{
  "$comment": "Machine-readable companion to https://valem.run/calculators/luxembourg/car-tax. Formula, inputs, outputs, engine-verified test vectors, cited sources and the re-runnable Valem ModelSpec behind the page.",
  "url": "https://valem.run/calculators/luxembourg/car-tax",
  "dataUrl": "https://valem.run/calculators/luxembourg/car-tax.json",
  "license": {
    "name": "CC BY 4.0",
    "url": "https://creativecommons.org/licenses/by/4.0/",
    "attribution": "Luxembourg taxe véhicule model by Valem (https://valem.run/calculators/luxembourg/car-tax), CC BY 4.0.",
    "note": "Covers the model — the expression of each rule and the arrangement of the catalog. The rates and thresholds themselves are law and are not licensed by anyone; the cited sources are where they come from."
  },
  "verificationUrl": "https://valem.run/calculators/luxembourg/car-tax/verify",
  "country": "luxembourg",
  "countryName": "Luxembourg",
  "formula": "car-tax",
  "formulaName": "Taxe véhicule",
  "title": "Taxe sur les Véhicules — Luxembourg car tax",
  "answer": "Luxembourg's annual vehicle tax scales with CO2 emissions and fuel type.",
  "lang": "en",
  "currency": "EUR",
  "taxYear": "2026",
  "verification": {
    "claim": "internal-consistency",
    "statement": "The Valem engine reproduces this model's stated formula through 3 self-test cases (below, and re-runnable against the spec). That asserts internal consistency, NOT that the formula matches current law — the cited sources are the evidence for that, and carry the date each was last checked.",
    "selfTestCases": 3,
    "ratesAreIllustrative": false,
    "sourcesCheckedOn": "2026-08-02"
  },
  "sources": [
    {
      "label": "Guichet.lu — taxe véhicules",
      "url": "https://guichet.public.lu",
      "checked": "2026-08-05"
    }
  ],
  "terminalOutput": "tax",
  "inputs": [
    {
      "name": "co2",
      "type": "number",
      "label": "CO₂ (g/km)",
      "minimum": 0
    },
    {
      "name": "diesel",
      "type": "boolean",
      "label": "Diesel"
    }
  ],
  "outputs": [
    {
      "name": "multiplicateur",
      "type": "number",
      "label": "Multiplicateur carburant (b)",
      "formula": "diesel ? $const.bDiesel : $const.bAutre"
    },
    {
      "name": "facteurExponentiel",
      "type": "number",
      "label": "Facteur exponentiel (c)",
      "formula": "($e := co2; $over := $e - $const.seuil; $steps := $over > 0 ? $ceil($over / 10) : 0; $round($const.cBase + $const.cPas * $steps, 4))"
    },
    {
      "name": "taxeCalculee",
      "type": "number",
      "label": "Taxe calculée",
      "format": "currency",
      "formula": "$round(co2 * multiplicateur * facteurExponentiel, 2)"
    },
    {
      "name": "tax",
      "type": "number",
      "label": "Taxe annuelle",
      "format": "currency",
      "formula": "$round(taxeCalculee > $const.minimum ? taxeCalculee : $const.minimum, 2)"
    }
  ],
  "testCases": [
    {
      "description": "C1 essence à 120 g/km — 120 x 0,6 x 0,8",
      "given": {
        "co2": 120,
        "diesel": false
      },
      "expect": {
        "multiplicateur": 0.6,
        "facteurExponentiel": 0.8,
        "taxeCalculee": 57.6,
        "tax": 57.6
      }
    },
    {
      "description": "C2 diesel à 150 g/km — multiplicateur 0,9 et facteur 1,1",
      "given": {
        "co2": 150,
        "diesel": true
      },
      "expect": {
        "multiplicateur": 0.9,
        "facteurExponentiel": 1.1,
        "tax": 148.5
      }
    },
    {
      "description": "C3 véhicule très peu émetteur — le minimum de 30 EUR s’applique",
      "given": {
        "co2": 50,
        "diesel": false
      },
      "expect": {
        "facteurExponentiel": 0.5,
        "taxeCalculee": 15,
        "tax": 30
      }
    }
  ],
  "spec": {
    "id": "car-tax-luxembourg",
    "version": "1.0.0",
    "schema": {
      "type": "object",
      "properties": {
        "co2": {
          "type": "number",
          "minimum": 0
        },
        "diesel": {
          "type": "boolean"
        },
        "multiplicateur": {
          "type": "number",
          "readOnly": true
        },
        "facteurExponentiel": {
          "type": "number",
          "readOnly": true
        },
        "taxeCalculee": {
          "type": "number",
          "readOnly": true
        },
        "tax": {
          "type": "number",
          "readOnly": true
        }
      }
    },
    "constants": {
      "bDiesel": 0.9,
      "bAutre": 0.6,
      "cBase": 0.5,
      "cPas": 0.1,
      "seuil": 90,
      "minimum": 30
    },
    "defaultValues": [
      {
        "path": "$",
        "expr": "{ 'co2': 120, 'diesel': false }"
      }
    ],
    "derivations": [
      {
        "path": "$.multiplicateur",
        "expr": "diesel ? $const.bDiesel : $const.bAutre"
      },
      {
        "path": "$.facteurExponentiel",
        "expr": "($e := co2; $over := $e - $const.seuil; $steps := $over > 0 ? $ceil($over / 10) : 0; $round($const.cBase + $const.cPas * $steps, 4))"
      },
      {
        "path": "$.taxeCalculee",
        "expr": "$round(co2 * multiplicateur * facteurExponentiel, 2)"
      },
      {
        "path": "$.tax",
        "expr": "$round(taxeCalculee > $const.minimum ? taxeCalculee : $const.minimum, 2)"
      }
    ],
    "constraints": [],
    "metaDerivations": [],
    "viewDefinition": {
      "renderer": "builtin",
      "defaultView": "main",
      "views": [
        {
          "id": "main",
          "label": "Taxe véhicule",
          "layout": "vertical",
          "components": [
            {
              "id": "co2",
              "type": "numericField",
              "label": "CO₂ (g/km)",
              "bind": "$.co2"
            },
            {
              "id": "diesel",
              "type": "checkboxField",
              "label": "Diesel",
              "bind": "$.diesel"
            },
            {
              "id": "tiles",
              "type": "group",
              "layout": "horizontal",
              "components": [
                {
                  "id": "taxTile",
                  "type": "statTile",
                  "label": "Taxe annuelle",
                  "bind": "$.tax",
                  "format": "currency",
                  "currency": "EUR"
                }
              ]
            },
            {
              "id": "breakdown",
              "type": "keyValueList",
              "label": "Calcul",
              "items": [
                {
                  "label": "CO2 (a)",
                  "bind": "$.co2"
                },
                {
                  "label": "Multiplicateur carburant (b)",
                  "bind": "$.multiplicateur"
                },
                {
                  "label": "Facteur exponentiel (c)",
                  "bind": "$.facteurExponentiel"
                },
                {
                  "label": "Taxe calculée",
                  "bind": "$.taxeCalculee",
                  "format": "currency",
                  "currency": "EUR"
                },
                {
                  "label": "Taxe due (minimum 30 EUR)",
                  "bind": "$.tax",
                  "format": "currency",
                  "currency": "EUR"
                }
              ]
            },
            {
              "id": "note",
              "type": "staticText",
              "text": "'Luxembourg 2026 : la taxe de circulation suit la formule officielle taxe = a x b x c, avec un minimum de 30 EUR. a est le taux de CO2 en g/km, b vaut 0,9 pour le diesel et 0,6 pour les autres carburants, et c part de 0,5 jusqu’à 90 g/km puis augmente de 0,10 par tranche de 10 g supplémentaires. Une essence à 120 g/km paie donc 120 x 0,6 x 0,8 = 57,60 EUR par an. Les véhicules 100% électriques paient le minimum. Estimation, pas un conseil fiscal.'"
            },
            {
              "id": "sources",
              "type": "sourceList",
              "label": "Sources",
              "items": [
                {
                  "label": "Guichet.lu — taxe véhicules",
                  "url": "https://guichet.public.lu",
                  "date": "2026-08-05"
                }
              ]
            }
          ]
        }
      ]
    },
    "tests": [
      {
        "description": "C1 essence à 120 g/km — 120 x 0,6 x 0,8",
        "given": {
          "$.co2": 120,
          "$.diesel": false
        },
        "expect": {
          "$.multiplicateur": 0.6,
          "$.facteurExponentiel": 0.8,
          "$.taxeCalculee": 57.6,
          "$.tax": 57.6
        }
      },
      {
        "description": "C2 diesel à 150 g/km — multiplicateur 0,9 et facteur 1,1",
        "given": {
          "$.co2": 150,
          "$.diesel": true
        },
        "expect": {
          "$.multiplicateur": 0.9,
          "$.facteurExponentiel": 1.1,
          "$.tax": 148.5
        }
      },
      {
        "description": "C3 véhicule très peu émetteur — le minimum de 30 EUR s’applique",
        "given": {
          "$.co2": 50,
          "$.diesel": false
        },
        "expect": {
          "$.facteurExponentiel": 0.5,
          "$.taxeCalculee": 15,
          "$.tax": 30
        }
      }
    ]
  }
}