PMP Formulas Cheat Sheet 2026: Every Formula Mapped to the New ECO

Quick Answer: The PMP exam draws its math from seven formula families: earned value, forecasting, schedule network analysis, communication channels, contracts and procurement, financial analysis, and risk. That is roughly 25 to 30 individual formulas, not hundreds. Formula questions sit mostly inside the Process domain, 41% of the exam and PMI's largest single domain, with financial and benefits math appearing in Business Environment (26%). Every formula below comes with a worked example so you can see which numbers go where.

How to Use This Sheet

Reading a formula is not the same as using it. For every family below, the worked examples use the same small project so you can see how the numbers connect. Here is the project:

Budget at Completion (BAC) = $200,000
Planned Value (PV) at month 4 = $80,000
Work actually completed = 30% of scope
Actual Cost (AC) at month 4 = $75,000

Keep those four numbers in mind. Every earned value and forecasting example below uses them.

Earned Value Formulas

Three inputs feed every EVM calculation: Planned Value (PV, the budgeted value of the work scheduled by now), Earned Value (EV, the budgeted value of the work actually completed), and Actual Cost (AC, what you actually spent).

Earned Value from percent complete, the step many candidates forget:

EV = % complete x BAC
EV = 0.30 x $200,000 = $60,000

Cost Variance (CV), positive means under budget:

CV = EV - AC
CV = $60,000 - $75,000 = -$15,000  (over budget)

Schedule Variance (SV), positive means ahead of schedule:

SV = EV - PV
SV = $60,000 - $80,000 = -$20,000  (behind schedule)

Cost Performance Index (CPI), above 1.0 means you are getting more value than you are paying for:

CPI = EV / AC
CPI = $60,000 / $75,000 = 0.80  (each dollar spent earns 80 cents of value)

Schedule Performance Index (SPI), above 1.0 means ahead of plan:

SPI = EV / PV
SPI = $60,000 / $80,000 = 0.75  (progressing at 75% of the planned rate)

Memory anchor: variances subtract and give a dollar amount; indexes divide and give a ratio. EV always comes first. If a question gives you percent complete instead of EV, convert it first.

Forecasting Formulas

Estimate at Completion (EAC) has three common versions. The question tells you which one to use through the assumption it describes. Applying the wrong one is the single most common formula mistake.

Typical:   EAC = BAC / CPI = 200,000 / 0.80 = 250,000
Atypical:  EAC = AC + (BAC - EV) = 75,000 + 140,000 = 215,000
Combined:  EAC = AC + (BAC - EV) / (CPI x SPI)
                = 75,000 + 140,000 / (0.80 x 0.75)
                = 75,000 + 233,333 = 308,333

Estimate to Complete (ETC), what is left to spend:

ETC = EAC - AC
ETC = 250,000 - 75,000 = 175,000   (using the typical EAC)

Two shortcuts you may also see: if the variance was atypical, ETC = BAC - EV; if current performance continues, ETC = (BAC - EV) / CPI. Both give the same answer as EAC - AC for their matching EAC.

Variance at Completion (VAC), projected overrun or underrun:

VAC = BAC - EAC
VAC = 200,000 - 250,000 = -50,000   (projected $50,000 overrun)

To-Complete Performance Index (TCPI), the efficiency you must achieve on the remaining work:

To hit the original budget:  TCPI = (BAC - EV) / (BAC - AC)
                                  = 140,000 / 125,000 = 1.12
To hit the revised forecast: TCPI = (BAC - EV) / (EAC - AC)
                                  = 140,000 / 175,000 = 0.80

Reading the result: a TCPI of 1.12 means every remaining dollar must earn $1.12 of value, which is harder than the 0.80 you have managed so far. A TCPI well above your current CPI signals that the original budget is probably unrealistic. Notice that the TCPI against the typical EAC equals the current CPI, which is a useful sanity check.

Schedule and Network Formulas

Three-point estimate (PERT), a weighted average that leans toward the most likely value. O is optimistic, M is most likely, P is pessimistic:

E = (O + 4M + P) / 6
O = 10, M = 14, P = 24 days
E = (10 + 56 + 24) / 6 = 15 days

Triangular estimate, the simple average, used when no weighting is specified:

E = (O + M + P) / 3 = (10 + 14 + 24) / 3 = 16 days

Standard deviation and variance, the uncertainty around the PERT estimate:

SD = (P - O) / 6 = (24 - 10) / 6 = 2.33 days
Variance = SD squared = 5.44

Confidence ranges, the normal-distribution rule of thumb:

Float and the critical path. Consider four activities: A (3 days) leads to both B (5 days) and C (4 days), and both B and C lead to D (2 days). Using a forward pass starting at day 0:

Path A-B-D = 3 + 5 + 2 = 10 days  (critical path)
Path A-C-D = 3 + 4 + 2 =  9 days
Total Float of C = LS - ES  =  (late start) - (early start) = 1 day
Free Float of C  = ES(D) - EF(C) = 8 - 7 = 1 day

Critical path activities have zero total float. Negative float means the schedule is already behind and needs compression. Be careful with numbering conventions: if a question counts the first day as day 1, free float is ES(next) - EF(current) - 1. Follow the convention the question uses.

Communication Channels Formula

Channels = n(n - 1) / 2
10 people: 10 x 9 / 2 = 45 channels
15 people: 15 x 14 / 2 = 105 channels

Adding 5 people more than doubles the channels. The exam uses this to test whether you recognize that communication complexity grows quadratically with team size. Count everyone who communicates, including the project manager, unless the question says otherwise.

Contract and Procurement Formulas

These appear less often, but candidates who skip them lose easy points. Both use the same project: a fixed-price or cost-plus contract with a target cost of $100,000, a target fee of $10,000, and an 80/20 share ratio (buyer 80%, seller 20%).

Point of Total Assumption (PTA), used with fixed-price incentive fee contracts. It is the actual cost above which the seller absorbs every further dollar of overrun:

PTA = (Ceiling Price - Target Price) / Buyer's Share + Target Cost
Target Price = 100,000 + 10,000 = 110,000;  Ceiling Price = 120,000
PTA = (120,000 - 110,000) / 0.80 + 100,000 = 12,500 + 100,000 = 112,500

Check: at an actual cost of 112,500 the overrun is 12,500, the buyer pays 80% of it (10,000), and the price reaches the 120,000 ceiling. Past that point, the seller is on the hook for everything.

Cost Plus Incentive Fee (CPIF) total payment. The buyer reimburses actual costs, pays the fee, and the seller gets its share of any savings (or loses its share of any overrun):

Total paid = Actual Cost + Target Fee + Seller's Share x (Target Cost - Actual Cost)
If actual cost = 90,000:  90,000 + 10,000 + 0.20 x (100,000 - 90,000) = 102,000

Check: the buyer pays 102,000 against a target of 110,000, saving 8,000, which is exactly 80% of the 10,000 saved. If the actual cost had been 110,000, the last term would be negative (-2,000), reducing the seller's fee.

Financial and ROI Formulas

These show up in Business Environment scenarios about project selection and benefits. The same example investment runs through all of them: $100,000 spent today, returning $40,000 a year for three years, with a 10% discount rate.

Return on Investment (ROI):

ROI = Net Profit / Investment  (as a percentage)
Net profit = 120,000 - 100,000 = 20,000;  ROI = 20,000 / 100,000 = 20%

Payback Period, ignores the time value of money:

Payback = Investment / Annual Cash Inflow = 100,000 / 40,000 = 2.5 years

Present Value (PV) and Future Value (FV):

PV = FV / (1 + r)^n        e.g. $10,000 in 3 years at 5%: 10,000 / 1.157625 = $8,638
FV = PV x (1 + r)^n        e.g. $10,000 today at 5% for 3 years: $11,576

Net Present Value (NPV), the sum of discounted cash flows minus the investment:

NPV = Sum[ Cash Flow(t) / (1 + r)^t ] - Initial Investment
Year 1: 40,000 / 1.10   = 36,364
Year 2: 40,000 / 1.21   = 33,058
Year 3: 40,000 / 1.331  = 30,053
Total present value    = 99,474
NPV = 99,474 - 100,000 = -526

This is a deliberately instructive example. The project looks profitable (ROI of 20%, payback in 2.5 years) but its NPV is slightly negative at a 10% discount rate, so it does not clear the cost of capital. A positive NPV means pursue; a negative NPV means reject, all else equal.

Internal Rate of Return (IRR) is the discount rate at which NPV equals zero. For this project it is about 9.7%, just below the 10% hurdle. You will not compute it by hand; know that a higher IRR is preferred and that it is compared against a hurdle rate.

Benefit-Cost Ratio (BCR), above 1.0 means benefits exceed costs:

BCR = Benefits / Costs = 360,000 / 300,000 = 1.2

Risk Formula

Expected Monetary Value (EMV), the probability-weighted outcome, used to rank risks and to choose between branches in a decision tree:

EMV = Probability x Impact
A 20% chance of a $50,000 loss: EMV = -$10,000

For a decision with several outcomes, sum the EMV of each branch, then compare options:

Option A: 60% chance of +50,000 and 40% chance of -20,000
  EMV(A) = 0.60 x 50,000 + 0.40 x (-20,000) = 30,000 - 8,000 = +22,000
Option B: guaranteed +15,000
  EMV(B) = +15,000
Choose A, since 22,000 > 15,000 (if the organization is risk-neutral).

Full Formula Reference Table

The domain column is our mapping of each formula to where it is most likely to appear; PMI does not publish a formula-by-domain list. The 2026 ECO does not use the old knowledge-area labels. Calculation-heavy formulas sit mostly inside the Process domain (41% of the exam), while financial and benefits formulas appear in Business Environment (26%).

The 8 Formula Traps That Cost Candidates Points

• Defaulting to BAC / CPI. Read the scenario for the assumption. "One-time" or "unusual" points to AC + (BAC - EV).
• Reversing the variance sign. EV always comes first: EV - AC and EV - PV. Negative means over budget or behind schedule.
• Mixing the TCPI denominators. BAC - AC for the original budget, EAC - AC for the revised forecast.
• Ignoring percent complete. EV is percent complete times BAC, never times AC.
• Confusing PERT and triangular. The 4M weighting and the divide-by-6 go together; the plain average divides by 3.
• Using target cost in CPIF. The buyer reimburses actual cost, then adds the fee and the share adjustment.
• Miscounting channels. Check whether the project manager is included in n.
• Trusting an attractive ROI. NPV accounts for the time value of money; a high ROI can still be a negative NPV.

Practice Questions With Worked Answers

These are original practice questions written by GSC in the style of the exam, not PMI items.

1. A project has a BAC of $500,000, EV of $200,000, and AC of $250,000. The overrun was caused by a one-time vendor penalty and the remaining work is expected to go to plan. What is the EAC?

The scenario says the variance was a one-time event, so use the atypical formula.

Answer: EAC = AC + (BAC - EV) = 250,000 + 300,000 = $550,000. (BAC / CPI would give $625,000, the tempting wrong answer.)

2. An activity has an optimistic estimate of 6 days, most likely 9 days, and pessimistic 18 days. Within what range is the duration 95% likely to fall?

First compute the PERT estimate and the standard deviation.

Answer: E = (6 + 36 + 18) / 6 = 10 days; SD = (18 - 6) / 6 = 2 days. 95% corresponds to plus or minus 2 SD, so 6 to 14 days.

3. A team grows from 8 to 12 members. How many additional communication channels does this create?

Compute channels before and after.

Answer: 8 people = 8 x 7 / 2 = 28; 12 people = 12 x 11 / 2 = 66. The increase is 38 channels.

4. On a fixed-price incentive fee contract, target cost is $100,000, target fee $10,000, ceiling price $120,000, and the share ratio is 80/20 (buyer/seller). At what actual cost does the seller begin absorbing all overruns?

That is the point of total assumption.

Answer: PTA = (120,000 - 110,000) / 0.80 + 100,000 = $112,500.

How to Memorize These Without Flashcard Fatigue

• Learn the earned value family as one story: plan, earn, spend. PV, EV, AC feed everything else.
• Rebuild the worked project from scratch twice, from a blank page, without looking.
• Say the assumption out loud before choosing an EAC formula.
• Write the formulas you miss on your brain sheet in the first minute of the exam, if your testing format allows a scratch aid.
• Do 10 mixed calculation questions a day for the last two weeks, and review every miss by naming which trap caught you.

Frequently Asked Questions

How many formulas do I actually need to know for the PMP exam?

Roughly 25 to 30 show up with any regularity, but most are variations on a few core ideas. Earned value alone produces more than a dozen formulas from one dataset.

Which EAC formula should I use?

It depends on the assumption the question states. BAC divided by CPI assumes current cost performance continues. AC plus the remaining budget assumes the variance was a one-time event. AC plus the remaining budget divided by CPI times SPI assumes both cost and schedule performance continue to affect the work.

Is PMP exam math still heavily tested after the 2026 ECO update?

Formula-based questions sit mostly inside the Process domain, which is 41% of the exam and PMI's largest single domain, so EVM and forecasting math remain a meaningful share of scored questions.

Is a calculator provided during the exam?

Yes. Study-prep sources report that an on-screen calculator is available in both test-center and online proctored formats, and personal calculators are not allowed. Confirm the current rule in PMI's exam-day guidance. You still need to know which formula applies and which inputs go where, which is the real skill being tested.

What is the most commonly missed formula category?

The EAC variants. Candidates default to BAC divided by CPI without checking whether the scenario describes a one-time variance or a situation where both cost and schedule performance matter.

Do I need to calculate IRR by hand?

No. IRR requires iterative trial and error. You need to understand what it represents and how to compare it to a hurdle rate or another project's IRR.

Related Reading

• PMP Certification Total Cost in 2026 
• PMBOK 8 Focus Areas Explained: What Happened to Process Groups
• PMP Domain Weightings 2026: What Changed and Why

Ready to Get Started?

A formula sheet tells you what to calculate. It does not tell you why a scenario calls for the atypical-variance EAC, or how to spot a PTA question dressed up as a procurement question. That judgment is what separates a memorized formula from an exam-day answer you can trust.

Gold Standard Certifications is a PMI Authorized Training Partner (ATP). Our 35-hour live PMP bootcamp is led by Stephen Mercer, PMP, a PMI ATP instructor with 10+ years of experience and 6,150+ professionals trained, and includes 2,000+ practice questions and mock exams, so every formula on this page is worked through in exam-style scenarios, not just memorized.

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