Methodology

Last reviewed: 2026-07-22. Changes are listed in the 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. 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.

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:

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.

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). 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).
• 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.

The full picture

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

Changelog

• 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).