Formulas (turquoise)
Acronym 
Terminology/Phrase 
Formula(s) 
Real Meaning /Reference 
EV or BCWP 
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. 
PV or BCWS 
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 
AC or ACWP 
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 
BAC 
Budget At Completion 
Budget at completion 
· How much did you budget for the job? The total budget. 

Variance 
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 

CV 
Cost Variance 
CV = EV – AC

· Any difference between the estimated cost of an activity and the actual cost of that activity 
SV 
Schedule Variance 
SV = EV – PV 
· Any difference between the scheduled completion of an activity and the actual completion of that activity 
CPI 
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.

SPI 
Schedule Performance Index 
SPI = EV/PV
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 
SPI * CPI 


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

EAC 
Estimate At Completion 

Several possible calculations depending upon the status of the project 
EAC 
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 
EAC 
Estimate At Completion 
EAC=AC+ETC 
· Used when original estimate is flawed · Actual plus new estimate for remaining work. 
EAC 
Estimate At Completion 
EAC=AC + (BAC –EV) 
· Used when current variances are atypical of the future. · Actual to date plus remaining budget. 
EAC 
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 
ETC 
Estimate To Completion 
ETC = EAC – AC 
· How much will the project cost 
VAC 
Variance At Completion 
VAC = BAC – EAC 
· How much over budget will we be at ten end of the project? 




Slack 

(LSES) or (LFEF) 

ES 
Early Start 
EF – duration + 1 

EF 
Early Finish 
ES + duration – 1 

LS 
Late Start 
LF – duration + 1 

LF 
Late Finish 
LS + duration 1 

FF 
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 
TF 
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 





EMV 
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 

BCR 
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 
IRR 
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 
NPV 
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 (N1) / 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
(PO)/6
Task Variance
[ (PO) / 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)
Mean
The mean is the sum of the measures divided by the number of measurements
Mode
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 bimodal distribution.
If the observations have three or more modes, then the mode is no longer a viable measure of central tendancy.
2,2,2,3,3,5,7,10,12
mode = 2
Measures of Variability
Range
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.
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.
Other
· 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)
Histogram 
Variance & Standard Deviation 
Add up your number of observations. (N) 
Find the mean (xbar) 
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 n1 (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.
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 
Sure. My Linkedin profile is http://www.linkedin/in/dritter. Congratulations on your PMP!!!
Comment by Donna Ritter — January 5, 2009 @ 11:52 am 
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
AND
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 
I will answer this soon. I am sorry – I have had some death in my family. I’ll work on this tomorrow.
Donna
Comment by Donna Ritter — August 19, 2010 @ 9:45 pm 
Igt would take longer to reply to this than answering a blog post. Contant ,e further and we can discuss it if you wish.
Donna
Comment by Donna Ritter — June 18, 2011 @ 11:59 am 
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 