Equation 2 · How Grok and Colossus Actually Work, as Far as the Record Shows
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 gives an approximation: it relates the quantities while allowing an approximation. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol barP_GPU,2
barPU,2 is part of the quantity the equation computes from the expression on the right.
Symbol P_total
otal occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Symbol N_2
occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
=
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.
Denominator: 555,000
The complete quantity below the fraction bar; it must be nonzero for this division.
How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction. Its accuracy depends on the assumptions and range of use described in the article. Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
Colossus 2 is the clearest example of a figure that belongs squarely in the vendor-claim column rather than the confirmed-fact one. On December 30, 2025, Elon Musk announced that xAI had purchased a third building in Memphis, expanding the campus toward a stated 2-gigawatt total capacity and roughly 555,000 GPUs, reported to represent about $18 billion in accelerator purchases — implying, by simple division, something on the order of $32,000 per GPU [ 10 ] . The reporting is explicit that this is Musk’s own announcement rather than an independently audited figure, and the newer accelerator generation involved (GB200- and GB300-class parts, alongside roughly 30,000 legacy H100/H200 units…
Read the full surrounding passage
Colossus 2 is the clearest example of a figure that belongs squarely in the vendor-claim column rather than the confirmed-fact one. On December 30, 2025, Elon Musk announced that xAI had purchased a third building in Memphis, expanding the campus toward a stated 2-gigawatt total capacity and roughly 555,000 GPUs, reported to represent about $18 billion in accelerator purchases — implying, by simple division, something on the order of $32,000 per GPU [ 10 ] . The reporting is explicit that this is Musk’s own announcement rather than an independently audited figure, and the newer accelerator generation involved (GB200- and GB300-class parts, alongside roughly 30,000 legacy H100/H200 units carried over from Colossus 1) is provisioned at markedly higher power density per chip than the H100 generation it succeeds [ 10 ] . Scaling the same simple arithmetic to the announced target illustrates the shift, while making clear it is a comparison of two different companies’ disclosed totals rather than a measured rack figure: . roughly five times the 700-watt figure for a single H100. xAI has not published a rack-level or chip-level power figure for Colossus 2 itself; this is an inference from two independently sourced totals, offered as illustration of direction and scale rather than as a disclosed specification. Musk has also stated a longer-run ambition of reaching roughly 1 million GPUs across xAI’s sites; that is a stated target and a forward-looking claim, not a completed buildout, and it is reported here as exactly that.
Sources cited in the surrounding passage
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