{
  "$comment": "Machine-readable companion to https://valem.run/calculators/germany/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/germany/car-tax",
  "dataUrl": "https://valem.run/calculators/germany/car-tax.json",
  "license": {
    "name": "CC BY 4.0",
    "url": "https://creativecommons.org/licenses/by/4.0/",
    "attribution": "Germany car tax model by Valem (https://valem.run/calculators/germany/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/germany/car-tax/verify",
  "country": "germany",
  "countryName": "Germany",
  "formula": "car-tax",
  "formulaName": "Car tax",
  "title": "Kfz-Steuer Rechner — Germany car tax",
  "answer": "German annual car tax is a displacement charge per started 100 cm³ (€2 petrol, €9.50 diesel) plus a stepped CO₂ charge on every gram above 95 g/km.",
  "lang": "en",
  "currency": "EUR",
  "taxYear": "2025",
  "verification": {
    "claim": "internal-consistency",
    "statement": "The Valem engine reproduces this model's stated formula through 2 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": 2,
    "ratesAreIllustrative": false,
    "sourcesCheckedOn": "2026-08-02"
  },
  "sources": [
    {
      "label": "Zoll — Kraftfahrzeugsteuer",
      "url": "https://www.zoll.de/DE/Privatpersonen/Kraftfahrzeugsteuer/kraftfahrzeugsteuer_node.html",
      "checked": "2026-08-02"
    }
  ],
  "terminalOutput": "annualTax",
  "inputs": [
    {
      "name": "displacement",
      "type": "number",
      "label": "Engine displacement (cm³)",
      "minimum": 0
    },
    {
      "name": "co2",
      "type": "number",
      "label": "CO₂ emissions (g/km)",
      "minimum": 0
    },
    {
      "name": "diesel",
      "type": "boolean",
      "label": "Diesel (otherwise petrol)"
    }
  ],
  "outputs": [
    {
      "name": "displacementUnits",
      "type": "number",
      "formula": "$ceil(displacement / 100)"
    },
    {
      "name": "displacementTax",
      "type": "number",
      "label": "Displacement part",
      "format": "currency",
      "formula": "$round(displacementUnits * (diesel ? $const.dieselPer100 : $const.petrolPer100), 2)"
    },
    {
      "name": "co2Tax",
      "type": "number",
      "label": "CO₂ part (above 95 g/km)",
      "format": "currency",
      "formula": "($c := co2; $b1 := (($c < 115 ? $c : 115) - 95); $b1 := ($b1 > 0 ? $b1 : 0) * 2.00; $b2 := ($c > 115 ? (($c < 135 ? $c : 135) - 115) : 0) * 2.20; $b3 := ($c > 135 ? (($c < 155 ? $c : 155) - 135) : 0) * 2.50; $b4 := ($c > 155 ? (($c < 175 ? $c : 175) - 155) : 0) * 2.90; $b5 := ($c > 175 ? (($c < 195 ? $c : 195) - 175) : 0) * 3.40; $b6 := ($c > 195 ? ($c - 195) : 0) * 4.00; $round($b1 + $b2 + $b3 + $b4 + $b5 + $b6, 2))"
    },
    {
      "name": "annualTax",
      "type": "number",
      "label": "Annual tax",
      "format": "currency",
      "formula": "$round(displacementTax + co2Tax, 2)"
    }
  ],
  "testCases": [
    {
      "description": "C1 petrol 1,398 cm³, 122 g/km",
      "given": {
        "displacement": 1398,
        "co2": 122,
        "diesel": false
      },
      "expect": {
        "displacementUnits": 14,
        "displacementTax": 28,
        "co2Tax": 55.4,
        "annualTax": 83.4
      }
    },
    {
      "description": "C2 diesel 1,968 cm³, 145 g/km",
      "given": {
        "displacement": 1968,
        "co2": 145,
        "diesel": true
      },
      "expect": {
        "displacementUnits": 20,
        "displacementTax": 190,
        "co2Tax": 109,
        "annualTax": 299
      }
    }
  ],
  "spec": {
    "id": "car-tax-germany",
    "version": "1.0.0",
    "schema": {
      "type": "object",
      "properties": {
        "displacement": {
          "type": "number",
          "minimum": 0
        },
        "co2": {
          "type": "number",
          "minimum": 0
        },
        "diesel": {
          "type": "boolean"
        },
        "displacementUnits": {
          "type": "number",
          "readOnly": true
        },
        "displacementTax": {
          "type": "number",
          "readOnly": true
        },
        "co2Tax": {
          "type": "number",
          "readOnly": true
        },
        "annualTax": {
          "type": "number",
          "readOnly": true
        }
      }
    },
    "constants": {
      "petrolPer100": 2,
      "dieselPer100": 9.5,
      "co2Free": 95
    },
    "defaultValues": [
      {
        "path": "$",
        "expr": "{ 'displacement': 1398, 'co2': 122, 'diesel': false }"
      }
    ],
    "derivations": [
      {
        "path": "$.displacementUnits",
        "expr": "$ceil(displacement / 100)"
      },
      {
        "path": "$.displacementTax",
        "expr": "$round(displacementUnits * (diesel ? $const.dieselPer100 : $const.petrolPer100), 2)"
      },
      {
        "path": "$.co2Tax",
        "expr": "($c := co2; $b1 := (($c < 115 ? $c : 115) - 95); $b1 := ($b1 > 0 ? $b1 : 0) * 2.00; $b2 := ($c > 115 ? (($c < 135 ? $c : 135) - 115) : 0) * 2.20; $b3 := ($c > 135 ? (($c < 155 ? $c : 155) - 135) : 0) * 2.50; $b4 := ($c > 155 ? (($c < 175 ? $c : 175) - 155) : 0) * 2.90; $b5 := ($c > 175 ? (($c < 195 ? $c : 195) - 175) : 0) * 3.40; $b6 := ($c > 195 ? ($c - 195) : 0) * 4.00; $round($b1 + $b2 + $b3 + $b4 + $b5 + $b6, 2))"
      },
      {
        "path": "$.annualTax",
        "expr": "$round(displacementTax + co2Tax, 2)"
      }
    ],
    "constraints": [],
    "metaDerivations": [],
    "viewDefinition": {
      "renderer": "builtin",
      "defaultView": "main",
      "views": [
        {
          "id": "main",
          "label": "Kfz-Steuer",
          "layout": "vertical",
          "components": [
            {
              "id": "disp",
              "type": "numericField",
              "label": "Engine displacement (cm³)",
              "bind": "$.displacement"
            },
            {
              "id": "co2",
              "type": "numericField",
              "label": "CO₂ emissions (g/km)",
              "bind": "$.co2"
            },
            {
              "id": "diesel",
              "type": "checkboxField",
              "label": "Diesel (otherwise petrol)",
              "bind": "$.diesel"
            },
            {
              "id": "tiles",
              "type": "group",
              "layout": "horizontal",
              "components": [
                {
                  "id": "annualTile",
                  "type": "statTile",
                  "label": "Annual tax",
                  "bind": "$.annualTax",
                  "format": "currency",
                  "currency": "EUR"
                }
              ]
            },
            {
              "id": "sep1",
              "type": "separatorLine"
            },
            {
              "id": "breakdown",
              "type": "keyValueList",
              "label": "Breakdown",
              "items": [
                {
                  "label": "Displacement part",
                  "bind": "$.displacementTax",
                  "format": "currency",
                  "currency": "EUR"
                },
                {
                  "label": "CO₂ part (above 95 g/km)",
                  "bind": "$.co2Tax",
                  "format": "currency",
                  "currency": "EUR"
                },
                {
                  "label": "Annual tax",
                  "bind": "$.annualTax",
                  "format": "currency",
                  "currency": "EUR"
                }
              ]
            },
            {
              "id": "note",
              "type": "staticText",
              "text": "'Germany Kfz-Steuer (first registration from 1 Jul 2009): €2.00/started 100 cm³ petrol or €9.50 diesel, plus a stepped CO₂ charge above 95 g/km. Estimate, not tax advice.'"
            },
            {
              "id": "sources",
              "type": "sourceList",
              "label": "Sources",
              "items": [
                {
                  "label": "Zoll — Kraftfahrzeugsteuer",
                  "url": "https://www.zoll.de/DE/Privatpersonen/Kraftfahrzeugsteuer/kraftfahrzeugsteuer_node.html",
                  "date": "2026-08-02"
                }
              ]
            }
          ]
        }
      ]
    },
    "tests": [
      {
        "description": "C1 petrol 1,398 cm³, 122 g/km",
        "given": {
          "$.displacement": 1398,
          "$.co2": 122,
          "$.diesel": false
        },
        "expect": {
          "$.displacementUnits": 14,
          "$.displacementTax": 28,
          "$.co2Tax": 55.4,
          "$.annualTax": 83.4
        }
      },
      {
        "description": "C2 diesel 1,968 cm³, 145 g/km",
        "given": {
          "$.displacement": 1968,
          "$.co2": 145,
          "$.diesel": true
        },
        "expect": {
          "$.displacementUnits": 20,
          "$.displacementTax": 190,
          "$.co2Tax": 109,
          "$.annualTax": 299
        }
      }
    ]
  }
}