PMP Formulas Cheat Sheet: What to Know for the Exam

The current PMP exam is not a math test. When a number appears, the harder part is usually deciding what it means and what the project manager should do next. Still, knowing a small set of formulas cold saves time and removes doubt.

Below, each formula gets a plain meaning and a one-line interpretation rule, followed by a master table. For earned value in depth, see Earned Value Management Explained.

Earned Value and Forecasting

PV is the budgeted value of work planned to date, EV the budgeted value of work actually done, AC the actual cost, and BAC the total budget.

Variances and indexes

CV = EV - AC (cost variance). Negative means over budget.
SV = EV - PV (schedule variance). Negative means behind schedule.
CPI = EV / AC (cost performance index). Below 1 means you get less than a dollar of work for each dollar spent.
SPI = EV / PV (schedule performance index). Below 1 means work is progressing slower than planned.

Interpretation rule: EV always comes first. Variance positive or index above 1 is good; negative or below 1 is bad.

Forecasts

EAC = BAC / CPI: current cost performance continues (the usual default).
EAC = AC + (BAC - EV): the variance was a one-off.
EAC = AC + (BAC - EV) / (CPI x SPI): cost and schedule both drive remaining work.
ETC = EAC - AC: remaining spend.
VAC = BAC - EAC: expected overrun (negative) or underrun.
TCPI = (BAC - EV) / (BAC - AC): CPI needed on remaining work to finish on budget.

Interpretation rule: a TCPI well above 1 means the original budget is unlikely to hold without corrective action or a revised baseline.

Mini-example

BAC = $100,000, PV = $50,000, EV = $40,000, AC = $50,000.

CV = 40,000 − 50,000 = −$10,000 (over budget)
SV = 40,000 − 50,000 = −$10,000 (behind schedule)
CPI = 40,000 / 50,000 = 0.80
SPI = 40,000 / 50,000 = 0.80
EAC = 100,000 / 0.80 = $125,000
ETC = 125,000 − 50,000 = $75,000
VAC = 100,000 − 125,000 = −$25,000
TCPI = (100,000 − 40,000) / (100,000 − 50,000) = 60,000 / 50,000 = 1.20

Reading it: the project earns 80 cents of value per dollar spent and has done only 80% of the planned work. Hitting the original budget needs a CPI of 1.20 from here, a big jump from 0.80. The PM should find root causes, report the forecast honestly, and pursue corrective action or a baseline change through change control.

Schedule: Critical Path, Float and Estimates

Float

Total float = LS - ES (or LF - EF): how long an activity can slip without delaying the project end date.
Free float = earliest ES among successors - EF of the activity: how long an activity can slip without delaying any successor. (Assumes day-0 start, so a 5-day activity starting at 0 has EF = 5.)
The critical path is the longest path through the network. It sets the shortest possible project duration, and its activities usually have zero total float.

Interpretation rule: zero float means any delay moves the end date; negative float means the schedule already misses its required date.

Mini-example: an activity has ES = 3, EF = 8, LS = 6, LF = 11. Total float = 6 − 3 = 3 days. If its only successor has ES = 10, free float = 10 − 8 = 2 days. A 2-day slip affects nobody; a 3-day slip delays the successor but not the project; a 4-day slip delays the project.

Three-point estimates (PERT and triangular)

PERT (beta) estimate = (O + 4M + P) / 6
Triangular estimate = (O + M + P) / 3
Standard deviation (beta) = (P - O) / 6

O is optimistic, M is most likely, P is pessimistic.

Interpretation rule: a wider spread between O and P means more uncertainty, so a larger standard deviation and a weaker commitment.

Mini-example: O = 4 days, M = 6 days, P = 14 days.

PERT = (4 + 24 + 14) / 6 = 42 / 6 = 7 days
Triangular = (4 + 6 + 14) / 3 = 24 / 3 = 8 days
Standard deviation = (14 − 4) / 6 = 1.67 days

Roughly 68% of outcomes fall within one standard deviation (about 5.3 to 8.7 days) and about 95% within two (about 3.7 to 10.3 days).

Communication Channels

Channels = n(n - 1) / 2, where n is the number of people, including the project manager.

Interpretation rule: channels grow much faster than headcount, so adding people adds communication complexity that the communications approach must cover.

Mini-example: a team of 8 has 8 × 7 / 2 = 28 channels. Grow to 12 and you have 12 × 11 / 2 = 66, an increase of 38. Watch for questions asking for the increase rather than the new total.

Risk: EMV and Decision Trees

EMV = Probability x Impact. Threats carry a negative impact, opportunities a positive one.

Interpretation rule: EMV is an average over many outcomes, not a prediction of what will happen once. Use it to compare options and size reserves.

Mini-example: a threat has a 30% chance of costing $50,000, so EMV = 0.30 × −50,000 = −$15,000. An opportunity has a 20% chance of saving $20,000, so EMV = 0.20 × 20,000 = +$4,000. Net EMV = −$11,000.

Decision trees

A decision tree applies EMV to each branch of a choice, then subtracts the cost of that choice.

Mini-example: you can build a component (cost $120,000) or buy it (cost $50,000). Demand is high with 60% probability and low with 40%.

Build: high demand returns $300,000, low returns $100,000. EMV = 0.6 × 300,000 + 0.4 × 100,000 = 180,000 + 40,000 = $220,000. Net = 220,000 − 120,000 = $100,000.
Buy: high demand returns $180,000, low returns $90,000. EMV = 0.6 × 180,000 + 0.4 × 90,000 = 108,000 + 36,000 = $144,000. Net = 144,000 − 50,000 = $94,000.

Interpretation rule: choose the branch with the best net EMV (highest value or lowest cost). Here, build wins by $6,000.

Project Selection: NPV, ROI, BCR, Payback and IRR

PV = FV / (1 + r)^n: today's value of future money at rate r over n periods.
NPV = sum of discounted inflows - initial investment: value created after accounting for the time value of money.
ROI = (Total benefit - Cost) / Cost: return as a percentage of cost. If the question already gives you net profit, ROI is simply net profit divided by cost.
BCR = Benefits / Costs: benefit received per unit of cost.
Payback period = Initial investment / Net cash inflow per period (for even cash flows): time to recover the investment.
IRR: the discount rate at which NPV equals zero. Concept only; higher is better.

Interpretation rules:

NPV: positive is acceptable, higher is better. The number of years is already built into NPV, so do not adjust for project length again.
ROI, BCR, IRR: higher is better. BCR above 1 means benefits exceed costs.
Payback: shorter is better, but it ignores later cash flows.
Ignore sunk costs. Opportunity cost is the value of the best option given up.

Mini-example (PV): $100,000 received in 3 years at 10%: 1.1 × 1.1 × 1.1 = 1.331, so PV = 100,000 / 1.331 = about $75,131.

Mini-example (payback): a $200,000 investment returning $50,000 per year pays back in 200,000 / 50,000 = 4 years.

Mini-example (BCR and ROI): benefits of $300,000 against costs of $200,000 give BCR = 1.5 and ROI = (300,000 − 200,000) / 200,000 = 50%.

Agile Metrics, Capacity and Flow

Velocity

Velocity = story points (or items) completed per iteration. Use an average over recent iterations.
Iterations remaining = remaining backlog / average velocity (round up).

Mini-example: the last three sprints delivered 30, 34 and 32 points, an average of 96 / 3 = 32. A remaining backlog of 192 points needs about 192 / 32 = 6 more sprints.

Interpretation rule: velocity is team-specific. Never compare velocity across teams or use it as a performance target.

Burndown and burnup charts

Burndown: remaining work over time. Above the ideal line means behind.
Burnup: completed work and total scope as separate lines, so scope growth stays visible.

Capacity and throughput

Capacity = people x available days x productive hours per day, adjusted for leave and other commitments.
Throughput = items completed per unit of time (Kanban).
Average cycle time = WIP / throughput (Little's Law).

Mini-example (capacity): 5 people, 10 working days, 6 productive hours each: 5 × 10 × 6 = 300 hours.

Mini-example (flow): 12 items in progress and a throughput of 4 items per week means an average cycle time of 12 / 4 = 3 weeks.

Master Reference Table

Formula	Expression	Good result	One-line rule
Cost variance	EV − AC	Positive	Negative means over budget
Schedule variance	EV − PV	Positive	Negative means behind schedule
CPI	EV ÷ AC	Above 1	Value earned per dollar spent
SPI	EV ÷ PV	Above 1	Rate of progress against plan
EAC (typical)	BAC ÷ CPI	At or below BAC	Default forecast if trends continue
EAC (atypical)	AC + (BAC − EV)	At or below BAC	Variance was a one-off
ETC	EAC − AC	Lower	Money still needed
VAC	BAC − EAC	Positive	Expected overrun or underrun at the end
TCPI	(BAC − EV) ÷ (BAC − AC)	At or below 1	Well above 1 means the budget is at risk
Total float	LS − ES or LF − EF	Zero or positive	Zero means critical, negative means late
Free float	ES of successor − EF	Positive	Slack before a successor is affected
PERT estimate	(O + 4M + P) ÷ 6	n/a	Weighted toward most likely
Standard deviation	(P − O) ÷ 6	Smaller	Wider spread means more uncertainty
Communication channels	n(n − 1) ÷ 2	n/a	Grows much faster than headcount
EMV	Probability × Impact	Higher (net)	Average outcome, used to compare and size reserves
NPV	Discounted inflows − investment	Positive, higher	Years already built in
ROI	(Benefit − Cost) ÷ Cost	Higher	Return as a share of cost
BCR	Benefits ÷ Costs	Above 1	Benefit per unit of cost
Payback period	Investment ÷ inflow per period	Shorter	Ignores later cash flows
IRR	Rate where NPV = 0	Higher	Concept only, no calculation
Velocity	Points completed per iteration	Stable	Forecasting tool, never a cross-team comparison
Cycle time	WIP ÷ throughput	Shorter	Limit WIP to improve flow

How Formula Questions Look on the Exam

Formula questions typically reward interpretation over arithmetic. Common patterns:

The number is given, the action is asked. "CPI is 0.85 and SPI is 1.10. What should the project manager do first?" Nothing to compute: the project is ahead of schedule but over budget, so pick the answer that investigates cost drivers through the proper process, not one that cuts scope unilaterally.
Pick the right forecast. Whether a variance was a one-off or a trend decides which EAC formula applies.
Compare options. Two projects with different NPVs, BCRs or payback periods. Know which direction is better and that NPV already accounts for duration.
Agile data in a situational wrapper. A flat burndown or falling velocity usually calls for the team to examine the cause together, not for pressure on individuals.
Distractors built from formula mistakes. Wrong answers often come from reversing EV and AC, forgetting to include the PM in communication channels, or using total float when the question asks about a successor.

A few habits help:

Translate the number into words: "CPI 0.85, so 85 cents of value per dollar."
Ask what the PM should do with it. A correct calculation paired with the wrong action is still wrong.
If a calculation drags, flag it and come back.

Quick Review

EV comes first in every variance and index (CV, SV, CPI, SPI). Positive variance and index above 1 are good.
Default EAC is BAC / CPI; TCPI well above 1 means the budget is at risk.
Total float protects the end date; free float protects the next activity.
PERT weights the most likely estimate; spread between O and P signals uncertainty.
Communication channels are n(n - 1) / 2, and n includes the PM.
EMV is probability times impact: threats negative, opportunities positive.
Higher NPV, ROI, BCR and IRR are better; shorter payback is better; sunk costs do not count.
Velocity forecasts one team's delivery; cycle time falls when WIP falls.
On the exam, the meaning of the number and the next action matter more than the arithmetic.