. Future work will be performed at the budgeted rate (atypical past variances):
\( \text{EAC} = \text{AC} + (\text{BAC} - \text{EV}) \)

3. Both cost and schedule performance influence remaining work:
\( \text{EAC} = \text{AC} + \frac{\text{BAC} - \text{EV}}{\text{CPI} \times \text{SPI}} \)

4. Initial plan is flawed and requires bottom-up re-estimation:
\( \text{EAC} = \text{AC} + \text{Bottom-up ETC} \)

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

Estimate to Complete (ETC): Expected cost to finish all remaining project work.
\( \text{ETC} = \text{EAC} - \text{AC} \)

Variance at Completion (VAC): The projected financial surplus or deficit at project closure.
\( \text{VAC} = \text{BAC} - \text{EAC} \)
Interpretation: \( \text{VAC} > 0 \) indicates an expected surplus; \( \text{VAC} < 0 \) indicates an expected cost overrun.

To-Complete Performance Index (TCPI)

\( \text{TCPI} \) calculates the cost performance that must be maintained on remaining work to meet a specified target.

To achieve original budget (\( \text{BAC} \)):
\( \text{TCPI}_{\text{BAC}} = \frac{\text{BAC} - \text{EV}}{\text{BAC} - \text{AC}} \)

To achieve revised budget (\( \text{EAC} \)):
\( \text{TCPI}_{\text{EAC}} = \frac{\text{BAC} - \text{EV}}{\text{EAC} - \text{AC}} \)

Rule of Thumb: A \( \text{TCPI} > 1.0 \) indicates that remaining work must be completed with greater cost efficiency than originally planned to hit the target, while \( \text{TCPI} < 1.0 \) means there is leeway to spend more liberally.

Critical Path Method (CPM) & Float Calculations

Network diagrams test your understanding of project pacing, resource allocation, and scheduling bottlenecks.

Total Float (Total Slack): The amount of time an activity can be delayed without delaying the project finish date.
\( \text{Total Float} = \text{Late Start (LS)} - \text{Early Start (ES)} \)
or
\( \text{Total Float} = \text{Late Finish (LF)} - \text{Early Finish (EF)} \)

Free Float: The amount of time an activity can be delayed without delaying the Early Start of any immediate successor activity.
\( \text{Free Float} = \min(\text{ES of Successors}) - \text{Early Finish (EF)} \)

Critical Path Characteristics:
Activities on the critical path have \( \text{Total Float} = 0 \). A project can have multiple critical paths, which increases overall delivery risk. Negative float indicates that the project schedule is currently delayed against its committed baseline.

Estimating & Communication Formulas

Three-Point Estimating (PERT)

PMI distinguishes between simple triangular distributions and weighted beta (PERT) distributions:

Triangular Distribution (Simple Average):
\( E = \frac{O + M + P}{3} \)

Beta / PERT Distribution (Weighted Average):
\( E = \frac{O + 4M + P}{6} \)

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

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

Where: \( O \) = Optimistic estimate, \( M \) = Most likely estimate, \( P \) = Pessimistic estimate.

Communication Channels Formula

As team size scales, the potential lines of communication increase exponentially:

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

Trap Alert: Check whether the question states "\( n \) stakeholders were added" versus "the team increased to \( n \) members". If 4 members join an existing team of 6, calculate the channels for \( n = 10 \) and subtract the channels from \( n = 6 \) to identify the net increase.

Project Selection & Financial Fundamentals

While deep accounting calculations are rare on the modern PMP exam, you must understand project selection principles:

Benefit-Cost Ratio (BCR): \( \text{BCR} = \frac{\text{Total Benefits}}{\text{Total Costs}} \). Select projects where \( \text{BCR} > 1.0 \). When comparing options, choose the higher ratio.
Net Present Value (NPV): Future cash flows discounted to present value minus initial outlay. Always select the project with the highest positive NPV.
Payback Period: Time required to recover the initial investment. Shorter payback periods carry lower exposure to financial risk.
Opportunity Cost: The value of the project opportunity foregone by choosing an alternative.

Four Exam-Room Tactics for Calculation Questions

1. Identify the Core Question First: Read the final sentence of long situational scenarios before reviewing the numerical data. Often, extensive background narratives are background noise, and the question merely tests whether a \( \text{CPI} \) of 0.82 implies a cost overrun.

2. Filter Numerical Distractors: Questions may provide AC, PV, EV, and planned completion dates when you only need EV and AC to solve for CV. Map out your required variables before touching the onscreen Pearson VUE calculator.

3. Master the Onscreen Tools: During your 230-minute exam sitting, you will have access to an onscreen scratch pad and calculator. Practise with digital interfaces during revision rather than relying entirely on physical paper and highlighters.

4. Benchmark Through Diagnostics: Review official score reports and diagnostic practice results (which PMI generally issues within 1 to 5 business days post-exam) by testing your formula recall under timed conditions. Explore expert professional exam preparation guides to structure your revision schedule effectively.

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