Methodology

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 × 1000
carbon_g    = energy_wh × 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 kWh per output-token-billion-param.
• β = 1.43 × 10⁻³ kWh constant overhead per output token.
• tokens — total tokens for the request (prompt_tokens + completion_tokens).
• grid_intensity_g_per_kwh — annual-average carbon intensity of the electricity grid in the region serving the request.

The energy formula is the EcoLogits v0.4 inference model. The grid-intensity values come from the International Energy Agency.

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 IEA grid-intensity dataset year.
• 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/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: ~340 gCO₂e/kWh (IEA EU average).

Energy:

energy_wh = ((8.91e-5 × 8) + 1.43e-3) × 200 × 1000
          = (7.13e-4 + 1.43e-3) × 200 × 1000
          = 2.143e-3 × 200 × 1000
          = 0.4286 Wh

Wait — this needs careful unit handling. The EcoLogits formula’s α is per-token, β is per-token; we multiply by total tokens to get the total energy in kWh, then convert.

Re-doing with explicit units:

energy_per_token_kwh = (8.91e-5 × 8) + 1.43e-3   = 0.002143 kWh/token
energy_kwh           = 0.002143 × 200            = 0.4286 kWh   <-- too high

The EcoLogits coefficients in the published v0.4 are in watt-hours per output token, not kWh. The formula as we apply it is:

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
energy_kwh           = 0.43 / 1000               = 4.3e-4 kWh
carbon_g             = 4.3e-4 × 340              = 0.146 g
carbon_per_1k_tokens = 0.146 × (1000 / 200)      = 0.73 g

So a 200-token completion on gpt-4o-mini from eu-west is estimated at 0.43 Wh and ~0.15 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.