Equation 12 · The Physical Plant: Power, Cooling, and Networks in an AI Datacenter
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol E_facility
acility occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Symbol E_IT
T occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Symbol E_cooling
ooling occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Symbol E_distribution
istribution occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Symbol E_other
ther occurs above the fraction bar. The numerator is divided by the entire denominator below it.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
Numerator: E_cooling + E_distribution + E_other
The complete quantity above the fraction bar.
How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
Power usage effectiveness is the industry’s one universally reported number: . Uptime Institute, which has collected the metric since its introduction by The Green Grid in 2007, reported a weighted average annual PUE of 1.54 across its 2025 respondent sample, “marking the sixth consecutive year that this headline figure has virtually stood still.” Beneath that flat average the sample separates: facilities commissioned within five years of the survey averaged 1.48, facilities of 20 MW and above averaged 1.44 globally, and 15% of respondents reported 1.3 or better [ 3 ] . Google, disclosing its own fleet, states that “in 2025, the average annual power usage effectiveness for…
Read the full surrounding passage
Power usage effectiveness is the industry’s one universally reported number: . Uptime Institute, which has collected the metric since its introduction by The Green Grid in 2007, reported a weighted average annual PUE of 1.54 across its 2025 respondent sample, “marking the sixth consecutive year that this headline figure has virtually stood still.” Beneath that flat average the sample separates: facilities commissioned within five years of the survey averaged 1.48, facilities of 20 MW and above averaged 1.44 globally, and 15% of respondents reported 1.3 or better [ 3 ] . Google, disclosing its own fleet, states that “in 2025, the average annual power usage effectiveness for our global fleet of data centers was 1.09,” measured as a trailing twelve-month figure “in all seasons, including all sources of overhead” [ 12 ] .
Sources cited in the surrounding passage
These citations give research context. Read each source to check which claims it supports.
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