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Equation 1 · How Grok and Colossus Actually Work, as Far as the Record Shows

What does this equation mean?

Pnameplate=N1⋅PGPU=100,000×700 W≈70 MW.P_{\text{nameplate}} = N_1 \cdot P_{\text{GPU}} = 100{,}000 \times 700\ \text{W} \approx 70\ \text{MW}.

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Inputs and operationsN_1 × P_GPU = 100,000 × 700 W ≈ 70 MW
Result or conditionP_nameplate
How to read the two sides of this formula. Follow the article passage for the meaning of each quantity.

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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PnameplateP_{\text{nameplate}}

Symbol P_nameplate

PnP_nameplate is part of the quantity the equation computes from the expression on the right.

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N1N_1

Symbol N_1

N1N_1 is one factor in the product that computes the quantity on the left.

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PGPUP_{\text{GPU}}

Symbol P_GPU

PGP_GPU is one factor in the product that computes the quantity on the left.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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≈

≈

Approximately equal to; the equality is not exact.

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multiplication

multiplication

Multiply the quantities on either side.

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subscript

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.

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How to interpret it

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

That reported 250-megawatt figure is worth pausing on, because a naive back-of-envelope estimate from the chips alone comes out much lower. Nvidia’s own datasheet lists the H100 SXM5 module’s maximum thermal design power at 700 watts [ 5 ] . Multiplying that by the disclosed size of the original cluster gives the accelerators’ own nameplate draw at launch: Pnameplate=N1⋅PGPU=100,000×700 W≈70 MWP_{\text{nameplate}} = N_1 \cdot P_{\text{GPU}} = 100{,}000 \times 700\ \text{W} \approx 70\ \text{MW}. Independently reported total generating capacity at the site during roughly that period ran several times higher than that — on the order of 570 megawatts once a documented 150-megawatt grid connection (below) is added to the roughly 420 megawatts of turbine capacity litigants and reporters separately counted on the…
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That reported 250-megawatt figure is worth pausing on, because a naive back-of-envelope estimate from the chips alone comes out much lower. Nvidia’s own datasheet lists the H100 SXM5 module’s maximum thermal design power at 700 watts [ 5 ] . Multiplying that by the disclosed size of the original cluster gives the accelerators’ own nameplate draw at launch: Pnameplate=N1⋅PGPU=100,000×700 W≈70 MWP_{\text{nameplate}} = N_1 \cdot P_{\text{GPU}} = 100{,}000 \times 700\ \text{W} \approx 70\ \text{MW}. Independently reported total generating capacity at the site during roughly that period ran several times higher than that — on the order of 570 megawatts once a documented 150-megawatt grid connection (below) is added to the roughly 420 megawatts of turbine capacity litigants and reporters separately counted on the ground (also below). None of that gap is evidence that either figure is wrong. It is what a real facility looks like once CPUs, memory, storage, networking gear and — above all — liquid-cooling infrastructure are added on top of the accelerators themselves, and once generation is sized with reserve margin rather than run flat to nameplate. The arithmetic is offered here for exactly that reason: to show why “GPU count” and “site power” cannot be inferred from one another without the buildout details neither company nor litigant fully discloses.

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