What does this equation mean?

The technical starting point is disclosed with unusual precision, because Nvidia had a marketing interest in disclosing it. In an October 2024 press release, Nvidia stated that Colossus connected up to 100,000 liquid-cooled H100 GPUs on a single RDMA fabric using its Spectrum-X Ethernet platform, built in 122 days from the first rack’s arrival, with only 19 days between first rack and the start of training, and quoted Musk calling it “the most powerful training system in the world” [ 4 ] . Nvidia’s own current H100 product page lists the SXM variant’s thermal design power at up to 700 watts, configurable [ 5 ] . That is enough to write a first, deliberately narrow equation — the power draw of the accelerator silicon alone, ignoring everything else in the building: $P_{\mathrm{GPU}} = N_{\mathrm{GPU}} \times \mathrm{TDP}_{\mathrm{GPU}} = 100{,}000 \times 700\ \mathrm{W} = 70\ \mathrm{MW}$. Seventy megawatts is the draw of the H100 dies themselves at that phase’s disclosed count, before a single fan, pump, switch, or host CPU is counted. Compare that to what was actually approved to feed the site at roughly that stage of its build: the Tennessee Valley Authority’s board approved a request, routed through the local distributor Memphis Light, Gas and Water, for just over 100 megawatts, with xAI stating it needed 150 megawatts in total to run the cluster it had built [ 7 ] . That is a site-level figure roughly twice the raw silicon draw computed above. The gap is not evidence of anything hidden; it is exactly what a datacenter’s overhead is supposed to look like — network switches, storage arrays, host CPUs, cooling plant, and power-conversion losses between the utility feed and the board. This article does not have a disclosed power usage effectiveness figure for Colossus to cite, so it stops at stating the ratio implied by the two disclosed numbers rather than asserting an industry-standard multiplier as fact.