A single-page reference for the project management formulas every PMP candidate and practicing PM should know — with the mathematical definition and a note on when to use each.
Use PERT when estimates are uncertain and you want a weighted expected duration plus a confidence range.
| Formula | Definition | When to use |
|---|---|---|
| Expected Duration (TE) | TE = (O + 4M + P) / 6 | Weighted average of Optimistic, Most Likely, and Pessimistic estimates. |
| Standard Deviation (σ) | σ = (P − O) / 6 | Measures spread of the estimate — larger σ means more uncertainty. |
| Variance | σ² | Sum variances across tasks on the critical path for a project-level confidence range. |
| 68% Confidence | TE ± 1σ | Rough one-sigma range for typical delivery. |
| 95% Confidence | TE ± 2σ | Practical planning range used in most schedules. |
| 99.7% Confidence | TE ± 3σ | Worst-case commitment range. |
Use EVM to measure cost and schedule performance against the baseline and forecast final cost.
| Formula | Definition | When to use |
|---|---|---|
| Cost Variance (CV) | CV = EV − AC | Positive = under budget. Negative = over budget. |
| Schedule Variance (SV) | SV = EV − PV | Positive = ahead of schedule. Negative = behind. |
| Cost Performance Index (CPI) | CPI = EV / AC | ≥ 1 is good. 0.9 means you get 90¢ of work per $1 spent. |
| Schedule Performance Index (SPI) | SPI = EV / PV | ≥ 1 means on or ahead of schedule. |
| EAC — typical | EAC = BAC / CPI | Assume current cost performance continues. |
| EAC — atypical | EAC = AC + (BAC − EV) | Assume the variance was a one-time event. |
| EAC — combined | EAC = AC + (BAC − EV) / (CPI × SPI) | Assume both cost and schedule pressure continue. |
| Estimate to Complete (ETC) | ETC = EAC − AC | Money still required to finish the project. |
| Variance at Completion (VAC) | VAC = BAC − EAC | Positive = expected to finish under budget. |
| TCPI (to BAC) | TCPI = (BAC − EV) / (BAC − AC) | Cost efficiency needed on remaining work to hit the original budget. |
Use EMV in quantitative risk analysis to size contingency reserves.
| Formula | Definition | When to use |
|---|---|---|
| EMV per risk | EMV = Probability × Impact | Threats are negative impact, opportunities positive. |
| Total EMV | Σ EMVᵢ | Portfolio value of all identified risks. |
| Contingency Reserve | Σ |EMV of threats| | Recommended reserve for identified negative risks. |
Use financial metrics to justify projects and compare investment options.
| Formula | Definition | When to use |
|---|---|---|
| Return on Investment (ROI) | ROI = (Gain − Cost) / Cost | Simple profitability measure, expressed as a percentage. |
| Net Present Value (NPV) | NPV = Σ CFₜ / (1 + r)ᵗ | > 0 means the project creates value at the given discount rate. |
| Payback Period | Time until cumulative CF ≥ 0 | How long to recover the initial investment. Shorter is safer. |
| Internal Rate of Return (IRR) | Rate r where NPV = 0 | Compare against the required rate of return; higher IRR is better. |
| Benefit-Cost Ratio (BCR) | BCR = PV(benefits) / PV(costs) | > 1 means benefits exceed costs. Higher BCR = better return. |
Common formulas for communication planning, scheduling, and agile forecasting.
| Formula | Definition | When to use |
|---|---|---|
| Communication Channels | n × (n − 1) / 2 | Number of one-to-one channels among n stakeholders. |
| Critical Path — Slack | Slack = LS − ES = LF − EF | Tasks with zero slack define the critical path. |
| Burn Rate | Burn = Spent / Periods Elapsed | Average spend per period; divide remaining budget by burn for runway. |
| Runway | Runway = Remaining Budget / Burn | How many periods the remaining budget will last at current spend. |
| Agile Sprints Remaining | Sprints = ⌈Backlog / Velocity⌉ | Estimate sprints to clear the backlog at current team velocity. |
| Agile Weeks Remaining | Weeks = Sprints × Sprint Length | Convert sprint count into a calendar forecast. |