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# What are the PMP Formulas and What are the PMP Concepts?

Jan 11, 2022

What are the PMP Formulas and What are the PMP Concepts?

We use PMP formulas in various project planning activities. These include but not limited to resource management, cost management and schedule estimation. We also use them in risk estimation activities like EMV (earned value management), in addition to monitor and control activities. Therefore, in this article, we will cover the most important PMP formulas and provide you a PMP formulas cheat sheet.

On the other hand, PMP Concepts include a number of concepts that PMI regularly uses in PMP exams alongside the PMP formulas. PMI uses these concepts to test your understanding of basic project management terminology. These concepts include OPA, EEF and other similar concepts. We will cover them in PMP cheat sheet as well.

Why must you know PMP Formulas?

The percentage of questions which are based on PMP formulas range from 5% to 10%. This means there are around 10 to 20 questions, so it seems a pretty small portion right?! Then you need to rethink your exam strategy! Although the number seems small, PMP formulas are quick wins, because PMP formulas based questions vary from direct to complex. The fact that PMI doesn’t reveal the exact PMP exam passing score, proves the significance of these questions. You can contact us to get details about the PMP exam pass rate in our Institute.

15 PMP Formulas You Must Know

In this section of the post, we will go through the 15 PMP formulas you must know to answer PMP math questions correctly. Note that, these formulas will be under two headings:

A- ) Critical Path Method (CPM) Related PMP Formulas

B- ) Earned Value Management (EVM) PMP Formulas

Let’s go over them one-by-one and learn the details of each PMP formula.

A- ) Critical Path Method (CPM) related PMP formulas

The first set of PMP formulas we will provide are related to Critical path method.

PMP Formulas #1: PERT Distribution

There are two types of this PERT distribution: triangular and beta.

PERT Triangular Distribution

It’s one of the most important PMP formulas and we use it to calculate duration, cost and resources estimates. To calculate Estimated Activity Duration (EAD), you need to determine the activity Optimistic (O), Most Likely (M) and Pessimistic (P) estimates first. Then you can use PERT Triangular Distribution to estimate the activity duration. Accordingly, the PMP formula for PERT Triangular Distribution is as follows:

EAD = (𝑂 + 𝑀 + 𝑃)/3

PERT Beta Distribution

It’s one of the most important PMP formulas and we use it to calculate duration, cost and resources estimates. Similar to the previous formula, to calculate (EAD), you need to determine activity (O), (M) and (P) estimates first. Then you can use PERT Beta Distribution estimate the activity duration. Accordingly, the formula for PERT Beta Distribution is as follows:

Standard Deviation (SD) of an Activity

Standard Deviation (SD) measures the Variation from Average. As a result, a low value of SD indicates that the data points are close to the Average. On the other hand, a high value of SD indicates the spread out of data points over a large range. Accordingly, the formula for Standard Deviation is as follows:

(SD)=(𝑃−𝑂)/6

The variance of an Activity

We use this formula result as an indicator to activity risk level, which prompts the course of action to take. Activity variance calculation involves taking the square of activity standard deviation.

Variance=((𝑃−𝑂)/6)^2

The range of an Activity Duration

The range of an Activity Duration serves the same purpose of Standard Deviation (SD) and Variance. To calculate the end of the range you add the Standard Deviation to Estimated Activity Duration. On the other hand, to calculate the start of the range you subtract Duration Standard Deviation from Estimated Activity. Accordingly, the formula for Range of an Activity Duration is as follows:

The range of an Activity Duration=EAD±𝑆𝐷

PMP Formulas #2: Float (Slack) Formulas

Float (Slack) of an activity determines how long an activity can be delayed without affecting the project end date. Accordingly, if an activity is on the critical path, float (slack) of that activity will be zero. In order to calculate an activity Float, first, we determine Late Start (LS) and Early Start (ES) values of the activity. Alternatively, we may use Late Finish (LF) and Early Finish (EF) values. Accordingly, the formula for Total Float is as follows:

Total Float = Late Start (LS) – Early Start (ES)

Total Float = Late Finish (LF) – Early Finish (EF)

B- )Earned Value Management (EVM) PMP Formulas

To understand PMP formulas related to Earned Value Management you need to know the following abbreviations:

Earned Value = EV

Planned Value = PV

Actual Cost = AC

Cost Variance = CV

Schedule Variance = SV

Cost Performance Index = CPI

Schedule Performance Index = SPI

Budget at Completion = BAC

Estimate to Complete = ETC

Estimate at Completion = EAC

Variance at Completion = VAC

To-Complete Performance Index = TCPI

PMP Formulas #3: Cost Variance (CV)

Cost Variance represents the amount of budget deficit or surplus at a given point in time. Basically, we express it as the difference between earned value and the actual cost. Accordingly, its formula is as follows:

CV=EV−AC

PMP Formulas #4: Schedule Variance (SV)

Schedule Variance’s aim is to measure schedule performance through the difference between the earned value and the planned value. Accordingly, its formula is as follows:

SV=EV−PV

PMP Formulas #5: Cost Performance Index (CPI)

One of the most common PMP formulas for control cost is CPI. It measures the cost efficiency of budgeted resources, expressed as a ratio of earned value to actual cost. Accordingly, its formula is as follows:

CPI=𝐸𝑉/𝐴𝐶

PMP Formulas #6: Schedule Performance Index (SPI)

The schedule performance index (SPI) is a measure of schedule efficiency, it represents the ratio of earned value to planned value. It is one of the most common PMP formulas for control schedule. Its aim is to measure how efficiently the project team is accomplishing the work. Accordingly, its formula is as follows:

SPI=𝐸𝑉/𝑃𝑉

PMP Formulas #7: Budget at Completion (BAC)

We determine BAC during the cost management activities, more specifically in Determine Budget Process of a project. BAC includes contingency reserves for activities and defines how much money will be spent during the project in total. Accordingly, its formula is as follows:

Total Budget = Total activity cost estimates + Total contingency cost reserves

PMP Formulas #8: Estimate to Complete (ETC)

Estimate to Complete (ETC) represents the expected cost to finish all the remaining project work. ETC can be determined by re-estimation of the remaining works in a project. In this case, its formula is as follows:

ETC=Re-estimation of Remaining Works

Also, we can calculate it by subtracting the Actual cost (AC) of the accomplished activities from EAC. Assuming the work is proceeding as planned, we can calculate it using this formula

ETC=EAC−AC

PMP Formula #9: Estimate at Completion (EAC)

The expected total cost of completing all work expressed as the sum of the actual cost to date and the estimated sum to complete the project. It is one of the most common PMP formulas. We can find EAC value by 3 different approaches using EV, SPI and CPI values.

Approach #1: It assumes that all future ETC work will be accomplished at the budgeted rate. Accordingly, its formula is as follows:

EAC=AC+(BAC−EV)

Alternatively, Approach #2: It assumes that we expect the achieved cost performance till now will continue in the future. Accordingly, its formula is as follows:

EAC=BAC/CPI

On the other hand,  Approach #3: It assumes that we will perform ETC work at an efficiency rate that considers both the cost and schedule performance indices. Accordingly, its formula is as follows:

EAC=AC+[(BAC−EV)/(CPI x SPI)]

PMP Formulas #10: Variance at Completion (VAC)

Variance at Completion is a projection of the amount of budget deficit or surplus, it represents the difference between the budget at completion and the estimate at completion. Accordingly, its formula is as follows:

VAC=BAC−EAC

PMP Formulas #11: To-Complete Performance Index (TCPI)

TCPI is a measure of the cost performance in order to achieve meeting a specified management goal with the remaining resources. It represents the ratio of the cost to finish the outstanding work to the budget available.

There are two approaches to calculate TCPI. Firstly, If there isn’t a new EAC value, we use the 1st approach. If there is an EAC value, then we use the 2nd approach.

Approach #1: TCPI=(𝐵𝐴𝐶−EV)/(BAC−AC)

Approach #2: TCPI=(𝐵𝐴𝐶−EV)/(EAC−AC)

PMP Formulas #12: Present Value Formula

One of the PMP formulas which focuses on the time value of money and the value of a future cash flow is less today than its amount in the future. It is used in the project selection process. We calculate this through Present Value (PV) formula. In order to understand the formula you need to know the following abbreviations of terms:

Present Value = PV

Future Value = FV

Interest rate = r

Number of periods = n

Thus the formula is PV=FV/(1+r)^n

PMP Formulas #13: Number of Communication Channels Formula

We use this formula to decide on the complexity of project communication. In other words, if there are N stakeholders in an environment, the following formula will give the total number of communication channels between stakeholders in this environment.

Number of Communication Channels=N*(N−1)/2

PMP Formulas #14: Expected Monetary Value

We usually use it in risk quantitative analysis to measure EMV of an opportunity or threat. we calculate it by the following formula:

EMV=Probability x Impact

PMP Formulas #15: Point of Total Assumption (PTA)

PTA is applicable only in Fixed Price Incentive Fee (FPIF) Contracts. Costs above PTA level are considered to be due to mismanagement. PTA is calculated by the following formula:

PTA= [(Ceiling Price − Target Price)/ Buyer′s Sharing Ratio )]+ Target cost