mmurr.ai · methods appendix

Impact Handbook — every number, derived

This page shows the working behind every figure on the site: how a prompt becomes watt-hours, watt-hours become grams of CO₂e and millilitres of water, and how the same workload is priced under a licence versus the raw API. Each section ends with a worked example you can redo by hand, every claim carries a numbered link to the source list (§14), and every value carries a confidence tag: SOURCED DERIVED VERIFY ASSUMPTION

← mmurr.ai

§1Units & first principles

Everything on this site reduces to one chain: work in → electricity used → by-products out. Four quantities carry the whole story.

1 prompt a question + answer T tokens ≈1,500 default E energy (Wh) the pivot quantity CO₂e (g) × grid intensity Water (mL) × WUE Cost (£) tokens × $/1M, or seats + embodied (§10–11)
Fig. 1 — the conversion pipeline. Energy is the pivot: get E right and carbon and water follow by multiplication. Cost forks earlier, at the token count.
QuantityUnitWhat it physically is
TokenA model's unit of text, ≈¾ of an English word. Both the prompt you send and the answer you get back are counted.
EnergyWh / kWh1 Wh = 3,600 J. A watt-hour is one watt for one hour; 1,000 Wh = 1 kWh — what a kettle draws in ~25 min.
CarbongCO₂eGrams of CO₂-equivalent: all greenhouse gases folded into one number via their 100-year warming potential.
WatermL / LConsumed water — evaporated in cooling, removed from immediate re-use. Not the same as water withdrawn and returned.

Two unit conversions do most of the work: Wh → kWh is ÷1,000, and grid intensity is quoted in kgCO₂e per kWh, so per-prompt carbon comes out in grams almost automatically. If a number ever looks wildly wrong, check the ÷1,000 first — it is where everyone slips.

§2The standard prompt

To compare models, licences and vendors like for like, the site defines one standardised unit of work and prices/footprints everything against it.

Tprompt=1,500 tokenscontext + question (~1,200)+answer (~300) ASSUMPTION

Vendors publish no canonical prompt size. 1,500 is an editable anchor representing a business prompt with working context (a pasted email, some instructions). Every model is charged the same T, so relative comparisons hold even if the absolute level is off. Note Google's disclosed median consumer prompt is far smaller — §3 quantifies the gap.

Input and output tokens cost different amounts; the site blends them 50/50 into one rate:

pblend=( pin + pout )/2  [$ per 1M tokens]

Example: GPT-5.5 lists $5 in / $30 out[1]pblend = 17.5 SOURCED. A 50/50 blend overweights output for context-heavy work (real traffic is often ~70/30 in/out); the split is exposed on the AI Impact Calculator as a single global traffic-mix slider (default 50/50) so every model and licence is compared on the same mix. Moving it changes API cost by up to ~40% — revisited in §13.

Honest caveat
Reasoning models bill their hidden "thinking" tokens as output. A 300-token visible answer can carry thousands of invisible billed tokens. The standard prompt does not model this — it is the main reason real API bills exceed this page's estimates for "thinking" model classes.

§3Energy per prompt — and the PUE double-count trap

Per-prompt energy is the most consequential input on the site, and the one where measurement quality varies most between vendors.

What the vendors actually disclose

ServiceWh / promptBasisConfidence
Gemini (Google)0.24Median Apps text prompt, in-production measurement, all-in facility (active silicon alone: 0.10)[3]SOURCED
Copilot (Microsoft)0.31Production disclosure, Jun 2026: median 0.31, range 0.16–0.60[2]SOURCED
ChatGPT (OpenAI)0.34Stated "average query" in a blog post; methodology unpublished, no range, no basis given[4]VERIFY
Anthropic / xAI / Mistral0.25–0.6No vendor figures exist — labelled per-model assumptions scaled by model classASSUMPTION

On the OpenAI figure, contested: 0.34 Wh has never been substantiated — no methodology, no percentile, no facility boundary. It is retained because it is the only first-party number OpenAI has published and it sits plausibly between Google's and Microsoft's measured medians, but it should be treated as a soft anchor, not a measurement. If Microsoft's disclosed range (0.16–0.60) is representative of production LLM serving generally, any single-point vendor claim inside that band is unfalsifiable anyway.

Why PUE is set to 1.0 (deliberate, not an error)

PUE=Efacility/EIT  (hyperscale fleets ≈ 1.09–1.20 · global all-facility average ≈ 1.56[13])

Google's 0.24 Wh is already an all-in facility measurement — cooling and overhead are inside it. Multiplying it by a PUE > 1 would count the cooling twice. So the site holds PUE at 1.0 for per-prompt figures, and only applies PUE > 1 in the facility model (§10), where the input is IT capacity rather than a measured all-in figure. If you ever swap in an IT-only per-prompt number, raise PUE with it — the two must move together.

Per-token cross-check (and where it doesn't reconcile)

etok=Eprompt/Tprompt0.31 Wh / 1,500 tok=0.21 Wh per 1k tokens
Honest caveat
The dashboard's per-token factor (0.70 Wh/1k, aligned to Gemini) implies a much smaller median prompt: 0.24 Wh ÷ 0.70 Wh/1k ≈ 343 tokens. Plausible — most real prompts are short — but it means the per-prompt and per-token bases do not reconcile under the 1,500-token standard prompt. They are two internally consistent frames, not one. Use per-prompt figures for personal-usage questions, per-token for API-metered workloads, and never mix them in one calculation.
Worked example · W3energy for one user-month of Copilot
  1. Eprompt=0.31 Wh
    Microsoft median, all-in facility basis[2]
  2. prompts/month=20 ppd × 22 workdays=440
  3. Emonth=440 × 0.31=136.4 Wh=0.136 kWh
  4. ≈ 0.14 kWh / user / month
    Roughly one kettle boil every two months. The per-user story is genuinely small; the aggregate story (§10) is not.

§4Carbon — and the T&D losses toggle

Carbon is energy times the grid. One multiplication — the intellectual content is in which grid factor you're allowed to use.

mCO₂e=E [kWh]×( Igrid + IT&D )×( 1 + uemb )

Igrid — UK 0.177 kgCO₂e/kWh (DESNZ/Defra 2025 location-based, down ~14.5% on 2024's 0.207)[5] SOURCED · US 0.36 (EPA eGRID 2023 Rev 2 national output rate; 2024 preliminary ≈ −1.8%)[6] SOURCED · EU 0.19 (EEA 2024 early estimate: −9% on 2023's ≈0.213)[7] SOURCED.
IT&D — transmission & distribution losses, UK ≈ 0.0185 kgCO₂e/kWh (~+10.5%)[5] SOURCED — controlled by the toggle below, off by default.
uemb — optional embodied uplift for hardware manufacturing, default 0.15 (10–25%)[22] ASSUMPTION.

carbon figures below: generation only

The electricity a data centre meters was generated somewhere else; ~7–8% of it is lost as heat in the wires getting there. Grid-average accounting attributes those losses to the consumer. With the toggle on, every dotted-underlined carbon figure on this page switches from the generation-only factor (0.177) to the delivered-energy factor (0.1955) — a uniform +10.5%. The live site should offer the same switch; the honest default is off with a visible label, since DESNZ publishes them as separate line items and most public comparisons quote generation-only.

Location-based vs market-based — the accounting fork

The site uses location-based intensity: the physical average of the grid where the electricity is drawn. Vendors' own reports typically use market-based accounting, where purchased renewable certificates net emissions down — sometimes dramatically (one academic analysis puts a major hyperscaler's 2024 footprint at ~25 Mt location-based vs ~15.5 Mt reported market-based[24]). Neither is wrong; they answer different questions. Location-based answers "what did the grid actually emit because of this load?" — the right frame for a footprint calculator. This page states its basis wherever a carbon figure appears.

Worked example · W4carbon for one prompt, and one user-month · responds to the T&D toggle
  1. one prompt:0.31 Wh=0.00031 kWh
  2. m=0.00031 × 0.177=0.055 g CO₂e
  3. user-month:0.136 kWh × 0.177=24.1 g CO₂e
  4. 1,000 seats ≈ 24.1 kg CO₂e / month
    Operational only, UK grid, no uplift. With the 15% lifecycle uplift: ≈ 27.7 kg.

§5Water

Same shape as carbon — energy times an intensity factor — but the factor spans a 10× range depending on climate and cooling technology, so the choice of default matters more than anywhere else on the site.

Vwater=E [kWh]×WUE [L/kWh]

WUE — Water Usage Effectiveness (The Green Grid): litres consumed per kWh of IT energy.

What "consumed" actually means — following the water

A common mental model: the heat load needs X litres flowing past the servers; some fraction of that flow evaporates in a cooling tower and is topped up. That is right in shape for evaporative systems, with three refinements that change the numbers:

1 — It is a recirculating loop, not a once-through flow. The water "flowing past" is reused continuously; only ~1–2% of the circulating flow evaporates per pass through the tower (roughly 1% per 5–6 °C of cooling range). Consumption is set by the heat rejected, not the flow rate: evaporating one litre removes ~0.63 kWh of heat, which is why a fully evaporative facility sits near 1.6 L per kWh of heat rejected — the physics floor beneath the 1.8–1.9 WUE average.

2 — Top-up exceeds evaporation. As pure water evaporates, dissolved solids concentrate in the loop, so the tower must bleed off concentrated water ("blowdown") and take in more make-up than was evaporated. At typical cycles of concentration (3–6), make-up ≈ evaporation × CoC/(CoC−1), i.e. ~20–50% above the evaporated volume. Evaporation is consumed (leaves the catchment as vapour); blowdown is withdrawn and returned (to sewer/drain) — the WUE metric counts the consumption, which is why "withdrawal" headlines can read several times higher than WUE-based figures for the same site.

3 — Many facilities barely use this loop at all. Air-cooled chillers, dry coolers and closed-loop liquid cooling reject heat without evaporation — trading water for electricity (a higher PUE). UK-climate facilities mostly run this way, drawing water only in heatwave peaks (hybrid/adiabatic assist)[11]. This water↔energy trade-off is the single most important design fork for the footprint.

Making L/kWh tangible. "Litres consumed per kWh of IT energy" means: for every kilowatt-hour the servers draw, this many litres end up as water vapour in the sky above the site. At the global evaporative average (1.9), one kWh of AI compute evaporates about two large water bottles; at the UK default (0.5), about a mug. Scaled to W3's 1,000-seat month (136 kWh): 68 L in the UK, ~259 L on the global figure — a few bathtubs either way. The per-prompt number really is three drops; the aggregate question is how many trillions of drops, and in whose catchment, in which month.

Choosing WUE is choosing a climate

ContextWUE (L/kWh)Source / note
Global evaporative-cooling average1.8–1.9Green Grid via EESI — the widely quoted "industry average"[9] SOURCED
European average (EED-reported)≈0.58WRc for MOSL (2026), from EU Energy Efficiency Directive filings[10] SOURCED
CNDCP target, new builds, cool climates0.40Climate Neutral Data Centre Pact — the UK qualifies[12] SOURCED
UK default used on this site0.50Midpoint of the two rows above; most English facilities use little or no water for cooling (POSTnote 762)[11] DERIVED
Vendor fleet disclosures0.02–1.52Microsoft Singapore 0.02 ↔ Arizona 1.52; Google fleet ≈1.1; AWS claims 0.15–0.19; newest closed-loop designs ≈ 0[2][14] VERIFY
Two things this number hides
1 · Off-site water. WUE counts cooling water at the facility. Generating the electricity (thermal-plant condensers) typically consumes several times more water upstream — adding it can triple-to-10× the total, depending on generation mix. The site reports on-site only, and says so.
2 · Peaks, not averages. The UK regulatory concern is that hybrid-cooled facilities draw water precisely during heatwaves — coinciding with peak domestic demand[10]. Annual-average WUE cannot show this. Facility water is a local, seasonal issue, not a national-average one.

The other two ways AI consumes water

On-site cooling (pathway 1, 0–1.9 L/kWh — what WUE measures, and the only pathway modelled on this site) is one of three. Pathway 2 is off-site: water consumed generating the electricity (thermal-plant condensers, hydro evaporation) — often several times the on-site figure, mix-dependent, and excluded as stated above. Pathway 3 is embodied: chips & construction — excluded, order-of-magnitude only.

On pathway 3: semiconductor fabrication is intensely water-hungry — ultra-pure water for wafer rinsing dominates, with industry figures of order several thousand gallons per finished 300 mm wafer and leading fabs consuming tens of millions of litres per day (much of it recycled at high rates). Construction adds mixing and curing water for concrete. Both are real, both are upstream scope-3-style burdens, and neither can honestly be divided into a per-prompt number today — which is why they appear here as context rather than in the calculator. VERIFY

Cross-check: Google discloses 0.26 mL per median Gemini prompt[3]. 0.26 mL ÷ 0.24 Wh = 1.08 L/kWh — matching their ~1.1 fleet WUE. The chain is internally consistent. ✓

Worked example · W5water for one prompt, UK vs global assumptions
  1. UK default:0.00031 kWh × 0.5=0.16 mL
    — three drops
  2. global evaporative:0.00031 × 1.9=0.59 mL
  3. 1,000 seats, month, UK:136.4 kWh × 0.5=68 L
  4. The same workload spans ~4× depending on where it runs.
    That spread is the finding, not a nuisance — location is a first-order control on AI's water footprint.

§6Everyday equivalences

Equivalences are division, dressed up. They exist to give grams a size, and each one imports its own assumptions — declared here.

dcar=mCO₂e/0.17 [kgCO₂e/km]·nphone=mCO₂e/0.0082 [kg/charge]

0.17 kg/km — UK average car, all fuel types, Defra 2025[5] SOURCED. A modern EV on the UK grid is ~4× lower; a 2010 diesel higher — "average car" is doing real work in that number.
8.2 g/charge — US EPA equivalencies, US grid[8] SOURCED. On the UK grid the same charge is ~half. Kept because the EPA figure is the recognised standard; labelled "(US grid)" on-site.

Physics of the car comparison — from rest, or rolling?
Rolling, warm, mid-journey. The 0.17 kg/km factor is a fleet average over full standardised drive cycles: total journey fuel ÷ total journey distance. It amortises accelerations, idling and the cold start across every kilometre — so "32 cm of driving" means 32 cm of an average car already warm and in motion on an average trip. It is a marginal-distance equivalence, not an event equivalence. Starting a cold engine specifically to move a car 32 cm would emit vastly more: cold-start enrichment and warm-up burn several grams of fuel (≈ tens of grams of CO₂) before the car has moved at all — two to three orders of magnitude above the 0.055 g being compared. The honest reading: a prompt adds as much CO₂ as extending an existing journey by ~32 cm. The same logic applies to every distance equivalence on the site.
Worked example · W6sizing one prompt · responds to the T&D toggle
  1. car:0.055 g ÷ 170 g/km32 cm of (in-motion) driving
  2. phone:0.055 ÷ 8.2=0.7% of one charge
  3. One prompt ≈ stretching an existing drive by a desk-length.
    Per-unit smallness × billions of units is the whole tension of this subject — §10 does the billions.

§7Licence vs API economics

The commercial question the site exists to ask: for the same workload, when does a flat per-seat licence beat metering the tokens raw?

The two cost functions

Cseat=N × pseat×( 1 − δ(N) )
CAPI=N × r × D × Tprompt×pblend / 10⁶×FX

N seats · pseat regional list £/seat/month (see §8 for how regional prices are set) · r prompts/user/day (default 20) · D workdays/month (22) · FX £ per $ (monthly reference series — §8) · δ(N) expected enterprise-agreement discount.

The EA discount model — piecewise-linear interpolation

Microsoft-style enterprise agreements discount ~15–30% at scale. Exact rates are confidential, so the site interpolates between editable anchors (1 seat → 0%, 1,000 → 10%, 5,000 → 20%, 10,000+ → 30%):

δ(N)=δi + ( δi+1 − δi )×( N − Ni ) / ( Ni+1 − Ni ) for N ∈ [Ni, Ni+1] ASSUMPTION

Self-checks the code runs: δ(5,000) = 20% exactly; δ floors at 30% beyond the last anchor; a manually entered contract rate overrides everything.

Break-even intensity

r*=pseat × ( 1 − δ )/( D × Tprompt × pblend / 10⁶ × FX )
Worked example · W71,000 Copilot seats, UK, GPT-5.5 underneath
  1. seat side: δ(1,000)=10%£24.70 × 0.9=£22.23Cseat = £22,230/mo
  2. API side, per user:20 × 22 × 1,500=660,000 tokens/mo
  3. 0.66 MTok × $17.5=$11.55× 0.78=£9.01CAPI = £9,010/mo
  4. r*=22.23 / (22 × 1,500 × 17.5 / 10⁶ × 0.78)=22.23 / 0.4505
  5. r* ≈ 49 prompts/user/day
    At the default 20 ppd the licence costs ~2.5× the raw tokens — the seat premium is the price of integration, governance and the bundle. When the flagship token price doubled (GPT-5.5, Apr 2026)[1], r* halved overnight: usage-billing risk now cuts both ways.
Reading the result
This is not a claim that any given firm overpays — enterprise licences bundle security, tenancy and app integration the raw API doesn't. The break-even is the honest yardstick for what that bundle costs, and for how the yardstick moves as token prices move.

§8FX & regional pricing — how a "£ price" actually gets made

Not all sterling prices are the same kind of number. Vendors use three distinct mechanisms, and the site now flags each product with which one applies.

ModeMechanismExamplesFX exposure
regional_listVendor sets a fixed local list price, repriced occasionallyM365 Copilot £24.70/seat[15]; ChatGPT Plus fixed ≈£20 incl VAT at UK checkout[16]None day-to-day; step-changes at vendor repricing
usd_fxBilled in USD; card/Stripe converts at point of sale; VAT addedClaude Pro: $20 + VAT, billed USD → lands ≈£19.50–£21.00 with the rate[16][17]Full — your bank's FX rate + 1–3% markup
usd_meteredAPI tokens, always USD per 1MAll API pricing[1]Full, continuous

So your "flat £20" Claude Pro is real but coincidental: Anthropic does not set a GBP price — $20 + 20% VAT at recent GBP/USD rates happens to land almost exactly on £20[17]. If sterling weakened 10%, your bill would rise; a Copilot seat would not (until Microsoft repriced). This asymmetry is itself a finding: seat licences carry hidden FX insurance; metered and USD-billed products do not.

The monthly FX reference series

£ cost at month m=$ price at m×FXm  FXm = ECB/BoE monthly reference GBP per USD

Rather than one hand-set FX anchor, the site's charts should convert each historical price point at the FX rate of that month, held in a small monthly series (js/data/fx-history.js, refreshed on the 1st of each month by the same GitHub Action that refreshes token prices). Two consequences worth showing: (1) the "true £ cost at the time" of API usage becomes honest — the 2023–2026 token-price decline partially reverses in £ terms whenever sterling weakens; (2) a small FX-attribution readout becomes possible: how much of this £ price change is the vendor, and how much is the currency? Decomposed as:

Δ£=Δ$ × FXnew+$old × ΔFX  (vendor effect + currency effect)

Implementation details are in the repo change notes; the data source is a free no-key reference-rate API (ECB rates via frankfurter.dev, cross-checked annually against Bank of England monthly averages). The current 0.78 anchor becomes the series' latest value rather than a constant.

§9Subscription capacity — the windows model

Personal plans (Claude Pro/Max, Google AI tiers) sell rolling usage windows, not tokens. The site converts them to a comparable daily token capacity.

nwin=⌊ 24 / ( hwindow + hgap ) ⌋⌊24 / (5+1)⌋=4 windows/day
Capday=nwin × Mwindow  [MTok/day at 100% usage] ASSUMPTION

Mwindow — estimated million tokens usable per window per plan (e.g. Claude Pro 0.5 → 2 MTok/day; Max 20× 10 → 40 MTok/day), scaled roughly with price[17]. Vendors publish no exact allowances; several now meter by compute credits whose token-equivalence varies with prompt complexity, and weekly caps can bind before the window arithmetic does. Treat plan-capacity numbers as order-of-magnitude — they exist so subscriptions can sit on the same chart as metered services at all.

§10Facility build-out — where the aggregate lives

The per-prompt numbers are small; the build-out is not. The facility model has four terms: one one-off, three recurring. The hardware term uses an industry per-MW anchor; the servers×mass alternative is discussed (and challenged) below.

Mconstruction=PMW × ccon  [tCO₂e, one-off]
Mhardware=PMW × hIT / R  [tCO₂e / yr, amortised]
Eannual=PMW × 1,000 × 8,760 × L × PUE [kWh/yr]·Mop=Eannual×Igrid / 1,000·V=Eannual×WUE

ccon — construction (core & shell) ≈ 200 tCO₂e/MW VERIFY, and genuinely contested: one LCA baseline gives 439 kgCO₂e/m² (≈380 t/MW at typical density)[21], Schneider's model puts core & shell at only ~6.6% of pre-operational scope 3[20], and Google reports construction <5% of total fleet emissions[22]. The honest statement: a one-off term of order 10² t/MW, small against lifetime totals. Show as a range on any slide.
hIT — IT hardware embodied ≈ 1,100 tCO₂e per MW of IT load (industry LCA range 750–1,500, CIBSE TM65-based assessment; servers dominate at ~920 kgCO₂e each, cooling plant 20–30%)[19] SOURCED range, DERIVED midpoint. A servers×mass method (1,000 servers × 2.5 t) gives 2,500 t/MW — above the industry range — because it applies Google's AI-accelerator server masses (1.8–3.3 t each[22]) at general-purpose densities. For AI-dense halls the per-MW figure likely runs above 1,500; for general halls below 1,000. Extending server life one year cuts cumulative embodied ~16%[20] — refresh cycle R is a live lever, not a constant.
R refresh 4 yr (3–5) · L load factor 0.8 ASSUMPTION — an upper-mid case; real fleets average lower · PUE 1.2 here because PMW is IT capacity (contrast §3) · 8,760 = hours/year.

Worked example · W10the UK's current fleet: 1.6 GW, defaults as above · responds to the T&D toggle
  1. construction:1,600 × 200=320 kt CO₂e, one-off
    (the shells — order-of-magnitude only)
  2. hardware:1,600 × 1,100 / 4=440 kt CO₂e / yr
    (amortised IT equipment on the per-MW anchor; the servers×mass method reads ~2× higher — see the challenge above)
  3. energy:1,600 × 1,000 kW × 8,760 h × 0.8=11.2 TWh(IT)×1.2=13.5 TWh/yr facility
  4. operational:13.5×10⁹ × 0.177 / 1,000=2.38 Mt CO₂e / yr
  5. water:13.5×10⁹ kWh × 0.5=6.7 bn L/yr
    (25.6 bn on the global-evap WUE — §5)
  6. 2.8 Mt CO₂e / yr total16.6 bn car-km
    Embodied ≈ 16% of the annual total on today's grid — and that share rises as the grid decarbonises. Sanity check: 13.5 TWh sits between NESO's 2023 estimate (~5 TWh) and its 2030 projection (~20 TWh)[25] — right decade, but the 0.8 load factor is doing heavy lifting; treat W10 as an upper-mid case, not central.

§11Mapping the model to Scope 1 / 2 / 3

The GHG Protocol's scopes are a routing table for the terms in §10 — useful because it lets the site's numbers line up against corporate disclosures.

ScopeWhat it isModel termWhat the disclosures say
1 — directBackup diesel generators, refrigerant leaksNot modelled — lifecycle studies put it at 0.2–0.5% of a data centre's total[20]Small but rising with the buildout — Google attributes its scope-1 growth to backup-generator fuel[14]. The local planning battleground.
2 — purchased electricityGrid power for IT + coolingMop = E × Igrid — 31–61% of lifecycle total depending on grid and vintage[20]Falling per-unit via clean-power purchases; watch the market- vs location-based fork (§4).
3 — value chainChip fabs, steel, concrete, construction, logisticsMconstruction + Mhardware (+ uemb)The dominant, growing term: 97% of Microsoft's reported footprint, +26% since 2020, while its scope 1+2 fell ~30%[15]; Google's scope 3 +22% year-on-year (2025)[14].

The synthesis: per-prompt operational energy is falling (0.9 → 0.31 Wh across the Copilot backend since 2023[2]) and operational emissions are the shrinking slice of the pie. The footprint is migrating upstream — into scope 3, into capex, into commodities. That is exactly the part of the model built from embodied terms, which is why "embodied share rises as the grid decarbonises" is the most forward-looking sentence on the site.

§12Minerals arithmetic

One transparent multiplication connects the capacity pipeline to commodity markets.

mCu=PMW × iCu8,000 MW × 27 t/MW216 kt copper DERIVED

iCu ≈ 27 t copper per MW of AI data-centre capacity (BloombergNEF; up to ~6% of capex)[18] VERIFY, applied to the UK's ~8 GW announced pipeline[23]. An illustration — intensity × pipeline — not a forecast: pipelines attrit, and intensity varies with design.

Context from the IEA[16b][16c] SOURCED: data-centre buildout adds ~+2% copper, +2% silicon, +3% rare-earths and +11% gallium to 2030 global demand (absolute: ~512 kt Cu, ~75 kt Si); >90% of refined aluminium, silicon, magnet rare-earths and gallium comes from three producers (China dominant, with Ga/Ge/Sb export restrictions since Dec 2024); and the copper mine pipeline points to a potential 30% supply shortfall by 2035. The AI buildout and the energy transition are bidding for the same metals.

§13Uncertainty, honestly

Not all inputs are equal. This is the rank order of what moves the answers, with the spread each input carries.

input plausible spread on the output it feeds (log scale →) construction embodied ~4–20× (contested LCAs, §10) WUE (facility water) ~10× (0.2 → 1.9 L/kWh) Wh per prompt ~4× (0.16 → 0.60 Wh, + model class) hardware embodied /MW ~2× (750 → 1,500 t/MW; more if AI-dense) grid intensity (region) ~2× (UK 0.18 ↔ US 0.36) token blend · prompt size · FX ~1.3–2× (cost only) Rule of thumb: anything downstream of an embodied-carbon input is order-of-magnitude; anything downstream of a price is ±20%.
Fig. 2 — sensitivity, ranked. Bar length ∝ log of the plausible multiplicative spread.

Standing challenges to the defaults (kept live on purpose)

DefaultThe challengeStatus
20 prompts/user/dayDeployment telemetry is scarce; heavy pilots report 5–40+. Break-even r* conveniently brackets this — which is why r* is reported, not a verdict.Editable; sensitivity shown
1,500-token promptGoogle's median consumer prompt implies ~343 tokens (§3); enterprise prompts with context run larger. The two frames are kept separate, never averaged.Documented tension
Load factor 0.8Fleet averages run lower; new builds ramp over years. W10 is an upper-mid case.Labelled in W10
OpenAI 0.34 WhUnverifiable single point (§3). Retained as the only first-party figure; treated as soft.VERIFY, contested
Construction 200 t/MWPublished bases disagree by an order of magnitude (§10). Small against lifetime totals either way.VERIFY, contested
Copper 27 t/MWSingle-analyst figure (BNEF via industry press); design-dependent. Used for illustration only.VERIFY

What the site knowingly does not model

· Training runs (all figures are inference-side) · reasoning-token inflation (§2) · off-site water (§5) · scope-1 diesel and refrigerants (§11) · "enabled emissions" from what AI is used for — absent from every disclosure, including the hyperscalers' own · pipeline attrition in §12's copper figure. FX and grid factors are dated reference values refreshed monthly/annually — never intraday feeds.

The design rule throughout: a labelled assumption beats a hidden one. Every default is editable in the UI precisely so a sceptical reader can replace it and watch the answer move.

§14Sources

Numbered as cited in the text. Anchor-linked: every [n] in the body jumps here; each entry links onward to the underlying source.

  1. OpenAI — API pricing (GPT-5.5: $5 in / $30 out per 1M tokens, Apr 2026). openai.com/api/pricing
  2. Microsoft — production LLM energy & water disclosure, 15 Jun 2026 (median 0.31 Wh/query, range 0.16–0.60; per-query water <0.5 mL for modern designs). blogs.microsoft.com
  3. Google Cloud — Measuring the environmental impact of AI inference, Aug 2025 (0.24 Wh, 0.03 gCO₂e, 0.26 mL per median Gemini Apps text prompt; all-in facility boundary). cloud.google.com/blog/…/measuring-the-environmental-impact-of-ai-inference
  4. Altman, S. — The Gentle Singularity, Jun 2025 (0.34 Wh "average query" claim; no methodology). blog.samaltman.com/the-gentle-singularity
  5. DESNZ / Defra — UK Government GHG Conversion Factors 2025 (electricity generated 0.177 kgCO₂e/kWh; T&D losses ≈0.0185; average car 0.17 kg/km). gov.uk/…/government-conversion-factors-for-company-reporting
  6. US EPA — eGRID 2023 Rev 2 (national output emission rate ≈0.36 kgCO₂e/kWh; 2024 preliminary ≈ −1.8%). epa.gov/egrid
  7. European Environment Agency — GHG emission intensity of electricity generation (2024 early estimate: −9% vs 2023; EU average ≈0.19 kgCO₂e/kWh). eea.europa.eu/…/greenhouse-gas-emission-intensity-of-1
  8. US EPA — Greenhouse Gas Equivalencies Calculator (smartphone charge ≈8.2 gCO₂e, US grid basis). epa.gov/energy/greenhouse-gas-equivalencies-calculator
  9. EESI — Data Centers and Water Consumption (Green Grid WUE metric; ~1.9 L/kWh evaporative-cooling average). eesi.org/articles/view/data-centers-and-water-consumption
  10. WRc for MOSL — Water Efficient Data Centres (2026): European average WUE ≈0.58 L/kWh from EED filings; summer peak-coincidence finding for England. mosl.co.uk
  11. UK Parliament POST — POSTnote 762, What are data centres and how sustainable are they? (most English facilities use little/no water cooling; PUE/WUE definitions; CNDCP 0.4 target). researchbriefings.files.parliament.uk/…/POST-PN-0762.pdf
  12. Climate Neutral Data Centre Pact — water target: WUE 0.4 L/kWh, new builds in cool climates. climateneutraldatacentre.net
  13. Uptime Institute — Global Data Center Survey 2024 (fleet-average PUE ≈1.56; hyperscale 1.1–1.2). uptimeinstitute.com
  14. Google — Environmental Report 2025 (scope 3 +22% YoY; scope-1 growth attributed to backup generators; fleet WUE ≈1.1; buildout "faster than the grid is decarbonizing"). sustainability.google/reports
  15. Microsoft — 2025 Environmental Sustainability Report (total +23.4% vs 2020; scope 3 = 97% of footprint, +26%; scope 1+2 −30%; 34 GW CFE contracted). microsoft.com/…/sustainability/report
  16. Vendor list pricing, UK: Microsoft 365 Copilot £24.70/seat list (held since Nov 2023; Business SKU $21 Dec 2025; premium-bundle inclusion Jul 2026); ChatGPT Plus fixed ≈£20 incl VAT at UK checkout. microsoft.com/en-gb/microsoft-365/copilot
  17. IEA — Energy and AI (2025): data-centre mineral demand to 2030 (+2% Cu, +2% Si, +3% REE, +11% Ga; 512 kt Cu, 75 kt Si; supply concentration). iea.org/reports/energy-and-ai
  18. IEA — Global Critical Minerals Outlook 2025 (potential 30% copper supply shortfall by 2035; China Ga/Ge/Sb export restrictions Dec 2024). iea.org/reports/global-critical-minerals-outlook-2025
  19. Anthropic — plans & pricing (Claude Pro $20/mo + tax, billed USD; annual ≈$17/mo; Max $100/$200; Team $25–$125/seat; Enterprise seat + usage at API rates). UK landed cost £19.50–£21.00 with FX and VAT. claude.com/pricing
  20. BloombergNEF (via Marsh / Canadian Mining Journal) — ≈27 t copper per MW of AI data-centre capacity; up to ~6% of capex. canadianminingjournal.com/…/the-ai-boom-beneath-our-feet
  21. ADW Developments — Embodied Carbon in Enterprise Data Centre IT Equipment (CIBSE TM65 / iMasons-based; 750–1,500 tCO₂e per MW IT load; servers ≈920 kgCO₂e each; cooling 20–30%). adwdevelopments.com/…/embodied-carbon-in-enterprise-data-centre-it-equipment
  22. Schneider Electric — Demystifying data center scope 3 carbon (scope 1 = 0.2–0.5%, scope 2 = 31–61% of lifecycle; core & shell ≈6.6% of pre-operational scope 3; +1 yr server life → −16% cumulative embodied). blog.se.com/…/demystifying-data-center-scope-3-carbon
  23. Bux et al. (2025) — data-centre LCA (core & shell baseline 439 kgCO₂e/m²), and the surrounding expert-assessment literature noting construction is <5% of fleet totals in hyperscaler studies. arxiv.org/abs/2512.11863
  24. Google — Life-Cycle Emissions of AI Hardware (2025): AI-accelerator server embodied 1.8–3.3 tCO₂e; embodied uplift context; construction <5% of TPU-fleet totals. arxiv.org/abs/2502.01671
  25. Computer Weekly / Barbour ABI — UK data-centre capacity series (≈1.6 GW operational 2024 at ~190 sites; ~8 GW pipeline; 4.9 GW consented by 2030; DSIT 6 GW AI-capable target). Note Oxford Economics' IT-power method gives 2.9 GW current — methodology, not contradiction. computerweekly.com
  26. Papaevangelou & Vogiatzoglou (2026) — analysis of big-tech 2025 sustainability reports (location- vs market-based gap: Microsoft ~25.2 vs 15.5 Mt; Google ~23.4 vs 15.2 Mt; "enabled emissions" absent from all disclosures). policyreview.info/…/big-techs-2025-sustainability-reports
  27. NESO — data-centre demand projections (~5 TWh 2023; ~20 TWh and ~5.2 GW connected by 2030; connection requests >70 GW). neso.energy