How the Luxembourg taxe véhicule calculator is verified
Inputs
| Input | Field | Type |
|---|---|---|
| CO₂ (g/km) | co2 | number |
| Diesel | diesel | boolean |
The formula
Each derived value below is computed by the Valem engine from the expression shown, in this order. Nothing else runs — there is no hidden code path.
| Derived value | Field | Formula (JSONata) |
|---|---|---|
| Multiplicateur carburant (b) | multiplicateur | diesel ? $const.bDiesel : $const.bAutre |
| Facteur exponentiel (c) | facteurExponentiel | ($e := co2; $over := $e - $const.seuil; $steps := $over > 0 ? $ceil($over / 10) : 0; $round($const.cBase + $const.cPas * $steps, 4)) |
| Taxe calculée | taxeCalculee | $round(co2 * multiplicateur * facteurExponentiel, 2) |
| Taxe annuelle | tax | $round(taxeCalculee > $const.minimum ? taxeCalculee : $const.minimum, 2) |
Rates and thresholds
The expressions above read these as $const. They are the figures the annual refresh replaces, so they live as data rather than being written into the formulas — which is what makes a year-on-year change a one-line diff instead of an edit to arithmetic.
| Constant | Value |
|---|---|
bDiesel | 0.9 |
bAutre | 0.6 |
cBase | 0.5 |
cPas | 0.1 |
seuil | 90 |
minimum | 30 |
Test vectors (3)
Every case is executed against this model on each build, by the Java engine and independently by a JavaScript one. A mismatch of a single cent fails the build, so the page cannot ship advertising a figure the model no longer produces.
Case 1 — C1 essence à 120 g/km — 120 x 0,6 x 0,8
given co2 | 120 |
|---|---|
given diesel | no |
expect multiplicateur | 0.6 |
expect facteurExponentiel | 0.8 |
expect taxeCalculee | 57.6 |
expect tax | 57.6 |
Case 2 — C2 diesel à 150 g/km — multiplicateur 0,9 et facteur 1,1
given co2 | 150 |
|---|---|
given diesel | yes |
expect multiplicateur | 0.9 |
expect facteurExponentiel | 1.1 |
expect tax | 148.5 |
Case 3 — C3 véhicule très peu émetteur — le minimum de 30 EUR s’applique
given co2 | 50 |
|---|---|
given diesel | no |
expect facteurExponentiel | 0.5 |
expect taxeCalculee | 15 |
expect tax | 30 |
Sources
- Guichet.lu — taxe véhicules · checked 2026-08-05
Check it yourself — and reuse it
The whole model as JSON — inputs, outputs, formulas, vectors and sources in one re-runnable document.
This model is published under CC BY 4.0: use it, adapt it, build on it, with attribution. The licence covers the model — the expression of each rule and the arrangement of the catalog. The rates and thresholds are law, and nobody licenses those; the sources above are where they come from.
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