📐 PMP Complete Formula Reference
All Knowledge Areas · All Domains · All Process Groups · All Formulas
📊 80+ Formulas
📚 10 Knowledge Areas
⚡ Conditions · Meaning · Actions
🎯 PMP Exam Ready
EVM — Three Core Values
PMBOK §7 · Cost| Metric | Formula | Condition / Result | Meaning | PM Action | Exam Tip |
|---|---|---|---|---|---|
| Planned Value (PV) BCWS | PV = % planned × BAC | Reference value | Authorized budget assigned to scheduled work at a point in time. What should be done by now? | Use as baseline for SV and SPI calculations | PV at 100% = BAC. PV is always time-phased. |
| Earned Value (EV) BCWP | EV = % complete × BAC | Performance value | Budget value of work actually accomplished. What IS done, expressed in budget dollars? | Calculate this first before CV, SV, CPI, SPI | EV uses % COMPLETE (not % spent). Classic trap question! |
| Actual Cost (AC) ACWP | AC = Actual $ spent | Reality check | Total cost incurred for work performed. How much has actually been spent? | Track against EV to identify cost overruns | AC has no upper limit. EV ÷ AC = CPI. |
| Budget at Completion (BAC) | BAC = Sum of all PV | Fixed baseline | Total approved project budget. PV at project end. | Never change without formal Change Control | BAC ≠ EAC. BAC is the plan; EAC is the forecast. |
EVM — Variances
PMBOK §7 · §6| Metric | Formula | Condition / Result | Meaning | PM Action | Exam Tip |
|---|---|---|---|---|---|
| Cost Variance (CV) | CV = EV − AC | CV > 0 = Under budget ✅ CV < 0 = Over budget ❌ | Dollar difference between earned value and actual cost. Are you spending more than the work is worth? | Negative: identify root cause, implement corrective action, update EAC | Formula starts with EV. "Earned before Actual." CV can stay negative at project end. |
| Schedule Variance (SV) | SV = EV − PV | SV > 0 = Ahead ✅ SV < 0 = Behind ❌ | Dollar value of schedule performance. How much ahead or behind are you in work accomplished? | Negative: crash schedule, fast-track, add resources, re-baseline if needed | SV = 0 at project end ALWAYS (EV=PV=BAC). Limitation of SV — doesn't measure time delay directly. |
| Variance at Completion (VAC) | VAC = BAC − EAC | VAC > 0 = Under budget ✅ VAC < 0 = Over budget ❌ | Expected dollar difference between original budget and forecast final cost | Present to sponsor; update funding requests if VAC is significantly negative | If CPI < 1, EAC > BAC → VAC will be negative. Report this proactively. |
EVM — Performance Indexes
PMBOK §7 · §6| Metric | Formula | Condition / Result | Meaning | PM Action | Exam Tip |
|---|---|---|---|---|---|
| Cost Performance Index (CPI) | CPI = EV ÷ AC | CPI > 1.0 = Efficient ✅ CPI < 1.0 = Inefficient ❌ CPI = 1.0 = On target | For every $1 spent, how much value is earned? CPI=0.80 means 80¢ of value per dollar spent. | CPI < 1: investigate cost drivers; update EAC; escalate if persistent | Most critical EVM index. Used in EAC = BAC/CPI. Research shows CPI rarely improves significantly after 20% complete. |
| Schedule Performance Index (SPI) | SPI = EV ÷ PV | SPI > 1.0 = Efficient ✅ SPI < 1.0 = Behind ❌ SPI = 1.0 = On schedule | For every $1 of planned work, how much is actually being accomplished? SPI=0.80 = only 80% of planned work done. | SPI < 1: schedule recovery plan, resource reallocation, scope reduction | SPI → 1.0 at project end (limitation). Does not directly measure time. Combine with CPM for schedule analysis. |
| Critical Ratio (CR) | CR = CPI × SPI | CR > 1.0 = Good overall ✅ CR < 1.0 = Problems ❌ | Combined measure of cost AND schedule efficiency. Single index showing overall project health. | CR < 0.80 is typically a trigger for escalation to management | Less common on exam but tests critical thinking — combines both indexes. |
EVM — Forecasting (EAC, ETC)
PMBOK §7.4| Metric | Formula | When to Use | Meaning | PM Action | Exam Tip |
|---|---|---|---|---|---|
| EAC — CPI Trend Most Common | EAC = BAC ÷ CPI | Past cost performance is expected to CONTINUE through project end | If inefficiency continues, final cost = BAC divided by cost efficiency ratio | Present to sponsor as most likely scenario if no corrective action taken | DEFAULT formula unless question specifies otherwise. Exam favorite! |
| EAC — New Estimate | EAC = AC + ETC | Original estimates are fundamentally flawed; team re-estimated remaining work | Actual spent + new bottom-up estimate for remaining work | Conduct bottom-up re-estimate; document assumptions; update schedule | Use when question says "re-estimated," "new estimate," or "original estimate was wrong" |
| EAC — Remaining at Plan Rate | EAC = AC + (BAC − EV) | Past variance was ATYPICAL and will NOT recur; remaining work at original rate | Assumes future CPI = 1.0. Only past work was over/under. | Document rationale for why variance was one-time event | Use when question says "atypical," "one-time," or "won't happen again" |
| EAC — CPI × SPI | EAC = AC + [(BAC−EV) ÷ (CPI×SPI)] | Both cost AND schedule efficiency influence remaining work (most pessimistic) | Schedule pressure compounds cost inefficiency going forward | Most conservative estimate; use when project is behind AND over budget | Used when project has BOTH cost and schedule problems. Results in highest EAC. |
| Estimate to Complete (ETC) | ETC = EAC − AC | Any time remaining cost is needed | How much MORE money is needed to finish? (not total — just remaining) | Use to update cost forecasts and funding requests | ETC ≠ EAC. EAC = total. ETC = remaining. ETC = EAC − AC. |
EVM — To-Complete Performance Index (TCPI)
PMBOK §7.4| Metric | Formula | Condition / Result | Meaning | PM Action | Exam Tip |
|---|---|---|---|---|---|
| TCPI (based on BAC) | TCPI = (BAC − EV) ÷ (BAC − AC) | TCPI > 1.0 = Challenging ❌ TCPI < 1.0 = Achievable ✅ | Required cost efficiency for remaining work to finish within ORIGINAL budget. Can you still make it? | Compare to current CPI. If TCPI > CPI, original budget likely unachievable. | If TCPI(BAC) significantly > CPI, tell sponsor the original budget is at risk. Classic exam scenario. |
| TCPI (based on EAC) | TCPI = (BAC − EV) ÷ (EAC − AC) | TCPI > 1.0 = New target also challenging TCPI < 1.0 = New budget achievable | Required efficiency to finish within REVISED (EAC) budget. Is the new forecast realistic? | If TCPI(EAC) also > current CPI, EAC may need further revision upward | Both TCPI formulas have same numerator (BAC−EV). Denominator changes: BAC−AC vs EAC−AC. |
Schedule Formulas
PMBOK §6 · Schedule Management| Metric | Formula | Condition / Result | Meaning | PM Action | Exam Tip |
|---|---|---|---|---|---|
| Total Float (TF) CPM | TF = LS − ES = LF − EF | TF = 0 → Critical Path ❌ TF > 0 → Flexibility ✅ TF < 0 → Behind schedule ❌ | Amount of time an activity can be delayed without delaying the project end date | Zero float = critical — prioritize resources. Negative float = must crash or fast-track. | Critical path = longest path = zero float. All activities on CP have TF=0. |
| Free Float (FF) | FF = ES(successor) − EF(current) − 1 | FF > 0 = Can delay w/o affecting successor | Amount of time an activity can delay without delaying the EARLY START of its successor | Use to manage resource leveling without affecting downstream tasks | FF ≤ TF always. FF is activity-level; TF is path-level. |
| Early Start (ES) | ES = EF(predecessor) + 1 | Forward pass calculation | Earliest an activity can start based on predecessors | Use forward pass to find all ES and EF values first | Forward pass: left to right. Use the LARGEST EF of all predecessors. |
| Early Finish (EF) | EF = ES + Duration − 1 | Forward pass calculation | Earliest an activity can finish | Track against baseline; EF of last activity = Project Early Finish | EF of last activity on CP = project duration. |
| Late Start (LS) | LS = LF − Duration + 1 | Backward pass calculation | Latest an activity can start without delaying project | If ES = LS, the activity is critical | Backward pass: right to left. Use the SMALLEST LS of all successors. |
| Late Finish (LF) | LF = LS(successor) − 1 | Backward pass calculation | Latest an activity can finish without delaying project | Compare LF to EF to find float | LF of last activity = Imposed project deadline (or EF if no constraint). |
| Project Duration | Duration = EF(last activity) − ES(first) + 1 | Sum of critical path | Total calendar duration from project start to finish | Compare to deadline; identify compression opportunities if exceeds target | Always calculate via CPM/forward pass, not just adding durations. |
Float Relationships & Lead/Lag
PMBOK §6.3| Metric | Formula / Concept | Condition / Result | Meaning | PM Action | Exam Tip |
|---|---|---|---|---|---|
| Lead | Negative lag (−lag) | Successor starts BEFORE predecessor finishes | Allows overlap between activities to compress schedule | Use carefully — increases risk. Document assumptions. | Lead is a schedule compression tool. Lead = negative lag on most software. |
| Lag | Positive delay (+lag) | Mandatory wait between activities | Required delay — e.g., concrete must cure 7 days before loading | Factor into schedule baseline; identify critical lags | Lag ADDS time. Lead SAVES time. Don't confuse them. |
| Project Buffer (CCPM) | Buffer = 50% of individual task safety time pooled | Protects project end date | Critical Chain PM: aggregated time buffer placed at end of critical chain | Monitor buffer consumption rate vs. chain completion rate | CCPM reduces Parkinson's Law and student syndrome effects. |
| Feeding Buffer (CCPM) | Buffer between non-critical chain and critical chain | Protects critical chain from delays on feeding chains | Prevents non-critical path delays from hitting the critical chain | Place at junction points where non-critical feeds into critical chain | Feeding buffer ≠ project buffer. Know the difference for CCPM questions. |
PERT — Three-Point Estimates
PMBOK §6.4| Metric | Formula | Condition / Result | Meaning | PM Action | Exam Tip |
|---|---|---|---|---|---|
| PERT Estimate (Beta Distribution) Most Common | tE = (O + 4M + P) ÷ 6 | Weighted average favoring Most Likely (4×weight) | Best estimate using Optimistic, Most Likely, Pessimistic. Beta weights most likely heavily. | Use for cost or duration estimates when uncertainty exists | Formula: O + 4M + P divided by 6. The "4" is the key. Beta = PERT = exam default. |
| Triangular Distribution | tE = (O + M + P) ÷ 3 | Equal weighting of all three estimates | Simple average of three estimates. Less sophisticated than Beta PERT. | Use when insufficient data to justify beta weighting | Triangular = ÷3. Beta PERT = ÷6 (with 4M). Exam will specify which to use. |
| PERT Standard Deviation (σ) | σ = (P − O) ÷ 6 | Larger σ = more uncertainty/risk | Measure of estimate uncertainty. Large P−O spread = high risk activity. | Activities with high σ need risk response plans | σ measures spread/uncertainty. Use to identify high-risk activities in schedule. |
| PERT Variance (σ²) | σ² = [(P − O) ÷ 6]² | Used for path variance calculation | Square of standard deviation. Used to calculate path-level uncertainty. | Sum variances along critical path to get path variance | Path σ = √(sum of individual σ²). Classic multi-activity PERT question. |
| Path Standard Deviation | σ(path) = √(Σ individual σ²) | Larger = more path uncertainty | Combined uncertainty of all activities on a path. Used with normal distribution tables. | Use to calculate probability of meeting a deadline | 68.27% within ±1σ, 95.45% within ±2σ, 99.73% within ±3σ. |
| Confidence Intervals | Range = tE ± zσ | 68%=±1σ, 95%=±2σ, 99.73%=±3σ | Probability that actual duration/cost falls within the range | Use to set contingency reserves and communicate schedule risk | ±1σ=68%, ±2σ=95%, ±3σ=99.73% — memorize these for exam! |
Cost Formulas
PMBOK §7 · Cost Management| Metric | Formula | Condition / Result | Meaning | PM Action | Exam Tip |
|---|---|---|---|---|---|
| Analogous Estimating | Cost based on similar past projects (expert judgment) | Rough estimate: ±25–50% accuracy | Top-down, fast, low accuracy. Best used in early project phases. | Use when detail data unavailable; document assumptions | Cheapest and fastest estimating technique. Least accurate. |
| Parametric Estimating | Cost = Unit cost × Quantity | Accuracy depends on quality of historical data | Statistical model using historical unit rates. Example: $150/sq ft × 2,000 sf = $300K. | Validate unit rates against current market data | More accurate than analogous if unit rates are valid. Scale-dependent. |
| Bottom-Up Estimating | Total = Σ (all work package estimates) | Most accurate: ±10–15% | Estimate each work package individually then aggregate. Most time-consuming but most accurate. | Use for definitive estimates; requires complete WBS | Most accurate, most expensive, most time-consuming. Done after WBS is complete. |
| Cost Baseline | Cost Baseline = Σ WBS budgets (time-phased) | Includes contingency | Authorized time-phased budget used to measure and monitor cost performance | Maintain as controlled document; change only via change control | Cost Baseline INCLUDES contingency reserves but EXCLUDES management reserves. |
| Project Budget | Budget = Cost Baseline + Management Reserve | Maximum authorized spend | Total funding required = performance baseline + management reserves for unknown unknowns | Management reserve requires sponsor approval to access | Cost Baseline + Mgmt Reserve = Project Budget. Know this hierarchy! |
| Contingency Reserve | Reserve = Σ(Probability × Impact) for known risks | Based on identified risks | Budget set aside for known-unknown risks (identified risks that may occur) | PM can access without special approval; track against risk register | Contingency = known-unknowns. Management Reserve = unknown-unknowns. |
| Depreciation — Straight Line | Annual Dep = (Asset Cost − Salvage) ÷ Useful Life | Equal annual reduction | Asset loses equal value each year of its useful life | Include in project financial planning for equipment-heavy projects | Straight line = constant depreciation. Sum of Years Digits and Double Declining = accelerated. |
| Depreciation — Double Declining Balance | Dep = 2/n × Book Value (each year) | Accelerated — more in early years | Front-loads depreciation. Book value never reaches zero (stop at salvage value). | Favorable for tax purposes; reduces taxable income in early years | DDB rate = 2/n where n = useful life years. Book value × rate each year. |
| Net Present Value (NPV) | NPV = Σ [CF_t ÷ (1+r)^t] − Initial Investment | NPV > 0 = Accept project ✅ NPV < 0 = Reject ❌ | Present value of all future cash flows minus investment. Accounts for time value of money. | Higher NPV = better investment. Use to compare competing projects. | If two projects: choose HIGHER NPV. Opportunity cost = NPV of project NOT chosen. |
| Present Value (PV) | PV(Finance) = FV ÷ (1+r)^n | PV always < FV (positive r) | Today's worth of a future cash flow. $1 tomorrow is worth less than $1 today. | Use to compare cash flows occurring at different times | Higher discount rate r = lower PV. Longer time n = lower PV. |
| Future Value (FV) | FV = PV × (1+r)^n | FV always > PV | Future worth of today's money invested at rate r for n periods | Use for financial modeling, lease vs buy analysis | FV is opposite of PV formula. Know both directions. |
| ROI (Return on Investment) | ROI = (Net Benefit ÷ Cost) × 100% | Higher ROI = better ✅ | Percentage return relative to investment. Used for project selection. | Compare ROI across project alternatives; report to portfolio committee | ROI does NOT account for time value of money (unlike NPV/IRR). |
| Payback Period | Payback Period = Investment ÷ Annual Cash Flow | Shorter payback = better (lower risk) | Time to recover initial investment. Simple but ignores time value and post-payback cash flows. | Use as tie-breaker or risk indicator; prefer shorter payback for uncertain environments | Payback period ignores time value of money. Simplest project selection method. |
| Benefit-Cost Ratio (BCR) | BCR = PV(Benefits) ÷ PV(Costs) | BCR > 1.0 = Worth it ✅ BCR < 1.0 = Not worth it ❌ | For every $1 invested, how much benefit is generated? BCR=1.5 = $1.50 benefit per $1 cost. | Select project with highest BCR when ranking alternatives | Higher BCR = better. BCR=2.0 means double your investment in benefits. |
| IRR (Internal Rate of Return) | NPV = 0 when discount rate = IRR | IRR > required rate = Accept ✅ | Discount rate that makes NPV equal zero. The "break-even" rate of return for the investment. | Compare to hurdle rate (required rate). If IRR > hurdle rate, project adds value. | Higher IRR = better. If IRR > cost of capital, project creates value. |
Reserves & Contingency Hierarchy
PMBOK §7.2| Metric | Formula / Concept | Who Controls? | For What? | Access Process | Exam Tip |
|---|---|---|---|---|---|
| Contingency Reserve | EMV of known risks + padding for identified risk events | Project Manager | Known-unknowns (identified risks in risk register) | PM accesses based on risk trigger; no separate approval needed | Included IN cost baseline. PM controls. |
| Management Reserve | % of total project budget (e.g., 5–10%) | Senior Management / Sponsor | Unknown-unknowns (unidentified, unforeseeable events) | Requires change request and management approval to use | NOT in cost baseline — added on top. Requires change control. |
Risk Formulas
PMBOK §11 · Risk Management| Metric | Formula | Condition / Result | Meaning | PM Action | Exam Tip |
|---|---|---|---|---|---|
| Risk Score (Priority) | Risk Score = Probability × Impact | Higher score = higher priority | Quantified risk priority for risk register ranking and resource allocation | High-score risks get active response strategies (avoid, transfer, mitigate, accept) | Used in qualitative risk analysis. Creates probability-impact matrix entries. |
| Risk Exposure | RE = Probability × Impact ($) | Represents expected monetary impact | Dollar value of the risk's expected impact weighted by probability | Sum RE across risks for contingency reserve calculation | Same concept as EMV. Higher RE = more contingency needed. |
| Expected Monetary Value (EMV) | EMV = Probability × Monetary Value | EMV > 0 = Opportunity ✅ EMV < 0 = Threat ❌ | Expected financial impact of a risk or decision. Used in decision tree analysis. | Sum EMVs of all paths to find best decision option | Threats = negative EMV. Opportunities = positive EMV. Sum all branches of decision tree. |
| Decision Tree Value | Node Value = Σ (EMV of each branch) | Select path with highest node value | Expected monetary outcome considering all possible outcomes and probabilities | Choose decision that maximizes expected value | Work right to left. Multiply probability × outcome, then sum. Choose highest at decision node. |
| Monte Carlo Simulation | Runs thousands of scenarios using probability distributions | Output: probability distribution of outcomes | Statistical technique giving range of possible outcomes with probability. Most sophisticated risk tool. | Use output to set contingency reserves and schedule buffers | Monte Carlo produces S-curve / probability distribution. "What is the probability of finishing by date X?" → Monte Carlo. |
| Sensitivity Analysis | Tornado Diagram: rank variables by impact on output | Wider bar = higher sensitivity = more impact | Identifies which variables (risks) have greatest influence on project objectives | Focus risk management efforts on top variables in tornado diagram | Tornado diagram = sensitivity analysis output. Widest bar = most sensitive variable. |
EMV & Decision Tree Example
PMBOK §11.4| Concept | Formula / Calculation | Result | Meaning | PM Action | Exam Tip |
|---|---|---|---|---|---|
| Decision Tree Node | Value = Σ(Pi × Outcome_i) − Cost of decision | Select highest value node | Expected value of each decision path considering all outcomes and their probabilities | Add cost of each decision option before comparing | Subtract the cost of the decision FROM the EMV. Exam commonly omits this step as a trap. |
| Risk-Adjusted NPV | R-NPV = NPV × (1 − risk probability) + Risk-adjusted payoff | More realistic project value | Adjusts NPV for risk. Lower than base NPV for projects with significant downside risks. | Use for portfolio decisions with uncertain cash flows | Less common but tests understanding of combining NPV with probability concepts. |
Quality Formulas
PMBOK §8 · Quality Management| Metric | Formula / Concept | Condition / Result | Meaning | PM Action | Exam Tip |
|---|---|---|---|---|---|
| Cost of Quality (COQ) | COQ = Cost of Conformance + Cost of Non-Conformance | Lower COQ = more efficient quality system | Total cost to achieve quality standards including prevention, appraisal, and failure costs | Invest in prevention to reduce failure costs. Prevention > Appraisal > Internal Failure > External Failure. | COQ has 4 components. Prevention is cheapest long-term. External failure is most expensive. |
| Cost of Conformance | = Prevention Costs + Appraisal Costs | Planned quality investment | Costs to do things right: training, inspections, testing, documentation | Increase conformance costs to decrease non-conformance costs | Prevention = training, process improvement. Appraisal = testing, inspections. |
| Cost of Non-Conformance | = Internal Failure + External Failure Costs | Higher = poorer quality system | Costs from NOT meeting quality standards: rework, scrap, warranty, liabilities, lost reputation | Track non-conformance costs to justify quality investment | Internal failure = found before delivery. External failure = found by customer. External costs more! |
| Control Chart — UCL/LCL | UCL = Mean + 3σ LCL = Mean − 3σ | Points within = in control. Points outside = out of control. | Statistical limits for process variation. ±3σ contains 99.73% of normal variation. | Investigate and correct any point outside control limits or 7 consecutive points on one side | ±3σ = control limits. Rule of 7: 7 consecutive points same side = out of control (even if within limits). |
| Rule of Seven (7) | 7 consecutive data points on same side of mean | Process is OUT of control (assignable cause) | Even without exceeding control limits, a run of 7 indicates a non-random pattern | Investigate for assignable (special) cause variation | 7 consecutive = out of control. Exam will ask: "7 points in a row below mean — what do you do?" → Investigate! |
| Process Sigma Level | Sigma = (USL − Mean) ÷ σ | Higher sigma = better quality | Measure of process capability. 6-sigma = 3.4 defects per million opportunities. | Define target sigma level in quality management plan | 6-sigma = near perfection. 3-sigma = 99.73% = 2,700 defects per million. Know the difference. |
Quality — Defect & Sampling Metrics
PMBOK §8.3| Metric | Formula | Condition / Result | Meaning | PM Action | Exam Tip |
|---|---|---|---|---|---|
| Defects Per Million Opportunities (DPMO) | DPMO = (Defects ÷ Opportunities) × 1,000,000 | Lower DPMO = better quality | Standardized measure of defect rate allowing comparison across different processes | Track DPMO trends; set reduction targets | 6-sigma target = 3.4 DPMO. Exam may give DPMO and ask what sigma level it represents. |
| Yield | Yield = (Good Units ÷ Total Units) × 100% | Higher yield = better quality | Percentage of output meeting quality standards without rework | Track first-pass yield; low yield = process problem | First Time Yield (FTY) = units passing inspection on first attempt / total units. |
| Pareto Principle | 80% of problems caused by 20% of causes | Focus on top 20% of causes | 80/20 rule: most defects come from a few root causes. Prioritize top causes for maximum improvement. | Use Pareto chart to identify and attack the vital few causes first | Pareto chart = bar chart ordered by frequency. Tallest bars = highest priority. Classic exam tool. |
Communications Formulas
PMBOK §10 · Communications Management| Metric | Formula | Condition / Result | Meaning | PM Action | Exam Tip |
|---|---|---|---|---|---|
| Communication Channels Most Tested | Channels = n(n−1) ÷ 2 | Grows exponentially with team size | Total number of potential communication paths between n stakeholders. Adding one person adds n-1 new channels. | Manage communications carefully as team grows. Large teams need formal comms plan. | n=10: 10×9÷2=45. n=11: 11×10÷2=55. Adding 1 person adds 10 channels. VERY common exam question! |
| New Channels Added | ΔChannels = (nₙₑw × (nₙₑw−1) ÷ 2) − (nₒₗd × (nₒₗd−1) ÷ 2) | Always positive when adding people | How many new communication paths are created when adding team members | Update Communications Management Plan when team size changes significantly | Formula: compute both before and after, then subtract. Simpler: new channels = n_old channels added for each new person. |
Procurement Contract Types
PMBOK §12 · Procurement| Contract Type | Formula / Structure | Risk: Buyer vs Seller | Meaning | When to Use | Exam Tip |
|---|---|---|---|---|---|
| Firm Fixed Price (FFP) Lowest buyer risk | Price = Fixed amount regardless of cost | Seller bears ALL cost risk | Seller agrees to deliver scope for a set price. Overruns are seller's problem. | When scope is well-defined and stable | FFP = buyer's favorite. Seller must manage costs carefully or absorb losses. |
| Fixed Price Incentive Fee (FPIF) | Final Price = Actual Cost + Fee, capped at Ceiling Price Seller's share = sharing ratio | Shared risk with incentive for efficiency | Fixed price with incentive for seller to reduce costs. Savings split per sharing ratio. | When cost control by seller is desired with some flexibility | Know the sharing ratio concept and ceiling price. Costs above ceiling = all seller's risk. |
| Fixed Price with Economic Price Adjustment (FP-EPA) | Price adjusted per pre-agreed index (CPI, labor rates) | Buyer absorbs inflation risk partially | Protects seller from inflation/market changes on multi-year contracts | Long-duration contracts where prices may shift | FP-EPA is used for long contracts. The index is pre-agreed (e.g., Bureau of Labor Statistics). |
| Cost Plus Fixed Fee (CPFF) | Payment = Actual Cost + Fixed Fee | Buyer bears ALL cost risk | Seller reimbursed for all costs plus a fixed fee regardless of performance | R&D or unknown scope projects where cost cannot be estimated | CPFF = highest buyer risk. Fixed fee = constant regardless of cost. No incentive for seller efficiency. |
| Cost Plus Incentive Fee (CPIF) | Fee = Target Fee ± (Target Cost − Actual Cost) × Sharing Ratio | Buyer bears most risk; seller has incentive | Reimbursed costs plus fee that grows if costs are below target | When cost reduction incentive desired on cost-reimbursable contracts | Sharing ratio splits savings/overruns. e.g., 80/20 means buyer takes 80% of variance, seller 20%. |
| Cost Plus Award Fee (CPAF) | Fee = Cost + subjective award fee based on performance | Buyer bears cost risk; seller motivated by award | Award fee based on buyer's subjective assessment of performance. Not disputable. | When performance criteria are hard to define objectively | Award fee is subjective and cannot be litigated. CPIF fee is objective and can be disputed. |
| Time and Materials (T&M) | Payment = Hourly Rate × Hours + Materials Cost | Buyer bears cost and schedule risk | Hybrid contract. Not fixed (like CR) but bounded by rates (like FP). Risk grows with duration. | Staff augmentation, short-duration, undefined scope | T&M has elements of both FP (fixed rates) and CR (no cap on hours). Use NTE clause to limit exposure. |
Point of Total Assumption (PTA)
PMBOK §12 · FPIF Contracts| Metric | Formula | Condition / Result | Meaning | PM Action | Exam Tip |
|---|---|---|---|---|---|
| Point of Total Assumption (PTA) FPIF Only | PTA = [(Ceiling Price − Target Price) ÷ Buyer's Share Ratio] + Target Cost | Actual Cost > PTA → Seller absorbs ALL additional cost | Cost threshold above which seller assumes ALL additional risk on FPIF contract. Above PTA, seller "owns" overruns. | Monitor contractor costs against PTA; if trending above, renegotiate or invoke contract clauses | PTA only applies to FPIF contracts. Extremely common exam question. Know the formula cold! |
🎯 PTA Example: Target Cost=$100K, Target Price=$110K, Ceiling Price=$125K, Sharing Ratio=80/20 (buyer/seller)
PTA = [(125K−110K) ÷ 0.80] + 100K = [15K ÷ 0.80] + 100K = 18,750 + 100,000 = $118,750
If actual costs exceed $118,750, seller absorbs 100% of all additional costs.
PTA = [(125K−110K) ÷ 0.80] + 100K = [15K ÷ 0.80] + 100K = 18,750 + 100,000 = $118,750
If actual costs exceed $118,750, seller absorbs 100% of all additional costs.
Resource / HR Formulas
PMBOK §9 · Resource Management| Metric | Formula | Condition / Result | Meaning | PM Action | Exam Tip |
|---|---|---|---|---|---|
| Resource Loading | Loading = Σ(hours assigned per resource per period) | Over-allocated = > availability | Total work assigned to each resource in each time period | Level resources to eliminate over-allocation; may extend schedule | Resource leveling can extend schedule. Resource smoothing does not extend schedule but may not resolve all conflicts. |
| Team Size Complexity | Interfaces = n(n−1) ÷ 2 (same as communication channels) | Larger team = exponential complexity | Number of interpersonal interfaces in a team. Same formula as comms channels. | Keep teams small (Scrum: 3–9) to reduce coordination overhead | Same formula as communication channels — tests if you recognize the connection. |
| Training Cost | Training ROI = (Productivity Gain − Training Cost) ÷ Training Cost × 100% | Positive = justified investment | Return on training investment in terms of improved productivity | Include training costs in project budget; track productivity improvement | Less commonly tested — but training is always considered an investment, not just a cost. |
Scope Formulas & Concepts
PMBOK §5 · Scope Management| Metric | Formula / Concept | Condition / Result | Meaning | PM Action | Exam Tip |
|---|---|---|---|---|---|
| WBS Decomposition | Work Package = Lowest level WBS element with cost + schedule | Typically 8–80 hours of effort | Deliverable-oriented hierarchy. 100% rule: WBS must capture 100% of project work — no more, no less. | Validate 100% rule; each parent = sum of children | 100% Rule is the most important WBS concept. Anything NOT in WBS = outside project scope. |
| Scope Baseline | Scope Baseline = Project Scope Statement + WBS + WBS Dictionary | Three components together | Approved version of scope — what IS and IS NOT included in the project | Measure scope performance against; change only via change control | Scope Baseline = 3 documents. Missing any one = incomplete baseline. |
| Scope Creep | Uncontrolled scope additions without change control | Always harmful — avoid ❌ | Growth of project scope without corresponding changes to cost, schedule, or resources | Enforce change control process; document all scope changes formally | Scope creep = unauthorized additions. Gold plating = PM adds unrequested features. Both are bad! |
Agile Velocity, Burndown & Burnup
PMI-ACP · Agile Practice Guide| Metric | Formula | Condition / Result | Meaning | PM Action | Exam Tip |
|---|---|---|---|---|---|
| Velocity | Velocity = Story Points completed per sprint | Higher velocity = more productive team | Measure of team's delivery capacity per sprint. Used for release planning. | Average 3+ sprints for reliable velocity estimate; don't pressure team to inflate | Velocity is team-specific — cannot compare across teams. Don't use to measure performance. |
| Release Planning | Sprints Needed = Total Story Points ÷ Velocity | More stories = more sprints | Estimate of how many sprints needed to deliver all backlog items | Use to set release dates and expectations with stakeholders | If velocity = 20 SP/sprint and backlog = 200 SP → 10 sprints needed. |
| Burndown Chart | Remaining Work = Total Backlog − Completed Work | Trending to zero = on track ✅ Flat/rising = behind ❌ | Shows remaining work over time. Ideal line goes from total to zero by sprint/release end. | Monitor daily; investigate when actual deviates significantly from ideal line | Burndown = remaining work. Goes DOWN to zero. Burnup = completed work. Goes UP to total. |
| Burnup Chart | Completed Work over Time (separate line for total scope) | Gap between lines = remaining work | Shows completed work AND total scope. Scope changes are visible as shifts in the total line. | Use burnup to show scope changes; preferred over burndown for scope creep visibility | Burnup shows scope changes explicitly. Burndown hides them. Burnup = better transparency. |
| Sprint Capacity | Capacity = Available Hours × Focus Factor | Realistic capacity < total hours | Actual usable hours for a sprint accounting for meetings, interruptions, vacations | Use focus factor (typically 60–80%) for realistic sprint planning | Don't plan at 100% capacity. Sustainable pace = key agile principle. |
| Team Happiness / NPS | Team Health = % Promoters − % Detractors (NPS concept) | Higher = healthier team | Measure of team morale and engagement. Correlates with productivity and retention. | Conduct regular retrospectives; address team health issues promptly | PMP exam now includes significant agile content. Team health metrics are increasingly tested. |
| Cumulative Flow Diagram (CFD) | Bands showing WIP in each state over time | Parallel bands = smooth flow. Widening band = bottleneck. | Visual tool showing workflow through Kanban states. Thick bands = work piling up = problem. | Identify and resolve bottlenecks shown by widening bands | CFD = Kanban metric. Widening band = WIP building up = process constraint. |
| Cycle Time | Cycle Time = Work Finish Date − Work Start Date | Shorter = more responsive ✅ | Time from when work starts to when it's done. Measure of process speed. | Track cycle time trends; use Little's Law to relate WIP, throughput, cycle time | Little's Law: WIP = Throughput × Cycle Time. Common in advanced agile metrics questions. |
| Lead Time | Lead Time = Work Finish Date − Request Date | Shorter = better customer experience ✅ | Time from customer request to delivery. Includes wait time before work starts. | Reduce lead time by reducing queue sizes and WIP limits | Lead Time > Cycle Time always (Lead includes waiting). Reduce WIP to reduce Lead Time. |
Stakeholder Engagement Metrics
PMBOK §13 · Stakeholder Management| Metric | Formula / Concept | Condition / Result | Meaning | PM Action | Exam Tip |
|---|---|---|---|---|---|
| Stakeholder Engagement Assessment Matrix | Gap = Desired Engagement − Current Engagement | Gap > 0 = Need to increase engagement | Compares current vs. desired engagement level for each stakeholder (Unaware→Resistant→Neutral→Supportive→Leading) | Develop targeted engagement strategies to close gaps | 5 levels: Unaware, Resistant, Neutral, Supportive, Leading. C=Current, D=Desired. Goal: C=D. |
| Power/Interest Grid | Categorize: Power (H/L) × Interest (H/L) | 4 quadrants define strategy | Stakeholder classification tool: High Power+High Interest=Manage Closely; High Power+Low Interest=Keep Satisfied | Tailor engagement approach based on quadrant placement | 4 strategies: Manage Closely (HH), Keep Satisfied (HL), Keep Informed (LH), Monitor (LL). |
General PM Formulas & Concepts
All Knowledge Areas| Metric | Formula | Condition / Result | Meaning | PM Action | Exam Tip |
|---|---|---|---|---|---|
| Expected Activity Duration | D = Effort ÷ Resources | More resources = shorter duration (to a point) | Time required = total work divided by number of people doing it. Linear relationship with caveats. | Apply resource leveling constraints; Brooks's Law applies (adding late resources slows project) | Adding people doesn't always reduce duration (Brooks's Law: "adding manpower to a late software project makes it later") |
| Heuristic 80/20 for WBS | Work package = 8–80 hours of effort | Below 8h = too granular; above 80h = too large | Rule of thumb for WBS decomposition granularity | Stop decomposing when you can realistically assign, track, and control the work package | 8-80 rule = heuristic, not a hard rule. Context matters. Very common exam concept. |
| Project Selection — Constrained Optimization | Linear programming, integer programming, goal programming models | Use for complex multi-project portfolios | Mathematical models to select optimal portfolio given constraints (budget, resources, time) | Use constrained optimization models for large portfolio decisions | Know the name and concept. Contrasted with "benefit measurement methods" (NPV, BCR, payback). |
| Rough Order of Magnitude (ROM) | ROM accuracy = −50% to +100% | Used in pre-project / initiation phase | Very rough estimate used before full project scope is defined. Wide range reflects high uncertainty. | Communicate ROM range explicitly; upgrade to definitive estimate when scope is defined | ROM = −50% to +100%. Budget estimate = −10% to +25%. Definitive = −5% to +10%. |
| Budget Estimate | Accuracy = −10% to +25% | Used in planning phase | Moderate accuracy estimate used for budgeting and resource allocation | Use budget estimates for portfolio-level planning | Know estimate accuracy ranges: ROM, Budget, Definitive. Common exam knowledge area. |
| Definitive Estimate | Accuracy = −5% to +10% | Used in execution phase (detailed design complete) | Most accurate estimate based on detailed scope, design, and historical data | Use for contract pricing and procurement | Definitive = most accurate. Requires complete WBS and detailed design. |
| Procurement Cost Models Target Cost, Target Fee | Target Price = Target Cost + Target Fee | Starting point for CPIF/FPIF contracts | Baseline for incentive contract — defines expected cost and fee at planned performance | Negotiate realistic target cost; unrealistic targets create adversarial relationships | Target Price ≠ Ceiling Price. Ceiling Price > Target Price. Know all contract price components. |
| Earned Schedule (ES) | ES = Time when PV should equal current EV | ES < AT = Behind schedule | Advanced EVM: translates EV-based SV into time units. Overcomes SV=0 at project end limitation. | Use ES-based metrics for more accurate schedule forecasting in later project phases | Earned Schedule converts dollar-based schedule metrics into time. SPI(t) = ES ÷ AT. More accurate late in project. |
MASTER CHEAT SHEET — All Formulas at a Glance
Quick Reference| Formula Name | Formula | Positive = Good? | Knowledge Area |
|---|---|---|---|
| PV (Planned Value) | % planned × BAC | — | Cost / EVM |
| EV (Earned Value) | % complete × BAC | — | Cost / EVM |
| AC (Actual Cost) | Actual $ spent | Lower = better | Cost / EVM |
| BAC | Total authorized budget | — | Cost |
| CV (Cost Variance) | EV − AC | ✅ Yes | Cost |
| SV (Schedule Variance) | EV − PV | ✅ Yes | Schedule |
| CPI | EV ÷ AC | ✅ > 1.0 | Cost |
| SPI | EV ÷ PV | ✅ > 1.0 | Schedule |
| EAC (CPI trend) | BAC ÷ CPI | Lower better | Cost |
| EAC (new estimate) | AC + ETC | Lower better | Cost |
| EAC (atypical past) | AC + BAC − EV | Lower better | Cost |
| EAC (CPI×SPI) | AC + (BAC−EV)÷(CPI×SPI) | Lower better | Cost |
| ETC | EAC − AC | Lower better | Cost |
| VAC | BAC − EAC | ✅ Yes | Cost |
| TCPI (BAC) | (BAC−EV)÷(BAC−AC) | ✅ ≤ 1.0 | Cost |
| TCPI (EAC) | (BAC−EV)÷(EAC−AC) | ✅ ≤ 1.0 | Cost |
| Critical Ratio | CPI × SPI | ✅ > 1.0 | Cost/Sched |
| Total Float | LS−ES or LF−EF | ✅ > 0 | Schedule |
| Free Float | ES(succ)−EF(curr)−1 | ✅ > 0 | Schedule |
| PERT (Beta) | (O+4M+P)÷6 | — | Schedule |
| PERT (Triangular) | (O+M+P)÷3 | — | Schedule |
| PERT Std Dev | (P−O)÷6 | Lower better | Schedule/Risk |
| PERT Variance | [(P−O)÷6]² | Lower better | Risk |
| EMV | Probability × Impact ($) | ✅ Positive | Risk |
| Communication Channels | n(n−1)÷2 | Lower = simpler | Comms |
| PTA | [(Ceiling−Target Price)÷Buyer Share]+Target Cost | — | Procurement |
| NPV | PV(benefits)−Initial Investment | ✅ > 0 | Cost/Finance |
| PV (Finance) | FV÷(1+r)^n | — | Finance |
| FV | PV×(1+r)^n | — | Finance |
| BCR | PV(Benefits)÷PV(Costs) | ✅ > 1.0 | Finance |
| ROI | (Benefit−Cost)÷Cost×100% | ✅ Higher | Finance |
| Payback Period | Investment÷Annual CF | ✅ Shorter | Finance |
| COQ | Conformance+Non-Conformance | Lower better | Quality |
| Control Chart UCL/LCL | Mean ± 3σ | Within = good | Quality |
| DPMO | (Defects÷Opportunities)×1M | ✅ Lower | Quality |
| Velocity (Agile) | SP completed per sprint | ✅ Stable/higher | Agile |
| Release Sprints (Agile) | Total SP÷Velocity | — | Agile |
| Straight-Line Depreciation | (Cost−Salvage)÷Life | — | Finance |
| Double Declining Balance | 2/n × Book Value | — | Finance |