PMP® Formulas

PMP® Formulas based on PMBOK® 5th edition:

Three point Estimating(For time as well as cost):

Triangular Distribution:

E = (O+M+P)/3

Beta Distribution:

E = (O+4M+P)/6

E = Expected Duration

O – Optimistic

M – Most Likely

P – Pessimistic

Standard Deviation of activity:

SD = (P-O)/6

Variance of activity:

V = SD²

Standard Deviation of Project:

Square root of sum of Critical Path Variances



Late Start – Early Start

Late Finish – Early Finish


Slope = (Crash Cost – Normal Cost)/(Crash Time – Normal Time)

Progress Reporting:

0/100; 50/50; 20/80

Cost Variance (CV):

Earned Value (EV) – Actual Cost (AC)

Schedule Variance (SV):

Earned Value (EV) – Planned Value (PV)

Tip: Positive CV and SV are good i.e., project is under budget and ahead of schedule and vice versa.

Cost Performance Index (CPI):


Schedule Performance Index (SPI):


Tip:CPI and SPI values greater than 1 are good i.e., project is under budget and ahead of schedule and vice versa.

Tip: All the four formulas – CV, SV, CPI and SPI start with EV as the first parameter. Schedule foumulas have PV as the second parameter and Cost formulas have AC as the second parameter. Variance formulas are differences and Index formulas are divisions.

Estimate to Complete (ETC):

When work is proceeding as planned: EAC = BAC/CPI

When the work is not proceeding as planned, re-estimate the ETC from bottom up.

Estimate at Completion (EAC):

When the future work will be performed at the present rate (CPI): EAC = BAC/CPI

Following formulas are based on EAC = AC + ETC

When current variances are considered atypical, i.e., future work will be performed at the planned rate: EAC = AC + (BAC – EV)

When variances have occurred and future work will be  performed at varied rate (CPI): EAC = AC + (BAC – EV)/CPI

When original estimate/plan is not valid any more: EAC = AC + Bottomed up ETC

When the future work would depend on both SPI and CPI: EAC = AC + [(BAC – EV) / (CPI x SPI)]

BAC – Budget at Completion

ETC – Estimate to Completion

Variance at Completion (VAC):


To Complete Performance Index (TCPI):

Efficiency with which the remaining work is to be performed to achieve the management goal. Calculate as the ratio of cost to complete the remaining work to the budget available.

When the work is to be completed on  plan: TCPI = (BAC – EV)/(BAC – AC)

When the work is to be completed as per the updated EAC: TCPI = (BAC – EV)/(EAC – AC)

TCPI > 1.0 – Harder to complete

TCPI < 1.0 – Easier to complete

Present Value:


FV – Future Value

r – Interest Rate

a – # of periods

Benefit Cost Ratio (BCR):

>1 is good

<1 is bad

=1 means costs equal benefits

Quality Standard Deviations (Sigmas):

+/- 1 sigma = 68.26%

+/- 2 sigma = 95.46

+/- 3 sigma = 99.73

+/- 6 sigma = 99.99

Number of Communication Channels:


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