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POSTER 21
Section 9 · Quick Reference — Every Formula in One Place

The Formulas Wall

All the maths across the wall, grouped by family. Golden rules: in EVM, EV starts every formula — a variance subtracts (EV − x), an index divides (EV ÷ x), and positive / > 1 is favourable. Cost pairs use AC; schedule pairs use PV.

Earned Value — Variances & Indices

SV = EV − PV
+ ahead · − behind

CV = EV − AC
+ under · − over

SPI = EV ÷ PV
>1 ahead

CPI = EV ÷ AC
>1 under budget

CV% = CV ÷ EV

SV% = SV ÷ PV

Earned Value — Forecasting

EAC = BAC ÷ CPI
current trend (default)

EAC = AC + (BAC − EV)
variance was one-off

EAC = AC + (BAC−EV) ÷ (CPI×SPI)
cost & schedule

EAC = AC + bottom-up ETC
re-estimate

ETC = EAC − AC

VAC = BAC − EAC

TCPI = (BAC−EV) ÷ (BAC−AC)
to hit BAC

TCPI = (BAC−EV) ÷ (EAC−AC)
to hit EAC

Estimating

PERT (Eₑ) = (O + 4M + P) ÷ 6
beta / weighted

σ = (P − O) ÷ 6
std deviation

Variance = ((P − O) ÷ 6)²

Triangular = (O + M + P) ÷ 3

Ranges: ±1σ ≈ 68% · ±2σ ≈ 95% · ±3σ ≈ 99.7% of outcomes.

Schedule / Critical-Path Network

Total Float = LS − ES = LF − EF

Free Float = ESₙₑₓₜ − EF − 1

Forward: EF = ES + Dur − 1

Backward: LS = LF − Dur + 1

Critical path = longest path = zero total float. (Drop the −1 / +1 if you count from day 0.)

Communication & Risk

Channels = n(n − 1) ÷ 2

EMV = Σ (Probability × Impact)
− threat · + opportunity

Finance (decision)

  • NPV — higher is better; already discounted.
  • IRR — higher is better.
  • ROI = (gain − cost) ÷ cost; higher better.
  • Payback — shorter is better.
  • BCR = benefits ÷ costs; > 1 good.

Contract (bonus)

PTA = ((Ceiling − Target Price) ÷ buyer share) + Target Cost

Point of total assumption — above it, the seller bears all extra cost (incentive contracts).

Sign-Reading & Golden Rules

  • EV first in every EVM formula.
  • Variance = subtract; index = divide.
  • Positive variance & index > 1 = good.
  • Cost ↔ AC; Schedule ↔ PV.
  • EV = % complete × BAC.
  • ETC = EAC − AC; VAC = BAC − EAC.
  • TCPI > CPI ⇒ recovery is hard.
  • Float 0 ⇒ on the critical path.

Most-Tested

  • CPI / SPI interpretation & EAC = BAC/CPI.
  • PERT (O+4M+P)/6 and σ = (P−O)/6.
  • Channels n(n−1)/2.
  • Total float = LS − ES.
  • EMV for decision trees.
Daily Drill All 4 EAC formulas PERT + σ + variance Float = LS − ES Channels for n = 10 Compute an EMV
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