# Methodology

*Last reviewed: 2026-07-22. Changes are listed in the
[changelog](#changelog) at the bottom of this page.*

LowRouter estimates the carbon footprint of every inference request
using the formula and data sources described on this page. This is
the reference document; the numbers on the dashboard, the model
browser, and the API responses all come from it.

## What we report

Two numbers per request:

- **Energy** in watt-hours (Wh).
- **Carbon** in grams of CO₂ equivalent (gCO₂e).

The carbon number is also normalised to **gCO₂e per 1,000 tokens** so
requests of different sizes are comparable.

## The formula

```
energy_wh   = ((α × P_active) + β) × tokens
carbon_g    = energy_wh × PUE × grid_intensity_g_per_kwh / 1000
```

Where:

- **`P_active`** — number of active parameters during inference, in
  billions. For dense models this is the parameter count; for
  Mixture-of-Experts (MoE) models it's the parameters activated per
  token, not the total count.
- **`α`** = 8.91 × 10⁻⁵ Wh per output-token-billion-param.
- **`β`** = 1.43 × 10⁻³ Wh constant overhead per output token.
- **`tokens`** — total tokens for the request (`prompt_tokens +
  completion_tokens`).
- **`PUE`** = 1.20 — data-center Power Usage Effectiveness, the
  overhead for cooling and power distribution on top of the compute
  energy itself. Applied to every request.
- **`grid_intensity_g_per_kwh`** — annual-average carbon intensity of
  the electricity grid in the region serving the request.

The `/ 1000` in the carbon line is the Wh → kWh conversion: energy is
carried in Wh (EcoLogits' native unit) while grid intensity is
published per kWh.

The energy formula is the
[EcoLogits v0.4 inference model](https://ecologits.ai/0.4/methodology/llm_inference/).
The grid-intensity values are Ember Climate annual country averages,
replaced by regional grid-operator data where a supported operator
publishes it — see [data sources](data-sources).

## Why this formula

The EcoLogits model is published, peer-reviewed in spirit if not
fully formally, and reproducible from public model parameter counts.
It is not the only credible estimate but it is the one with the
clearest derivation and the most active maintenance. Adopting it lets
us compare numbers across providers using the same yardstick rather
than reconciling each provider's bespoke estimate.

## Confidence bands

Every estimate carries one of three labels:

| Band | When |
|------|------|
| `accurate` | Model size verified by the provider or in the EcoLogits registry; recent grid data. |
| `medium` | Model size from a credible third party (research paper, well-supported leak); grid data current. |
| `gross` | Model size estimated from the model name or industry rumour; or grid data older than 12 months. |

These bands are about *uncertainty in the inputs*, not about whether
the formula itself is right. The formula has its own model-class
limits documented on the [limits page](limits).

The bands are **ordinal, not quantified**: `accurate` rests on
better-grounded inputs than `medium`, which is better-grounded than
`gross`. We deliberately do **not** publish a percentage error for
each band. We have not run a validation study against measured
energy consumption, and we are not willing to attach a number to a
carbon figure without one — an invented error bar reads as a measured
one. The dominant source of error is the model's active-parameter
count, which enters the formula multiplicatively and asymmetrically,
so a symmetric ± would misrepresent it even if we had measured it.

When the band is `gross`, the dashboard widgets that aggregate carbon
across many requests show a reduced-confidence indicator and link
back to this page.

## Methodology versioning

Every estimate stores the `methodology_version` that produced it
(see [per-request metadata](../models/per-request-metadata)). The
version captures:

- The values of α and β.
- The grid-intensity dataset version (Ember Climate country averages
  plus regional grid-operator data — see [data sources](data-sources)).
- The model parameter-count dataset version.

When any of these change, the version is bumped and the change is
noted in the dashboard's footer with the date. Old generations are
*not* retroactively recomputed — their `methodology_version` is the
one in effect when the request was served.

## Worked example

A request:

- Resolved model: `openai/openai/gpt-4o-mini`.
- Active parameters: 8B (this is the value we use; the provider has
  not officially confirmed it, so the band is `medium`).
- Total tokens: 200.
- Provider region: `eu-west`.
- Grid intensity: 270 gCO₂e/kWh (Ember 2024 EU average).

The EcoLogits v0.4 coefficients are in **watt-hours per output
token**, and that is the unit energy is stored and reported in — no
conversion sits between the published formula and `energy_wh`:

```
energy_wh_per_token  = (α × P_active) + β
                     = (8.91e-5 × 8) + 1.43e-3   = 0.002143 Wh/token
energy_wh            = 0.002143 × 200            = 0.43 Wh
carbon_g             = 0.43 × 1.20 × 270 / 1000  = 0.139 g
carbon_per_1k_tokens = 0.139 × (1000 / 200)      = 0.70 g
```

So a 200-token completion on `gpt-4o-mini` from `eu-west` is
estimated at **0.43 Wh** and **~0.14 gCO₂e**, with `medium`
confidence. These are the numbers your `eco` block would carry.

If you find a discrepancy between this worked example and what the
gateway returns, the gateway is the source of truth — please file an
issue so we can fix the documentation.

## Everyday equivalences

The dashboard and model pages translate a measured gCO₂e figure into
everyday terms — kilometres driven, phone charges, tree-days. These are
**illustrative framing, not part of the estimate**. Each one divides the
measured emissions by a single published factor:

| Equivalent | Factor | Source |
|------------|--------|--------|
| Phone charge | **12.4 gCO₂e** per full smartphone charge | [US EPA Greenhouse Gas Equivalencies Calculator](https://www.epa.gov/energy/greenhouse-gas-equivalencies-calculator-calculations-and-references) |
| Car travel | **106.7 gCO₂e** per kilometre | [European Environment Agency](https://www.eea.europa.eu/en/analysis/indicators/co2-performance-of-new-passenger) |
| Tree uptake | **60.3 gCO₂** per tree-day | [European Environment Agency](https://www.eea.europa.eu/articles/forests-health-and-climate-change) |

```
phone_charges = carbon_g / 12.4
car_km        = carbon_g / 106.7
tree_days     = carbon_g / 60.3
tree_years    = tree_days / 365
```

Some surfaces show **tree-years** (or `trees/yr`) instead of tree-days;
those divide the tree-day count by 365 at the same per-day factor, so
both readings trace back to the one published number.

### What each factor is, precisely

- **Phone charge — 12.4 gCO₂e.** The EPA calculator's figure
  (1.24 × 10⁻⁵ metric tons per charge). Its derivation: a charge draws
  `28.446 Wh − (22 h × 0.411 W) = 19.404 Wh`, which at the 2022 US
  national weighted average rate for delivered electricity
  (1,405.3 lb CO₂/MWh, including transmission and distribution losses)
  gives 12.4 gCO₂e. The EPA page displays the energy rounded to
  0.019 kWh but carries the unrounded value through; using the rounded
  figure yields 12.1 g, so we quote the unrounded one to keep the
  arithmetic reproducible. This is a **US grid** number; the same charge
  on a lower-carbon grid emits less. We use it because it is the most
  clearly documented per-charge figure available, not because US grid
  intensity is representative of our routing.

- **Car travel — 106.7 gCO₂e/km.** The EEA's average for passenger cars
  **newly registered in the EU in 2024**. Two caveats a citing reader
  should know: it covers new registrations rather than the whole on-road
  fleet (older cars in service emit more), and type-approval values are
  known to understate real-world emissions — the ICCT has documented a
  widening gap, most sharply for plug-in hybrids. Treat this as a
  conservative floor, not a fleet-wide figure.

- **Tree uptake — 60.3 gCO₂/day.** Derived from the EEA's statement
  that a mature tree takes up roughly 22 kg of CO₂ per year
  (22,000 ÷ 365). This is the weakest-sourced of the three: it is a
  widely-repeated rule of thumb rather than a result traceable to a
  specific field study, and real uptake varies substantially by species,
  age, and site. We keep it because it is the figure the public
  conversation uses, and we flag it rather than dressing it up.

The factors live in one place in the codebase
(`frontend/src/utils/carbonEquivalents.ts`) and this page is checked
against that module by a test, so the numbers here and the numbers on
the dashboard cannot drift apart.

## The full picture

Read the [data sources](data-sources) page next for where each number
in the formula comes from. The
[limits](limits) page lists what we explicitly do not claim.

## Changelog

- **2026-08-19** — Everyday equivalence factors published with their
  sources for the first time (#438). Two of the three were corrected in
  the process: the phone-charge factor moved from 8.22 g to the EPA's
  documented 12.4 g, and the car factor from 171 g/km to the EEA's
  106.7 g/km for 2024 new registrations — the previous values did not
  match the bodies they were attributed to. The tree factor moved from
  57.5 to 60.3 gCO₂/day to match the EEA's 22 kg/year figure exactly.
  Displayed equivalences changed accordingly; the underlying emissions
  estimates did not. The dashboard's carbon unit toggle carried a
  separate, third set of factors (121 gCO₂/km, 21 kg/tree/year); it now
  reads the same published values, so every surface answers a given
  measurement identically.
- **2026-07-22** — Grid-intensity attribution corrected: country
  averages come from Ember Climate, refined by regional grid-operator
  data; the IEA figure is used for the global aggregate only. Worked
  example recomputed against the Ember 2024 EU average
  (270 gCO₂e/kWh, previously ~340).
- **2026-07-06** — API parameters, endpoints, and metadata field
  names corrected to match the backend (#279).
- **2026-04-29** — First published (#117).