Life and Spiritual Coaching

May 23, 2008

PMP Formulas

Filed under: PMP — by Donna Ritter @ 3:06 pm
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Formulas (turquoise)






Real Meaning /Reference


Earned Value or

Budgeted[1] Cost of the Work Performed

EV = %completed * BAC

·         How much work was actually done as described in the budget

·         A method for measuring project performance.  It compares the amount of work planned with what was actually accomplished to determine if cost and schedule performance is as planned.   Earned  Value (EV), is a percentage of the total budget equal to the work actually performed.


Planned Value or

Budget Cost of Work Scheduled


·         How Much work should be done (The estimated value of the planned work)

·         The budget that is part of the approved cost estimate planned to be spent on the activity during a given period


Actual Cost or

Actual Cost of the Work Performed


·         What is the actual cost incurred? 

·         What have we spent to date?

·         The actual cost that is the total of direct and indirect costs incurred in accomplishing work on the activity during the given period


Budget At Completion

Budget at completion

·         How much did you budget for the job? The total budget.



Variance = BAC – AC

·         Planned – actual (i.e. planned was three weeks, actual was two weeks – resulting in a one week variance)


Percentage complete

%complete = EV/BAC



Cost Variance

CV =   EV – AC    


·         Any difference between the estimated cost of an activity and the actual cost of that activity


Schedule Variance

SV =    EV – PV    

·         Any difference between the scheduled completion of an activity and the actual completion of that activity


Cost Performance Index

CPI = EV/AC[2]

CPI <1 means over budget

CPI >1

 cost are below budget

CPI equal to 1 means costs equal benefits

·         Used to forecast project cost at completion

·        The ratio of budget cost to actual costs.



Schedule Performance Index



SPI <1  project will be late

SPI  > 1`project is ahead of schedule

SPI equal to 1 means costs equal means project is on scheule

·         Used to forecast project completion date

·        The SPI is used in some application areas to forecast the project completion date.



Cumulative CPI

Sum of all individual EV divided by the sum of all individual AC



Critical Ratio




Critical Path uncertainty

The Critical Path uncertainty = the sum of the (square root of the variances)



Estimate At Completion


Several possible calculations depending upon the status of the project


Estimate At Completion

  EAC = BAC  / CPI

·         Used if no variances from BAC or you will continue at the same rate of spending.

·         Most commonly used on PMP exams


Estimate At Completion


·         Used when original estimate is flawed

·         Actual plus new estimate for remaining work.


Estimate At Completion


·         Used when current variances are atypical of the future.

·         Actual to date plus remaining budget.


Estimate At Completion

EAC=(AC + (BAC -EV))/CPI .

·         Used when variances are thought to be typical of the future

·         Actual to date plus remaining budget modified by performance


Estimate To Completion


·         How much will the project cost


Variance At Completion


·         How much over budget will we be at ten end of the project?







 (LS-ES) or (LF-EF)



Early Start

EF –  duration + 1



Early Finish

ES + duration – 1



Late Start

LF – duration + 1



Late Finish

LS +  duration -1



Free Float

ES (of successor) – EF (of current task) – 1

·         amount of time the current activity can be delayed without delaying the early start of the successor task


Total Float

LF – EF (of current task)

·         amount of time the current activity can be delayed without delaying the LF of the entire project.


Budget Burn Rate (linear)

BAC / planned duration

·         Example ($1,000 / 4 weeks = $250 per week)


Actual Burn Rate (linear)

AC / Actual duration

·         Example ($1,200 / 5 weeks = $240 per week)






Excepted Value

Probability (%) * consequences







Simple Interest


Interest = Principle X Rate x Time







Expected Monetary Value


EMV = Odds of occurrence x amount at stake




Present Value

Present Value = FV/(1+r)n

FV = Future Value

r = Interest Rate

n    = # of periods


Future Value

FV = PV x (1 + i)


n = Number of time periods (years)

PV = Present value (of money)

i = interest rate



Pay back

Pay back = period of time to recover investment through cash flow



Benefits Cost Ratio

BCR greater than 1 is good

BCR less than 1 is bad

BCR equal to 1 means costs equal benefits



Opportunity cost

No calculation

·         Defines the opportunity given up by selecting one project over another


Internal Rate of Return

Complex calculations requiring computer

·         If a company has more than one project to invest, the company may look at projects’ return and then select the highest one.


Fixed Cost


·         Resource constrained scheduling, end date may vary


Fixed Time


·         Resource variable scheduling, end date fixed


Net Present Value

To calculate you need to calculate the present value of both income and revenue figures and then add up the present values 

·         The present value of the total benefits (income or revenue) less the costs.




Valuable Hint NOT Written in Project Management Books About Costs


(Or more succinctly “How to know you’re in trouble”)


When EV (BWCP) is used in an equation, it always goes first:


CV = EV – AC


If you get a negative number, your project is over budget.


SV = EV – PV


Again, if you get a negative number, your project will overrun its schedule.



Communication channels (assuming a binary distribution)


N (N-1) / 2




Program Evaluation and Review Technique (PERT)



Other Notes

PERT assumes a beta distribution

Weighting –  Pessimistic = 1, Most likely = 2  and  Optimistic =3


Standard Deviation


Task Variance

[ (P-O) / 6]



Project Variance

Project Variance = Take the square root of the sum of the task variances





Conventional Critical Path Methodology


A to B


Finish to Start  (FS)

zero delay

Start to Start (SS)

implies delay on B after Start of A

Finish to Finish

A must finish before B

Start to Finish

A must start before B can finish



Measures of Central Tendency (Mean, Median, Mode)



The mean is the sum of the measures divided by the number of measurements




The mode is the most frequent occurring observation in the data under consideration.


If the observation has two modes, then the data is said to be bi-modal distribution.


If the observations have three or more modes, then the mode is no longer a viable measure of central tendancy.




mode = 2



Measures of Variability



The range is the difference between the largest measure and the smallest measurement.


The range does not use all available observations.  It uses only the two extreme values.  It will have the same dimension, or unit of measure as the original data.


Standard Deviation

The standard deviation is the positive square root of the variance.


   12.67  = 3.56


Normal Distribution

  = 68.26

  = 94.36

  = 99.73

  = 99.99


Note   68.26/2 = 34.13   which is 50% above the one sigma mean and  50% below one sigma mena.





·         UCL / LCL Upper Control Lime & Lower Control Limit on a control chart

·         Pareto:  80% of problems come from 20% of the work

·         Crashing:  Slope = Crash Cost – Normal Cost/Crash Time – Normal Time

·         Progress Reporting:  0/100; 50/50; 20/80

·         Standard Deviation of a project = Square Root of  Sum of Critical Path Variances

·         Slack = LST – EST (Latest Start Time – Earliest Start Time)

    = LFT – EFT (Latest Finish Time – Earliest Finish Time)



Variance & Standard Deviation

Add up your number of observations. (N)

Find the mean (x-bar)

Determine the Range (R)   

Subtract the mean from every observation (n)

Determine Classes (K)

Square each result

Determine Class Width (H) where H = R/K

Add up all the squares

Construct Frequency table

Divide that number by n-1 (for the sample) or N (for the population)    

This is the Variance

Plot Data

Square root the answer

This is the Standard Deviation


Binomial Distribution (Success or Failure)

·         A coin will be tossed 5 times but the coin is biased so that the probability of heads for each toss is 0.04. Heads is success, tails is failure.

·         N = number of items in the sample (the number of coin tosses)

·         X = number of items for which the probability is desired (number of Heads)

·         In Appendix A we go to column N and find where N = 5

·         In Appendix A we go to where p = 0.40

·         Each row represents the probability of 0, 1,2, 3, 4, and 5 successes

·         Add them up


Poisson Distribution

·         A light bulb manufacturer has a known defective rate of 4%. From a sample of 40, the probability of 4 or more defective light

·         µ = np = (40) (.04) = 1.6

·         Probability of 4 or more defective is = 1 – probability of 3 or less defective

·         In the table, find where µ = 1.6

·         Add up the numbers where x has a value of 0, 1, 2, or 3 (this is the P of 3 or less defectives)

·         Subtract that number from 1.0

·         Find np (sample x defective rate)

·         Calculate up to by going to the table, finding np, adding it up

·         Subtract that answer from 1 to x or greater probability


Normal Distribution (also known as Gaussian)

·         If process produces parts with mean of _ and standard Deviation of _, what is the P that one random part has a measurement of _?

·         Mean time of a bank transaction is 5.25 with a standard deviation of 0.75 minutes and the values are normally distributed. What is the probability that a transaction will occur between 4.0 and 5.25 minutes and below 4.0?

·         Z = 4.0 – 5.25/ 0.75 = -1.67

·         Go to Appendix A and find 1.67 = 0.4525

·         Because we know that µ is 5.25, the probability that a transaction will take less than 5.25 is .05 (1/2)

·         Therefore, the probability that a transaction will be less than 4 minutes = 0.5 – 0.4525 = 0.0475


Sampling Distributions (number of standard Deviations that a sample mean is away from the population mean)

·         If normal distribution with mean of _ and SD of _. From sample of _ what is P that the sample mean is >, <, =, or between _?

·         Hospital emergency room where it has a record waiting time of 30 minutes with a standard deviation of 5 minutes. If a sample of 35 is measured, what is the probability that the sample mean would be greater than 31.5 minutes?

·         Do the Z calculation to get 1.77

·         Find 1.77 in Appendix A (go to 1.7 and then across to 0.07)

·         Subtract that probability from the .5 probability = .50 – .4616 = .0384

·         This tells us that there is only a .0384 probability that, from the sample of 35, the sample mean will be greater than 31.5.


Measure of shapes (skewness)


Symmetrical (Bell sphere)


Positive skew (shift to right)


Negative skew (shift to left)

Beta Distribution = skewed in one direction


[1]   Some of the literature refers to this as Basic rather than budgeted.

[2]    The simple way to remember CPI and SPI is these are ratios of the CV and SV.  If you know the CV and SV formulas, remember CPI and SPI are rations.


  1. Thanks Thanks Thanks Donna — I just got my PMP. I revised every word in this blog in the morning before leaving for the exam — it was extremely helpful. Superb notes – U ROCK!!

    It would be great if we connect in LinkedIn?

    Comment by Maruti — January 5, 2009 @ 6:35 am |Reply

  2. Hello Donna,

    I am confused on some of the formulas. It would be great if you could help me with the answers of the following questions.

    1) What is uncertainty of Critical path and What is the formula to calculate it?

    You post mentions the formula as

    The Critical Path uncertainty = the sum of the (square root of the variances)

    I am quiet confused on formulae for Critical Path uncertainty and Standard deviation of the project.

    Does it mean to calculate Critical Path uncertainty first take the square root of variances of critical path activities and then sum these values?

    And for Calculation Standard Deviation of the project, First sum up the variances of all critical path activities and then take the square root?

    2) What is the difference between Variance of the Project and Standard Deviation of the project. The formulae on your post are as below.

    Standard Deviation of a project = Square Root of Sum of Critical Path Variances
    Project Variance = Take the square root of the sum of the task variances

    Please could your confirm or correct my understanding as below..

    To Calculate Standard Deviation of a project, sum up the variances of critical path actvities and then take square root. Is it correct?

    To Calculate Project Variance, sum up the standard deviations of all the critical path activity and then take the square root. Is it correct.

    Thanks and Regards,
    Prasad Shadangule

    Comment by Prasad Shadangule — June 23, 2010 @ 9:24 am |Reply

    • I will answer this soon. I am sorry – I have had some death in my family. I’ll work on this tomorrow.


      Comment by Donna Ritter — August 19, 2010 @ 9:45 pm |Reply

    • Igt would take longer to reply to this than answering a blog post. Contant ,e further and we can discuss it if you wish.


      Comment by Donna Ritter — June 18, 2011 @ 11:59 am |Reply

  3. future value formula is incorrect. should read: PV * (1+i*n)
    thanks for posting this information. i am preparing for the pmp exam and found this very helpful.

    Comment by j hickman — November 2, 2010 @ 12:58 pm |Reply

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