As you prepare for the PMP exam, some of the most important things you should know are the PMP formulas. Although, PMI does not give a specific breakdown on the number of formula questions you can expect, as a former tester, I can assure you, if you do not know these formulas, a magic 8-ball might warn, “Outlook Not So Good.”

Having a firm grasp on the PMP formulas themselves will serve you well, as there are a number of straightforward questions to assess your general understanding of the formulas. However, it is arguably more important to understand why you would use a formula and what each number represents.

Let’s take some time and review the most common PMP formula questions to study for the exam. We will break the formula down to understand the name, the actual formula, the terms used within that formula, an explanation of the answer, what knowledge area the formula is used for, and finally a sample question you can expect to see on the exam.

The answers to the formula questions can be found after the table.

## PMP Formulas to Study

Name | Formula | Terms | Explanation of Solution | Knowledge Area | Sample Question |
---|---|---|---|---|---|

Numbers of Communication Channels | n (n-1)/2 | n is the number of project members | The solution provides you the amount of communication channels your project has with a given number of project members. A quick hint, n includes the PM. | Communication Management | 1. Jerry recently took over a project after another project manager left. He needed to determine how many communication channels existed to ensure he was effectively reaching all his stakeholders. Looking through his stakeholder registry and removing the prior PMP, the project has 43 members. How many communication channels exist? |

Pert Estimation (aka Beta Distribution) | E= (O+4M+P)/6 | E is the best estimate of the time it will take to complete a task O is the optimistic estimate M is the most likely estimate P is the pessimistic estimate. | The solution provides you the best estimate on how long a task will take to complete. Hint: Pert or beta is the most common estimation formula, as it is more exact. Additionally, this could also be referred to as weighted estimation. | Time Management | 2. If the task has an estimate of 13 days, an optimistic estimate of 10 days, and a pessimistic estimate of 20 days. What is the weighted estimate to complete this task? |

Triangular Estimation | E= (O+M+P)/3 | E is the best estimate of the time it will take to complete a task O is the optimistic estimate M is the most likely estimate P is the pessimistic estimate. | The solution provides you the best estimate on how long a task will take to complete. Hint: On the exam this formula could also be referred to as straight estimation. | Time Management | 3. If the task has an estimate of 6 days, an optimistic estimate of 4 days, and a pessimistic estimate of 10 days. What is the straight estimate to complete this task? |

Standard Deviation | (P-O)/6 | P is the pessimistic estimate O is the optimistic estimate | This formula helps you determine the possible range an activity could take. Once you determine the standard deviation, add it and subtract it from the estimated duration you found using Pert or Triangular estimation. This will give you the range in activity. | Time Management | 4. If the task has an optimistic estimate of 7 days and a pessimistic estimate of 15 days, what is the standard deviation of the task? |

Cost Variance | CV=EV-AC | EV is earned value, or the actual value of the work completed to a certain point in a project AC is the actual cost, or the actual amount spent to a certain point in a project. | CV, cost variance, helps you determine the difference in the actual cost to date to what work is complete to date. If CV 0, the project is within budget In the simplest of terms, if CV 0, things are good! | Cost Management | 5. If planned value is 400, earned value is 350, and actual cost is 450, what is the cost variance? |

Schedule Variance | SV=EV-PV | EV is earned value, or the actual value of the work completed to a certain point in a project. PV is planned value, or the budgeted value of the work at a certain point in a project. | SV, schedule variance, helps you determine the difference in the actual work completed for the project from what was planned. If SV 0, the project is ahead of schedule In the simplest of terms, if SV 0, things are good! | Cost Management | 6. If planned value is 500, earned value is 575, and actual cost is 450, what is the schedule variance? |

Cost Performance Index | CPI= EV/AC | EV is earned value, or the actual value of the work completed to a certain point in a project AC is the actual cost, or the actual amount spent to a certain point in a project. | CPI, or cost performance index helps you determine the amount of work you are getting based on the money spent. If CPI 1, the project is within budget In the simplest of terms, if CPI 1, things are good! | Cost Management | 7. If planned value is 500, earned value is 575, and actual cost is 450, what is the cost performance index? |

Schedule Performance Index | SPI= EV/PV | EV is earned value, or the actual value of the work completed to a certain point in a project EV is earned value, or the actual value of the work completed to a certain point in a project. PV is planned value, or the budgeted value of the work at a certain point in a project. | SPI, or schedule performance index helps you determine the percentage of work complete based on the planned work rate. If SPI 1, the project is ahead of schedule. In the simplest of terms, if SPI 1, things are good! | Cost Management | 8. If planned value is 400, earned value is 350, and actual cost is 450, what is the cost variance? |

Estimate at Completion (EAC) (There are four variations of this formula based on what the question asks for. This is why it is important to understand what the numbers mean.) | 1. AC + Bottoms - up ETC 2. BAC/CPI 3. AC + (BAC - EV) 4. AC + (BAC - EV)/ (CPI x SPI) | AC is the actual cost, or the actual amount spent to a certain point in a project. EV is earned value, or the actual value of the work completed to a certain point in a project. ETC is the estimate to completion, or how much more money the project will cost to complete. BAC is budget at completion, or what was budgeted for the entire project at completion. CPI is the cost performance index, or the evaluation of work completed for the money spent. SPI is the schedule performance index, or the evaluation of work completed to work planned. | EAC, or estimate at completion helps you determine from this date forward how much you can expect the project to cost at completion. The word “at” is very important for this formula! Let’s discuss why you would use these four formulas to assess this estimate. Formula 1 uses the actual cost to date and adds the new estimated cost to completion. You would use this formula if there was a flaw in the original estimate. Formula 2 is used if the project is on target, tracking to the budget at completion and there are no variations in rate of spending expected. Formula 3 is used when there have been atypical differences in the actual cost of the project, but those differences are believed to be corrected and the remaining expenditures should be inline with what was budgeted Formula 4 is used if there are differences in the project that are expected to continue. The main difference with this formula and formula 2 is the project schedule is critical and must be met, so all expenses will need to be flexible to meet the deadline. | Cost Management | Let’s test if you can pick the right formula with these two examples: 9. In your current project the planned value is 400, earned value is 350, and actual cost is 450. Based on the work effort needed to date the team determined the original $1000 estimate is no longer valid. A reestimate of the remaining tasks is 750. What is the current estimate at completion for this project? 10. In your current project the planned value is 400, earned value is 350, and actual cost is 450. The project budgeted 1,500 at completion. Considering the challenges experienced early in the project are resolved, what is the current estimate at completion? |

To-Complete Performance Index (TCPI) | (BAC-EV)/(BAC-AC) | AC is the actual cost, or the actual amount spent to a certain point in a project. EV is earned value, or the actual value of the work completed to a certain point in a project. BAC is budget at completion, or what was budgeted for the entire project at completion. | TCPI, or to-complete performance index helps you understand what pace the remaining tasks must be completed to keep the project within budget. TCPI 1, the project does not need to change speed to complete within budget. In the simplest terms, TCPI 1 things are good! | Cost Management | 11. The project was originally budgeted to spend $2,000. At this point your actual cost is 1,500 and 1,200 worth of work is complete. What is the TCPI for the project? |

Estimate to Complete (ETC) There are two ways to find ETC | EAC - AC Reestimate | EAC, or estimate at completion helps you determine from this date forward how much the project is expected to cost at completion. AC is the actual cost, or the actual amount spent to a certain point in a project. Reestimate, means just what the name implies, use the same strategies that you used during project planning to reestimate the cost of the work remaining. | ETC, or estimate to complete helps you understand the cost remaining to complete the project. | Cost Management | 12. Your project, with a budget at completion of $1,500, currently has a planned value of 400, earned value of 350, and actual cost of 450. The current work and all variances to date are expected to continue; based on this, what is the estimate to complete the project? |

Variance at Completion (VAC) | BAC - EAC | BAC is budget at completion, or what was budgeted for the entire project at completion. EAC, or estimate at completion helps you determine from this date forward how much you expect the project to cost at completion. | VAC, variance at completion is the difference in what the budgeted cost of the project was to what we now expect the project to cost. If VAC 0, the project is within budget In the simplest terms, VAC 0 things are good! | Cost Managment | 13. Your project, with a budget at completion of $1,500, currently has a planned value of 400, earned value of 350, and actual cost of 450. The current work and all variances to date are expected to continue; based on this, what is variance at completion? |

## PMP Formulas Answers

1. **There are 946 communication channels.** * Did you remember to add yourself back into the equation? Remember the PM is always included and you removed the other PM from the team member total.*

2. **The PERT estimate is 13.667.** Did you use the PERT formula? Remember weighted, beta, and PERT all mean the same thing.

3. **The Triangular estimate is 6.667.** *Did you use the triangular formula? Remember straight and triangular are the same thing. *

4. **The Standard Deviation is 3.667.** *Note, you might get some PMP exam questions that ask you to find the range. Don’t let these fool you. You’ll need to find both the estimate and the standard deviation.*

5. **The CV is -100.** *Considering this answer is this a good thing or a bad thing? Since CV is <0, the project is over budget – which is a bad thing.*

6. **The SV is 75.** *Considering this answer is this a good thing or a bad thing? Since SV is >0, the project is ahead of schedule – which is a good thing. *

7. **The CPI is 1.278. ***Considering this answer is this a good thing or a bad thing? Since CPI is >1, the project is tracking within budget – which is a good thing. *

8. **The SPI is 0.875** *Considering this answer is this a good thing or a bad thing? Since SPI is <1, the project is tracking off schedule and not getting as much work complete for the money spent – which is a bad thing.*

9. **The EAC is $1,200.** *Did you catch that the budget was no longer valid? This should have clued you into using formula one. The additional information you need was the new estimate to completion (ETC), which was 750.*

10.** The EAC is $1,600. ***Did you catch that the challenges are corrected? This should have clued you into using formula three. *

11. **The TCPI is 1.6.** *Did you realize when the question stated work complete of 1,200 that was the earned value of the project? Remember we need to quantify work and the easiest way is using a dollar amount. Considering the answer, is this a good thing or a bad thing? Since, TCPI is > 1, the project is tracking on pace and no adjustment is need – which is a good thing.*

12. **The ETC is $1,478.** *To find ETC you probably noticed that you first need to find EAC. Reading this question, the information that variances are expected to continue should have alerted you to use formula two for EAC. Finding out that EAC is $1,928 allowed you to then find ETC. *

13. **The VAC is -$428.** *This question used the same logic as above. You must first find EAC and with the variances continuing you knew to use formula two. Finding out that EAC is $1,928 allowed you to then find VAC. Considering the answer is this a good thing or a bad thing? Since VAC is <0, the project is overspending – which is a bad thing.*

## Final Thoughts on PMP Formulas Questions to Study

Overall this is a helpful overview of the PMP Formulas to expect on the exam.

However, if this is your first time through this blog, I would suggest spending some time reviewing the entire communication, cost, and time M=management knowledge areas. Once you review these areas and have a better grasp of why and when you use these formulas, let’s work through them again! I promise with a better understanding of what these numbers mean and why they are important, you will soar through your future attempts completing these formulas.

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hi, i did not understand, question 12, it says ” The current work and all variances to date are expected to continue; based on this, what is the estimate to complete the project? ”

hence shouldnt both CPI and SPI be considered, because it says ALL variances are expected to continue

Sonal, thank you for the thoughtful question. You could use formula 4 to find EAC for this question, which includes both CPI and SPI. The reason I did not in the example was because the question did not stress a need to stay on schedule. If you look at the explanation to use Formula 4 it notes that this choice is typically used when schedule is of critical importance. Knowing how to complete the equation both ways is helpful for the exam, specifically in case you don’t see the answer when you complete it with the first equation. Keep up this great critical thinking on exam day!

In question 8 the formula is for CPI but the Explanation of the Solution refers to SPI. Was this a mistake?

Daisy, thank you so much for this comment. You actually found a bigger problem then just a typo. Content from two rows in the table consolidated into one. The start of the row discussed CPI and the end of the row was referencing SPI. I have updated the table to include both CPI and SPI as they are both critical for the PMP exam. The questions and answers are now correct. Again, I greatly appreciate your great catch.

Can you help me understand the TCPI example? I am coming up with 0.8 from using the formula BAC – EV/BAC – AC – filled in with the information from the problem – 2000 – 1200 / 2000 – 1500.

Can you also help me understand the standard deviation problem? I am coming up with 1.333 days from using (15-7)/6 = 8/6 = 1.333.

Question 2 –

2. If the task has an estimate of 13 days, an optimistic estimate of 10 days, and a pessimistic estimate of 20 days. What is the weighted estimate to complete this task?

My query:

Here the M value is 13, P is 20 and O is 10

By putting this in formula – [20 + 10 + (4*13)]/6 = 12

Please let me know where I am wrong. My answer is not matching with the answer provided above for Question 2

Hi Shahab!

The formula is: E= (O + 4M + P)/6 and M = 13, O = 10, and P = 20.

Plugging this all in, we’ll get:

E = (10 + (4*13) + 20)/6

E = (30 + 52)/6

E = (82)/6

E = 13.667

It looks like you have the formula correct, so I’m not sure what error you’re making. Hope this helps!