{
  "$comment": "Machine-readable companion to https://valem.run/calculators/luxembourg/vat. Formula, inputs, outputs, engine-verified test vectors, cited sources and the re-runnable Valem ModelSpec behind the page.",
  "url": "https://valem.run/calculators/luxembourg/vat",
  "dataUrl": "https://valem.run/calculators/luxembourg/vat.json",
  "license": {
    "name": "CC BY 4.0",
    "url": "https://creativecommons.org/licenses/by/4.0/",
    "attribution": "Luxembourg tva (vat) model by Valem (https://valem.run/calculators/luxembourg/vat), 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/vat/verify",
  "country": "luxembourg",
  "countryName": "Luxembourg",
  "formula": "vat",
  "formulaName": "TVA (VAT)",
  "title": "Calcul TVA Luxembourg 2026 — 17% / 14% / 8% / 3%",
  "answer": "Luxembourg TVA is 17%, the lowest standard rate in the European Union, with an intermédiaire rate of 14%, a réduit of 8% and a super-réduit of 3%.",
  "lang": "en",
  "currency": "EUR",
  "taxYear": "2026",
  "verification": {
    "claim": "internal-consistency",
    "statement": "The Valem engine reproduces this model's stated formula through 6 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": 6,
    "ratesAreIllustrative": false,
    "sourcesCheckedOn": "2026-10-05"
  },
  "sources": [
    {
      "label": "Administration de l enregistrement - loi TVA du 12 fevrier 1979, art. 39 (17% / 14% / 8% / 3%)",
      "url": "https://pfi.public.lu/dam-assets/pdf/legislation/tva/loi/loi-tva-2023-01-01.pdf",
      "checked": "2026-10-05"
    }
  ],
  "terminalOutput": "grossAmount",
  "headlineOutput": "vatAmount",
  "inputs": [
    {
      "name": "amount",
      "type": "number",
      "label": "Amount",
      "minimum": 0
    },
    {
      "name": "direction",
      "type": "string",
      "label": "Direction",
      "enum": [
        "add",
        "remove"
      ]
    },
    {
      "name": "category",
      "type": "string",
      "label": "What is being supplied",
      "enum": [
        "standard",
        "superReduced",
        "reduced1",
        "reduced2"
      ]
    },
    {
      "name": "reverseCharge",
      "type": "boolean",
      "label": "B2B reverse charge applies"
    }
  ],
  "outputs": [
    {
      "name": "rate",
      "type": "number",
      "formula": "category = 'reduced1' ? $const.reducedRate1 : category = 'reduced2' ? $const.reducedRate2 : category = 'superReduced' ? $const.superReducedRate : $const.standardRate"
    },
    {
      "name": "effectiveRate",
      "type": "number",
      "formula": "reverseCharge ? 0 : rate"
    },
    {
      "name": "netAmount",
      "type": "number",
      "formula": "direction = 'remove' ? $round(amount / (1 + effectiveRate), 2) : $round(amount, 2)"
    },
    {
      "name": "vatAmount",
      "type": "number",
      "formula": "$round(netAmount * effectiveRate, 2)"
    },
    {
      "name": "grossAmount",
      "type": "number",
      "formula": "$round(netAmount + vatAmount, 2)"
    }
  ],
  "testCases": [
    {
      "description": "S1 100.00 EUR net at the taux normal",
      "given": {
        "amount": 100,
        "direction": "add",
        "category": "standard",
        "reverseCharge": false
      },
      "expect": {
        "vatAmount": 17,
        "grossAmount": 117,
        "netAmount": 100
      }
    },
    {
      "description": "S2 117.00 EUR gross back to net at 17%",
      "given": {
        "amount": 117,
        "direction": "remove",
        "category": "standard",
        "reverseCharge": false
      },
      "expect": {
        "netAmount": 100,
        "vatAmount": 17
      }
    },
    {
      "description": "S3 100.00 EUR at the 14% taux intermediaire",
      "given": {
        "amount": 100,
        "direction": "add",
        "category": "reduced2",
        "reverseCharge": false
      },
      "expect": {
        "vatAmount": 14,
        "grossAmount": 114
      }
    },
    {
      "description": "S4 100.00 EUR at the 8% taux reduit",
      "given": {
        "amount": 100,
        "direction": "add",
        "category": "reduced1",
        "reverseCharge": false
      },
      "expect": {
        "vatAmount": 8,
        "grossAmount": 108
      }
    },
    {
      "description": "S5 100.00 EUR at the 3% taux super-reduit",
      "given": {
        "amount": 100,
        "direction": "add",
        "category": "superReduced",
        "reverseCharge": false
      },
      "expect": {
        "vatAmount": 3,
        "grossAmount": 103
      }
    },
    {
      "description": "S6 reverse charge: the supplier charges no TVA",
      "given": {
        "amount": 100,
        "direction": "add",
        "category": "standard",
        "reverseCharge": true
      },
      "expect": {
        "vatAmount": 0,
        "grossAmount": 100
      }
    }
  ],
  "spec": {
    "id": "vat-luxembourg",
    "version": "1.0.0",
    "schema": {
      "type": "object",
      "properties": {
        "amount": {
          "type": "number",
          "minimum": 0
        },
        "direction": {
          "type": "string",
          "enum": [
            "add",
            "remove"
          ]
        },
        "category": {
          "type": "string",
          "enum": [
            "standard",
            "superReduced",
            "reduced1",
            "reduced2"
          ]
        },
        "reverseCharge": {
          "type": "boolean"
        },
        "rate": {
          "type": "number",
          "readOnly": true
        },
        "effectiveRate": {
          "type": "number",
          "readOnly": true
        },
        "netAmount": {
          "type": "number",
          "readOnly": true
        },
        "vatAmount": {
          "type": "number",
          "readOnly": true
        },
        "grossAmount": {
          "type": "number",
          "readOnly": true
        }
      }
    },
    "constants": {
      "standardRate": 0.17,
      "superReducedRate": 0.03,
      "reducedRate1": 0.08,
      "reducedRate2": 0.14
    },
    "defaultValues": [
      {
        "path": "$",
        "expr": "{ 'amount': 100, 'direction': 'add', 'category': 'standard', 'reverseCharge': false }"
      }
    ],
    "derivations": [
      {
        "path": "$.rate",
        "expr": "category = 'reduced1' ? $const.reducedRate1 : category = 'reduced2' ? $const.reducedRate2 : category = 'superReduced' ? $const.superReducedRate : $const.standardRate"
      },
      {
        "path": "$.effectiveRate",
        "expr": "reverseCharge ? 0 : rate"
      },
      {
        "path": "$.netAmount",
        "expr": "direction = 'remove' ? $round(amount / (1 + effectiveRate), 2) : $round(amount, 2)"
      },
      {
        "path": "$.vatAmount",
        "expr": "$round(netAmount * effectiveRate, 2)"
      },
      {
        "path": "$.grossAmount",
        "expr": "$round(netAmount + vatAmount, 2)"
      }
    ],
    "constraints": [],
    "viewDefinition": {
      "renderer": "builtin",
      "defaultView": "main",
      "views": [
        {
          "id": "main",
          "label": "VAT",
          "layout": "vertical",
          "components": [
            {
              "id": "note",
              "type": "staticText",
              "text": "Four rates, and the LOWEST standard rate in the European Union at 17%. Which rate applies is decided by whether the supply appears in annexe A, B or C of the 1979 law, so the labels here give examples rather than reproducing the annexes. One caution if you are checking this against an older source: Luxembourg cut all three upper rates for the single year 2023 - normal 16%, intermediate 13%, reduced 7% - and the consolidated law still carries that derogation as a footnote scoped to \"l annee 2023\". It has expired; the standing article 39 figures are the ones above. This page covers the rate schedule only."
            },
            {
              "id": "inputs",
              "type": "fieldSet",
              "label": "Your figures",
              "components": [
                {
                  "id": "amount",
                  "type": "numericField",
                  "label": "Amount",
                  "bind": "$.amount",
                  "helperText": "Net amount when adding VAT, gross amount when removing it."
                },
                {
                  "id": "direction",
                  "type": "selectField",
                  "label": "Direction",
                  "bind": "$.direction",
                  "options": [
                    {
                      "value": "add",
                      "label": "Add VAT (net → gross)"
                    },
                    {
                      "value": "remove",
                      "label": "Remove VAT (gross → net)"
                    }
                  ]
                },
                {
                  "id": "category",
                  "type": "selectField",
                  "label": "What is being supplied",
                  "bind": "$.category",
                  "helperText": "The rate follows the category. Exports and intra-EU supplies are zero-rated or exempt — a different mechanism, not a rate you pick here.",
                  "options": [
                    {
                      "value": "standard",
                      "label": "Taux normal - 17%"
                    },
                    {
                      "value": "superReduced",
                      "label": "Taux super-reduit - 3% (annexe B: food, books, childrens clothing)"
                    },
                    {
                      "value": "reduced1",
                      "label": "Taux reduit - 8% (annexe A: gas, electricity, hairdressing, repairs)"
                    },
                    {
                      "value": "reduced2",
                      "label": "Taux intermediaire - 14% (annexe C: wine, advertising, custody)"
                    }
                  ]
                },
                {
                  "id": "reverseCharge",
                  "type": "checkboxField",
                  "label": "B2B reverse charge applies",
                  "bind": "$.reverseCharge",
                  "helperText": "The customer accounts for the VAT, so you charge none."
                }
              ]
            },
            {
              "id": "sep",
              "type": "separatorLine"
            },
            {
              "id": "vatTile",
              "type": "statTile",
              "label": "VAT",
              "value": "$.vatAmount"
            },
            {
              "id": "netTile",
              "type": "statTile",
              "label": "Net",
              "value": "$.netAmount"
            },
            {
              "id": "grossTile",
              "type": "statTile",
              "label": "Gross",
              "value": "$.grossAmount"
            },
            {
              "id": "breakdown",
              "type": "keyValueList",
              "label": "Detail",
              "items": [
                {
                  "label": "Rate applied",
                  "value": "$.effectiveRate"
                },
                {
                  "label": "Statutory rate for this category",
                  "value": "$.rate"
                }
              ]
            },
            {
              "id": "sources",
              "type": "sourceList",
              "label": "Sources",
              "layers": 1,
              "items": [
                {
                  "label": "Administration de l enregistrement - loi TVA du 12 fevrier 1979, art. 39 (17% / 14% / 8% / 3%)",
                  "url": "https://pfi.public.lu/dam-assets/pdf/legislation/tva/loi/loi-tva-2023-01-01.pdf",
                  "date": "2026-10-05",
                  "covers": [
                    "standardRate",
                    "reducedRate1",
                    "reducedRate2",
                    "superReducedRate"
                  ]
                }
              ]
            }
          ]
        }
      ]
    },
    "tests": [
      {
        "description": "S1 100.00 EUR net at the taux normal",
        "given": {
          "$.amount": 100,
          "$.direction": "add",
          "$.category": "standard",
          "$.reverseCharge": false
        },
        "expect": {
          "$.vatAmount": 17,
          "$.grossAmount": 117,
          "$.netAmount": 100
        }
      },
      {
        "description": "S2 117.00 EUR gross back to net at 17%",
        "given": {
          "$.amount": 117,
          "$.direction": "remove",
          "$.category": "standard",
          "$.reverseCharge": false
        },
        "expect": {
          "$.netAmount": 100,
          "$.vatAmount": 17
        }
      },
      {
        "description": "S3 100.00 EUR at the 14% taux intermediaire",
        "given": {
          "$.amount": 100,
          "$.direction": "add",
          "$.category": "reduced2",
          "$.reverseCharge": false
        },
        "expect": {
          "$.vatAmount": 14,
          "$.grossAmount": 114
        }
      },
      {
        "description": "S4 100.00 EUR at the 8% taux reduit",
        "given": {
          "$.amount": 100,
          "$.direction": "add",
          "$.category": "reduced1",
          "$.reverseCharge": false
        },
        "expect": {
          "$.vatAmount": 8,
          "$.grossAmount": 108
        }
      },
      {
        "description": "S5 100.00 EUR at the 3% taux super-reduit",
        "given": {
          "$.amount": 100,
          "$.direction": "add",
          "$.category": "superReduced",
          "$.reverseCharge": false
        },
        "expect": {
          "$.vatAmount": 3,
          "$.grossAmount": 103
        }
      },
      {
        "description": "S6 reverse charge: the supplier charges no TVA",
        "given": {
          "$.amount": 100,
          "$.direction": "add",
          "$.category": "standard",
          "$.reverseCharge": true
        },
        "expect": {
          "$.vatAmount": 0,
          "$.grossAmount": 100
        }
      }
    ]
  }
}