Shashank Shastri
When I first sat down to prepare for the PMP, I remember opening a forum thread that listed forty-something formulas and feeling a brief wave of panic. I had a master's degree, I had run programmes for years, and yet someone on the internet had convinced me that the exam was going to be a calculus quiz. It is not. The PMP is mostly situational, mostly behavioural, and mostly about how you think as a project manager. But the math is still there, and on a four-hour exam where every question matters, knowing your formulas cold can be the difference between target and above-target.
PMP Formulas Cheat Sheet 2026: All the Math You Actually Need
I have coached hundreds of PMP candidates over the years, and I keep coming back to the same observation: the people who fail the math section have not usually failed at calculation. They have failed at recognition. They could not tell, in twelve seconds, whether a question was asking for SPI or CPI, EAC or ETC, or what the difference was between PERT mean and standard deviation. This cheat sheet is built to fix that. I have grouped the formulas by domain, walked through worked examples for every one that tends to trip people up, and added the memory tricks I use in my own bootcamps.
If you read this once and bookmark it, you will already be ahead of most of the room on exam day. Read it twice and practise the worked examples, and the math becomes the easy part of your test.
How the PMP Tests Math in 2026
In my experience coaching candidates through the post-2021 ECO, calculation-heavy questions are no longer the majority of the exam. Of the 180 questions you will see, somewhere between 8 and 15 typically involve direct computation. The rest are situational. But here is the thing nobody tells you: roughly another 20 to 30 questions reference math concepts even when they do not ask you to calculate. A question might tell you the CPI is 0.85 and ask what you should do next. If you do not instantly know that CPI below 1 means over budget, you are guessing.
That is why I tell every cohort to treat formulas as recognition tools first and calculation tools second. You should be able to look at any of the formulas below and know, within five seconds, what it is for and what direction "good" looks like. The calculation itself is easy if you set it up correctly. Setup is where points are lost.
The other thing worth noting: PMI gives you a basic on-screen calculator. You will not need anything beyond addition, subtraction, multiplication, division, and parentheses. There is no algebra to rearrange, no integrals to compute. If your formula needs a graphing calculator, you are using the wrong formula.
The Earned Value Family: PV, EV, AC
Earned Value Management (EVM) is the single biggest source of math on the PMP. Get these three core values right and everything else follows.
| Term | Full Name | What It Means |
|---|---|---|
| PV | Planned Value | Budgeted cost of work that should have been done by now |
| EV | Earned Value | Budgeted cost of work actually completed |
| AC | Actual Cost | What you actually spent on the work completed |
The formula for EV is the one most people get wrong:
EV = % complete x BAC (Budget at Completion)
So if your project has a BAC of GBP 100,000 and you are 40% complete, your EV is GBP 40,000. Simple, but only if you know what BAC is.
Worked example: You are running a six-month project with a total budget of GBP 120,000. At the end of month three, you should be 50% complete (PV = 60,000), but you are only 40% complete (EV = 48,000), and you have spent 55,000 (AC). With these three numbers, you can answer almost any earned value question on the exam.
In my bootcamps, I make people memorise this rule: every EVM question starts by identifying PV, EV, and AC. If you cannot list those three numbers from the question stem, you cannot solve it. Pause, re-read, and list them before you do any other calculation.
Variances and Indices: SV, CV, SPI, CPI
Once you have PV, EV, and AC, you can calculate the four most-tested derivatives in five seconds each.
- Schedule Variance (SV) = EV - PV
- Cost Variance (CV) = EV - AC
- Schedule Performance Index (SPI) = EV / PV
- Cost Performance Index (CPI) = EV / AC
The interpretation rule is the same for all four: positive variance or index above 1 is good, negative variance or index below 1 is bad. The memory trick I teach is "EV is always first." If you start every formula with EV, you will never get the sign wrong.
Using our previous example (PV 60,000, EV 48,000, AC 55,000):
- SV = 48,000 - 60,000 = -12,000 (behind schedule by 12,000)
- CV = 48,000 - 55,000 = -7,000 (over budget by 7,000)
- SPI = 48,000 / 60,000 = 0.80 (working at 80% of planned pace)
- CPI = 48,000 / 55,000 = 0.87 (getting 87 pence of value per pound spent)
I tell candidates that if they see any of these four numbers in a question and cannot instantly say "ahead/behind, over/under," they need another lap of EVM practice before exam day.
Forecasting: EAC, ETC, VAC, TCPI
This is where most candidates lose points, because there are four different EAC formulas and the question stem tells you which to use - if you know how to read it.
| Formula | When to Use |
|---|---|
| EAC = BAC / CPI | Current cost variances are expected to continue at the same rate. |
| EAC = AC + (BAC − EV) | Current cost variance is atypical; the remaining work will proceed according to the original plan. |
| EAC = AC + Bottom-up ETC | The original estimate is no longer valid; re-estimate all remaining work from scratch. |
| EAC = AC + (BAC−EV)/(CPI×SPI)(BAC − EV) / (CPI × SPI)(BAC−EV)/(CPI×SPI) | Both current cost and schedule performance are expected to continue for the remainder of the project. |
The keyword decoder I use:
- "Typical" or "continue at the same rate" - use BAC / CPI
- "Atypical" or "one-off variance" - use AC + (BAC - EV)
- "Re-estimate" or "original assumptions no longer hold" - bottom-up
- "Both schedule and cost matter going forward" - use the CPI x SPI version
Then:
- Estimate to Complete (ETC) = EAC - AC (what is left to spend)
- Variance at Completion (VAC) = BAC - EAC (how much under or over you will end up)
- To-Complete Performance Index (TCPI) = (BAC - EV) / (BAC - AC) if you still trust BAC
- TCPI = (BAC - EV) / (EAC - AC) if you have abandoned BAC and are working to EAC
TCPI tells you what CPI you need to hit from this point forward to land on budget. If TCPI is 1.15, you need to be 15% more efficient than planned for every remaining pound. If TCPI is over 1.10 in real life, I tell sponsors the budget is in trouble.
Communication Channels Formula
The most over-tested two-second formula on the exam:
Communication Channels = n(n - 1) / 2
Where n is the number of stakeholders or people involved. The catch the exam loves: it will ask you the difference when one or more people join. Always compute both numbers and subtract.
Worked example: A project starts with 5 stakeholders. Three more are added. How many additional channels?
- Before: 5(4) / 2 = 10 channels
- After: 8(7) / 2 = 28 channels
- Additional: 28 - 10 = 18
I have watched candidates compute 28 and tick that as the answer. Read the question. "Additional" and "total" are not the same word.
Also: some exam questions include the project manager in the count and some do not. If the question says "the PM has 5 team members," that is 6 people total. If it says "5 stakeholders including the PM," that is 5. Read it literally.
PERT and Three-Point Estimating
PERT (Program Evaluation and Review Technique) is a weighted average of three estimates: optimistic (O), most likely (M), and pessimistic (P).
PERT (Beta) = (O + 4M + P) / 6
Triangular = (O + M + P) / 3
The exam will tell you which distribution to use. If it does not specify but mentions "PERT" or "beta," use the weighted formula. If it just says "three-point estimate" without naming the distribution, the triangular average is the safer default.
Worked example: O = 8 days, M = 10 days, P = 18 days.
- PERT = (8 + 40 + 18) / 6 = 66 / 6 = 11 days
- Triangular = (8 + 10 + 18) / 3 = 12 days
Notice the PERT value is closer to "most likely" because of the x4 weighting, while triangular gives all three equal weight. This is exactly what the exam will test.
The reason PMI loves PERT: it dampens optimistic and pessimistic outliers. In my own programme estimating, I still use a variation of this for any task with high uncertainty. It is one of the few PMP formulas I use weekly in real work.
Standard Deviation, Variance, and Range
These three appear in maybe one or two exam questions, but they are gimmes if you know them.
Standard Deviation = (P - O) / 6
Variance = ((P - O) / 6)^2
Range = PERT mean +/- standard deviation (for the requested confidence interval)
The confidence intervals you need to remember:
| Confidence Level | Range |
|---|---|
| 68.26% (±1 Sigma) | Mean ± 1 Standard Deviation (SD) |
| 95.46% (±2 Sigma) | Mean ± 2 Standard Deviations (SD) |
| 99.73% (±3 Sigma) | Mean ± 3 Standard Deviations (SD) |
Worked example using O=8, M=10, P=18:
- PERT mean = 11
- SD = (18 - 8) / 6 = 1.67
- 95.46% range = 11 +/- 3.33 = 7.67 to 14.33 days
If a question asks "what is the range of duration we can be 95% confident in," that is what they want.
Float, Slack, and Critical Path Math
Float (sometimes called slack) is the time an activity can slip without delaying the project.
Total Float = LS - ES = LF - EF
Free Float = ES of next activity - EF of current activity - 1 (if you are using a day-based schedule with start-of-day numbering)
Critical path activities have zero total float. If a question asks "which activity is on the critical path," you are looking for the one with zero float.
The PMP loves to test this with a network diagram. The fastest method:
- 1. Forward pass: compute ES and EF for each activity, taking the maximum EF when paths converge.
- 2. Backward pass: compute LS and LF, taking the minimum LS when paths diverge.
- 3. Float = LS - ES (or LF - EF) for each activity.
- 4. The path with all zeros is critical.
I drill this with my cohorts using a five-node diagram until they can do it in 90 seconds. Anything longer and you will run out of time.
Negative float is also possible: if a constraint forces an LF that is earlier than the EF, you have negative float, meaning the project is already late against its target.
Beta vs Triangular Distribution
I get asked about this constantly. The short answer:
- Beta (PERT) distribution weights the most likely estimate four times. Use when the project has historical data or expert judgement that makes the "most likely" estimate genuinely most likely.
- Triangular distribution weights all three points equally. Use when you have no basis to favour one estimate over the others.
The exam will sometimes ask "which distribution gives a higher estimate?" The answer depends on the gap between M and the other two points. If P is much further from M than O is, triangular gives a higher estimate because PERT pulls toward M. If O is much further from M than P is, the same is true.
In real practice, I tell teams to use PERT for activities they have done before and triangular for first-time work. The exam does not ask you that subtlety, but it informs the kinds of questions PMI writes.
Financial Formulas: NPV, IRR, ROI, Payback
You will see one or two of these in selection-criteria questions early in the exam, usually framed as "which project should the organisation pick?"
Net Present Value (NPV): Sum of discounted future cash flows minus initial investment. You do not need to calculate NPV on the exam - PMI gives it to you. You need the rule: higher NPV is better. Positive NPV means the project is worth doing.
Internal Rate of Return (IRR): The discount rate at which NPV equals zero. Higher IRR is better. Again, PMI gives you the number; you choose the higher one.
Return on Investment (ROI):
ROI = (Benefit - Cost) / Cost x 100%
Payback Period: The time it takes to recover the initial investment. Shorter is better, but payback does not account for the time value of money or anything after payback.
The cheat sheet rule:
| Metric | Better When |
|---|---|
| NPV (Net Present Value) | Higher (Positive) |
| IRR (Internal Rate of Return) | Higher |
| ROI (Return on Investment) | Higher |
| Payback Period | Shorter |
| BCR (Benefit-Cost Ratio) | Higher (Greater than 1) |
If a question gives you four projects with different metrics, choose the one with the best value on the metric named. Do not overthink it.
Expected Monetary Value (EMV) and Decision Trees
EMV is risk management math:
EMV = Probability x Impact
For multiple outcomes, sum the EMVs. EMV is positive for opportunities and negative for threats.
Worked example: A risk has a 40% probability of costing GBP 50,000. Its EMV is 0.40 x -50,000 = -20,000. That is the amount you should be willing to spend now to fully mitigate the risk.
Decision trees combine multiple EMVs at branching choices. The exam might show a diagram with two paths:
- Path A: 60% chance of +GBP 100,000, 40% chance of -GBP 30,000. EMV = 60,000 - 12,000 = +48,000
- Path B: 80% chance of +GBP 40,000, 20% chance of -GBP 20,000. EMV = 32,000 - 4,000 = +28,000
You pick Path A because its EMV is higher. The trick the exam plays: it sometimes asks "what is the value of the decision," not "which path do you pick." Read the question.
Point of Total Assumption (PTA)
PTA appears in Fixed-Price Incentive Fee (FPIF) contract questions. Above the PTA, the seller bears 100% of any cost overrun.
PTA = ((Ceiling Price - Target Price) / Buyer's Share Ratio) + Target Cost
Worked example: Target cost = GBP 100,000. Target fee = GBP 10,000. Ceiling price = GBP 130,000. Buyer/seller share ratio = 70/30.
- (130,000 - 110,000) / 0.70 + 100,000 = 28,571 + 100,000 = 128,571
So if actual cost reaches GBP 128,571, the buyer's cost contribution caps out, and the seller absorbs everything above that.
You will see at most one PTA question. Know the formula, know which number is the buyer's share, and move on.
Procurement and Contract Math
Beyond PTA, a few procurement formulas occasionally appear:
Savings = Target Price - Actual Price
Sharing Ratio = Buyer Share / Seller Share (e.g., 80/20)
Incentive Fee = (Target Cost - Actual Cost) x Seller Share + Target Fee
Worked example: Target cost GBP 100,000, actual cost GBP 90,000, target fee GBP 10,000, sharing ratio 80/20.
- Underrun = 10,000
- Seller share = 10,000 x 0.20 = 2,000
- Total fee = 10,000 + 2,000 = 12,000
- Total payment to seller = 90,000 + 12,000 = 102,000
I rarely see more than one of these on a single exam, but the formulas are short and worth memorising.
Memory Tricks I Actually Use
Here are the mnemonics I have given to every cohort I have taught:
- "EV is always first." Every EVM formula either starts with EV or has EV in the numerator. If you start with EV, you cannot accidentally reverse a sign.
- "Plan minus actual is variance; plan over actual is index." Variance is subtraction, index is division. The order matters: schedule numbers vs cost numbers stay in the same position.
- "Four-M-six is PERT, three is triangular." (4M)/6 rhythm vs /3.
- "Channels: n times n-minus-one over two, always." Say it like a chant.
- "Higher NPV/IRR/ROI/BCR, lower payback." One rule for all selection criteria.
- "EMV is bad news with a number on it." Threats produce negative EMV, opportunities produce positive.
- "Zero float means critical." Nothing else does.
- "TCPI above 1.1 means you are praying." I added that one myself.
I have my candidates write all of these on a single index card during the first day of class. By exam day they do not need the card.
Worked Mini-Exam: Ten Math Questions
Time yourself: ten minutes total.
- 1. PV 50,000, EV 45,000, AC 48,000. What is CPI? (Answer: 0.94)
- 2. BAC 200,000, CPI 0.80. What is EAC if variances are typical? (Answer: 250,000)
- 3. A team grows from 6 to 10 people. How many additional channels? (Answer: 30)
- 4. O=6, M=12, P=24. What is PERT mean? (Answer: 13)
- 5. Same numbers. What is standard deviation? (Answer: 3)
- 6. Same. What is the 95.46% range? (Answer: 7 to 19)
- 7. EV 30,000, PV 35,000. What is SV? (Answer: -5,000)
- 8. Two projects: NPV 50K vs NPV 80K. Which do you pick? (Answer: 80K)
- 9. A risk has 25% probability of costing GBP 40,000. What is EMV? (Answer: -10,000)
- 10. BAC 100K, EV 60K, AC 70K. What is TCPI to original BAC? (Answer: 1.33)
If you got eight or more in under ten minutes, you are ready. If not, run through the worked examples in sections 2 through 12 again before moving on.
Shashank Shastri is a PMP trainer with over 14 years of experience and co-founder of Oven Story. He is an inspiring product leader who is a master in product strategies and digital innovation. Shashank has guided many aspirants preparing for the PMP examination thereby assisting them to achieve their PMP certification. For leisure, he writes short stories and is currently working on a feature-film script, Migraine.
Questions people ask
Published