PMI Formulas

This is a very basic study aid for typing and memorizing the PMI’s Project Management formulas. The answers are available by scrolling down to a completed table below. You can use the first table to test yourself.

As recommended by Rita, I generally tried to express each formula description at least once in my own words. I find it helps me initially to understand them and later to recall them, but this does leave room for variance in interpretation. Feel free to advise me of any corrections, clarity needed, or suggestions.

Acronym Name or Formula Interpretation
EAD
Activity Standard Deviation
Activity Variance
EV
PV
AC
BAC
CV
SV
CPI
SPI
EAC
ETC
VAC
TCPI
AWCS
EAD
AV
SD
Activity Range
Project Expected Duration
Project SD
Project Range
EMV
Communication Channels
PTA
Final Fee
Final Price
Float
Formula
Formula
Formula
Formula

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Notes:

  1. Except for TCPI, the 4 letter formula acronyms are either dated or invalid.
  2. EV comes first
  3. Actual cost must be provided in the question
  4. “Not enough information is provided.” is a possible correct answer
  5. Variance formulas are EV – something
  6. Index formulas are EV / something
  7. Cost formulas use CV
  8. Schedule formulas use PV
  9. For variance, negative is bad. Positive is good.
  10. For indices, > 1 is good. < 1 is bad.
Acronym Name or Formula Interpretation
EV Earned Value The estimated value of the work completed.
The completed portion of the originally estimated, total value.
PV Planned Value The value of the work planned to be be done by now
AC Actual Cost The current amount spent.
The total cost so far for the work completed.
BAC Budget At Completion The total project budget
How much did we originally expect the total project to cost?
BAC = PV of entire project
CV Cost Variance
EV – AC
Value of work accomplished – cost incurred
SV Schedule Variance
EV – PV
The value of work completed – The value of work planned to be completed.
Work completed – Expected work completed
Negative is behind schedule. Positive is ahead of schedule.
CPI Cost Performance Index
EV / AC
We are getting X value out of each $ spent.
Also as: “Cumulative CPI” when figures used are costs to date.
SPI Schedule Performance Index
EV / PV
We are progressing at X rate originally planned.
We are getting X value per original planned value.
EAC Estimate At CompletionAC + Bottom-up ETC

BAC / CPI

AC + (BAC – EV)

AC + [ (BAC - EV) / ( CPI * SPI) ]

What we currently expect the total cost to be.Current cost + Bottom up (redone) estimate of remaining cost. Used when original estimate was flawed.

Currently, the total cost estimate per (cumulative) performance.
Used when there is no variance from BAC. Most common on exam.

Current cost + Remaining work TBD.
What you’ve spent + What you need to spend.
Used when current variance is expected to change.

Current cost plus remaining budget per performance.
Used when variance is typical, CPI is poor, and completion date priority is high

TCPI To Complete Performance Index
(BAC – EV) / (BAC – AC)
The remaining work TBD per the remaining money.
In order to stay on budget, what remaining performance is needed?
ETC Estimate To Complete
EAC – AC


Reestimate

How much more will the project cost?
Updated total cost – current cost


Reestimating the work from the bottom up.

VAC Variance At Completion
BAC – EAC
How much over/under budget will we be?
AWCS Actual Cost of Work Scheduled Not a real term!
Oxymoron
May be an incorrect test question choice.
EAD Expected Activity Duration( P + 4M + O ) / 6 The most likely estimated is weighed 4 times the pessimistic or optimistic.This and all formulas below can be used for activity time and cost
AV Activity Variance[ ( P - O ) / 6 ] ^2 A quantifiable deviation from an expected baseline or estimate. Also equal to standard deviation squared.
SD Standard Deviation( P – O ) / 6 The square root of the variance. Used to calculate the activity range. EAD +/- SD
Activity Range EAD +/- SD The estimated scope from EAD – Standard Deviation to EAD + Standard Deviation.
Project Expected Duration EAD + EAD + EAD The sum of the EAD’s / PERT estimates
Project SD Standard deviation of the projectsqrt[AV + AV + AV ...] Each of the activity variances (AV) on the critical path are calculated individually. The square root of their sum is the project standard deviation. It is used to calculate the project range.
Project Range The project expected duration +/- Project SD The sum of the project EADs +/- the project standard deviation.
EMV Expected Monetary ValueEMV = P * I EMV = Probability times Impact
Communication Channels [ n (n-1) ] / 2 The number of channels between people. n is the number of people
PTA [(CP - TP) / BSR] + TC Point of total assumption.
The amount at which seller pays all additional costs. Used in FPIF contracts.
The margin between the maximum and target prices is divided by the buyer’s portion of the sharing ratio and added to the target cost
Final Fee FF = (TC – AC) x SSR + TF Sellers fee/profit is adjusted for cost performance.
The target fee is adjusted by adding: target cost – actual cost times the sellers portion of the sharing ratio
Final Price FP = AC + FF (or CP, whichever is lower) Final price equals actual cost plus final fee (or ceiling price)
Buy or Lease Purchase CostOwning Cost * Time = Leasing Cost * Time So if something costs $1,000 to buy and $10 / day to maintain but costs $50 / day to rent, how many days does it take to break even?  1,000 + 10 * t = 50 * t The break even point is 25 days.
Float Float = LF – EF or LS – ES Late Finish – Early Finish or Late Start – Early Start

14 comments to PMI Formulas

  • Murali

    Hi Mark,

    Small Typo in the formulae listed..
    Float Float = LF – LS or LS – ES Late Finish – Early Finish or Late Start – Early Start

    I guess it should be Float Float = LF – EF or LS – ES Late Finish – Early Finish or Late Start – Early Start. (i.e, Late Finish – Early Finish).

    Thanks for sharing all formulae at one place. I keep coming back to this page just to make sure I got my formula right (during my practice test).

    Regards,
    Murali

  • mark

    Hi Murali,

    You are exactly right. Good catch. I’ve made the update (changing LS to EF) in the abbreviation column.

    Thanks for the heads-up!

    Best,
    Mark

  • For the Project SD (Standard deviation of the project), shouldn’t the AVs be squared?
    sqrt[AV^2 + AV^2 + AV^2 ...]

    Your definition of SD says, “The square root of the variance.” According to your formulas, it’s the other way around; SD is the square of the variance.

    It’s important to sticklers for math to realize that the PMI formula for SD is a quick approximation. Using data for an exercise for the course I’m taking, the PMI formula consistently overestimated the SD by 30% to 40%, compared to the formula used in statistics.

    I’ve been very frustrated with the number of inaccuracies and inconsistencies in the PMBOK. Could it be that they’re intentionally conditioning people to put up with less-than-Six Sigma quality?

  • Dave

    Nice Job! Thanks!

  • mark

    Thanks Dave!

    Hi Richard, Sorry for the delay. I missed your post notification.

    It looks like formulas above are accurate. The Activity Variances are already squares (they are squares of the standard deviations) in your first example regarding Project Standard Deviation. So you do not square them again. You would be correct if it was written as: Project SD = sqrt[SD^2 + SD^2 + ...] But this is the same as written above: Project SD = sqrt[AV + AV + ...]

    Similarly, Activity Variance is in fact the square of Standard Deviation and Standard Deviation is the square root of Activity Variance:

    AV = SD^2
    SD = ( P – O ) / 6
    AV = [ ( P - O ) / 6 ] ^2
    SD = sqrt[AV]

    I don’t think the calculations should ever be off by the 30% – 40% you reference, if the underlying estimates are assumed to be accurate. If I provide 2 PMPs hundreds of work and cost estimates from my project team members, they should return me exactly the same standard deviation results. While my team members may have estimated inaccurately, it is precisely the value of standard deviation and activity variance to mitigate that error and increase the accuracy of planning.

    Best,
    Mark

  • Mark, I have a problem getting from the statistical definition of SD,

    s = SQRT( [(O-EAD)^2 + 4(M-EAD)^2 + (P-EAD)^2]/6 )

    to

    SD = ( P – O ) / 6

    One simplification, EAD=M, got me close, but no cigar. My formula is higher than PMI’s by a factor of SQRT(3). I’ll post or send you my derivation if you like. Maybe you can spot my error(s).

  • Linda

    Thank you so much for this listing, I was going to take the PMP but I don’t have enough hours… so I will take the CAPM. I hope this will help me

  • [...] whole bunch of formulas: (Quiz Yourself!) http://markpreynolds.com/pmp/formulas 0 Comments – Leave a comment! « Previous [...]

  • tariq badsha

    In BAC formula where you are normalizing the remaining duration by CPI as well as SPI you are using CPI + SPI in the denominator. This should be CPI * SPI. Adding the two indices will give you a value of greater than one when in fact one or both are less than one

  • Hi Tariq. You’re right and that is not a typo on my part. I’ve had that there since my studies, the reason being my prep guide: PMP Exam Prep 6th Edition, by Rita Mulcahy, lists the performance indexes as a sum on page 242, the only reference to it in the book that I’ve found.

    I’ll update the post. Thanks!

  • Michelle

    I appreciate this it will help with my CAPM studies

  • Michael

    The formula for lease or buy was stumping me but what appears to work is to subtract the daily maintenance cost from the daily lease cost and divide the purchase price by the result gives you the amount of break even days.

  • Pierre

    Hey Mark, missing

    NPV = (for i:1 to years do CF(i)/(1+d)^i done) – initial investment
    Payback = numbers of years to have the payments of the initial investment (nominal : without anual discount rate or present , with NPV casf flows)
    ROI = anual profit / investment
    IRR, Internal Rate of Return = rate (d) to obtain NPV = 0 for a determined number of year. Find it by estimations.

    Thanks for your work !

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