{
  "$comment": "Machine-readable companion to https://valem.run/calculators/luxembourg/holiday-entitlement. Formula, inputs, outputs, engine-verified test vectors, cited sources and the re-runnable Valem ModelSpec behind the page.",
  "url": "https://valem.run/calculators/luxembourg/holiday-entitlement",
  "dataUrl": "https://valem.run/calculators/luxembourg/holiday-entitlement.json",
  "license": {
    "name": "CC BY 4.0",
    "url": "https://creativecommons.org/licenses/by/4.0/",
    "attribution": "Luxembourg congé annuel model by Valem (https://valem.run/calculators/luxembourg/holiday-entitlement), 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/holiday-entitlement/verify",
  "country": "luxembourg",
  "countryName": "Luxembourg",
  "formula": "holiday-entitlement",
  "formulaName": "Congé Annuel",
  "title": "Congé Annuel Luxembourg 2026 — 26 Jours Ouvrables",
  "answer": "The legal annual leave is 26 jours ouvrables a year, regardless of the employee’s age, and it accrues at one twelfth per full month worked in the first year. A new employee must generally complete three months of uninterrupted work with the same employer before the accrued leave can be taken.",
  "lang": "en",
  "currency": "EUR",
  "taxYear": "2026",
  "verification": {
    "claim": "internal-consistency",
    "statement": "The Valem engine reproduces this model's stated formula through 9 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": 9,
    "ratesAreIllustrative": false,
    "sourcesCheckedOn": "2026-10-11"
  },
  "sources": [
    {
      "label": "Guichet.lu, Demander un congé légal annuel — guichet.public.lu (26 jours ouvrables a year regardless of age; a twelfth per full month in the first year; three months before the leave may be taken)",
      "url": "https://guichet.public.lu/fr/citoyens/travail/conges-jours-feries/annuel/conge-legal-annuel.html",
      "checked": "2026-10-11"
    },
    {
      "label": "Inspection du travail et des mines, D8a1 — itm.public.lu (the 26 days in force since 1 January 2019, raised from 25 by art. L. 233-4 of the Code du travail)",
      "url": "https://itm.public.lu/fr/questions-reponses/droit-travail/conges/a/a1.html",
      "checked": "2026-10-11"
    }
  ],
  "terminalOutput": "daysRemaining",
  "headlineOutput": "daysEntitled",
  "inputs": [
    {
      "name": "monthsWorked",
      "type": "number",
      "label": "Full months worked this year",
      "minimum": 0,
      "maximum": 12
    },
    {
      "name": "daysTaken",
      "type": "number",
      "label": "Days already taken",
      "minimum": 0
    }
  ],
  "outputs": [
    {
      "name": "daysEntitled",
      "type": "number",
      "formula": "($m := $clampFloorCap($floor($n(monthsWorked)), 0, $const.monthsPerYear); $round($const.annualWorkingDays * $m / $const.monthsPerYear, 1))"
    },
    {
      "name": "monthsUntilTakeable",
      "type": "number",
      "formula": "($r := $const.qualifyingMonths - $n(monthsWorked); $r < 0 ? 0 : $round($r, 1))"
    },
    {
      "name": "daysRemaining",
      "type": "number",
      "formula": "($r := daysEntitled - $n(daysTaken); $r < 0 ? 0 : $round($r, 1))"
    }
  ],
  "testCases": [
    {
      "description": "N1 a full year is 26 working days",
      "given": {
        "monthsWorked": 12,
        "daysTaken": 0
      },
      "expect": {
        "daysEntitled": 26,
        "monthsUntilTakeable": 0
      }
    },
    {
      "description": "N2 six full months accrue half",
      "given": {
        "monthsWorked": 6,
        "daysTaken": 0
      },
      "expect": {
        "daysEntitled": 13
      }
    },
    {
      "description": "N3 a twelfth per month, so one month is 2,2 days",
      "given": {
        "monthsWorked": 1,
        "daysTaken": 0
      },
      "expect": {
        "daysEntitled": 2.2
      }
    },
    {
      "description": "N4 a part month does not count — 1,9 months is one full month",
      "given": {
        "monthsWorked": 1.9,
        "daysTaken": 0
      },
      "expect": {
        "daysEntitled": 2.2
      }
    },
    {
      "description": "N5 at two months the leave has accrued but cannot be taken for another month",
      "given": {
        "monthsWorked": 2,
        "daysTaken": 0
      },
      "expect": {
        "daysEntitled": 4.3,
        "monthsUntilTakeable": 1
      }
    },
    {
      "description": "N6 at three months the waiting period is over",
      "given": {
        "monthsWorked": 3,
        "daysTaken": 0
      },
      "expect": {
        "daysEntitled": 6.5,
        "monthsUntilTakeable": 0
      }
    },
    {
      "description": "N7 no full month earns nothing",
      "given": {
        "monthsWorked": 0,
        "daysTaken": 0
      },
      "expect": {
        "daysEntitled": 0
      }
    },
    {
      "description": "N8 days already taken come off the remainder",
      "given": {
        "monthsWorked": 12,
        "daysTaken": 10
      },
      "expect": {
        "daysRemaining": 16
      }
    },
    {
      "description": "N9 taking more than the entitlement never goes negative",
      "given": {
        "monthsWorked": 12,
        "daysTaken": 40
      },
      "expect": {
        "daysRemaining": 0
      }
    }
  ],
  "spec": {
    "id": "holiday-entitlement-luxembourg",
    "version": "1.0.0",
    "schema": {
      "type": "object",
      "properties": {
        "monthsWorked": {
          "type": "number",
          "maximum": 12,
          "minimum": 0
        },
        "daysTaken": {
          "type": "number",
          "minimum": 0
        },
        "daysEntitled": {
          "type": "number",
          "readOnly": true
        },
        "monthsUntilTakeable": {
          "type": "number",
          "readOnly": true
        },
        "daysRemaining": {
          "type": "number",
          "readOnly": true
        }
      }
    },
    "constants": {
      "annualWorkingDays": 26,
      "qualifyingMonths": 3,
      "monthsPerYear": 12
    },
    "library": {
      "layers": [
        {
          "id": "statutory",
          "define": "(\n  /* Shared statutory helpers — the canonical copy (docs/sandbox/d8-statutory-families.md §5.4).\n     DO NOT EDIT A SPEC'S INLINED COPY. Edit this file and run `npm run sync:helpers`; a vitest\n     assertion and a Java assertion both require every inlined copy to be byte-identical to this one.\n\n     Why inlined rather than referenced: the `library` section's `ref` form — a library shared\n     between models — is still proposed, gated on the model-references design (see\n     ../../../../docs/design/library/jsonata-library.md). Inlining keeps each spec self-contained,\n     which is what lets `#e=` embedding, `#share=` import and MCP forking work with no resolver.\n\n     TWO TRAPS, both of which fail SILENTLY and both of which bit during the debt-payoff build:\n\n       1. A library function sees ONLY its arguments. It cannot read the consuming document — not\n          through a bare field name, not through `$`, not through `$$`. Everything these helpers\n          need is passed in. (`$const` is late-bound and so would resolve, but relying on it would\n          couple a shared helper to one spec's constant names.)\n       2. ONE null member wrecks a whole aggregate, and the two engines disagree about how. The JS\n          reference implementation THROWS (\"Argument 1 of function sum must be an array of\n          numbers\"); the Java port can instead yield null for the entire aggregate. Neither gives a\n          partial total, and the null-yielding form is the dangerous one because it is silent. So\n          callers coerce with `$n()` below before aggregating, which makes the behaviour identical\n          in both engines — measured, not assumed: see helpers.test.ts.\n\n       3. A PATH STEP DIRECTLY ON A CALL RESULT RETURNS NOTHING in the Java engine. This matters for\n          every caller of $amortize, which is the one helper here returning an object:\n\n              $amortize(p, r, n, 0).months            -> empty in Java, 360 in JS.  WRONG\n              ($a := $amortize(p, r, n, 0); $a.months) -> 360 in both.               RIGHT\n\n          Bind the result to a variable, then step into it. The JS reference accepts both forms, so\n          this is invisible until the page is served by the real engine, and it fails as a blank\n          field rather than an error. Measured with a probe, not inferred — the field simply does\n          not appear. */\n\n  /* Number coercion with an explicit zero default. The guard against trap 2. */\n  $n := function($v) { $v = null or $not($exists($v)) ? 0 : $number($v) };\n\n  /* ISO date -> its year / month / day parts. String slicing rather than $fromMillis formatting:\n     these are statutory dates (\"2026-04-06\"), and a timezone-sensitive round-trip through millis\n     can shift the day, which silently moves a service anniversary across a band boundary. */\n  $isoY := function($d) { $number($substring($d, 0, 4)) };\n  $isoM := function($d) { $number($substring($d, 5, 2)) };\n  $isoD := function($d) { $number($substring($d, 8, 2)) };\n\n  /* Whole years of completed service between two ISO dates. Counts an anniversary as reached only\n     when the month-and-day has arrived, which is what \"completed years of service\" means in every\n     severance statute — not a 365.25-day division, whose drift crosses a 5-year band boundary in\n     the wrong direction roughly one year in four. */\n  $yearsBetween := function($from, $to) { (\n    $y := $isoY($to) - $isoY($from);\n    $beforeAnniversary := $isoM($to) < $isoM($from)\n      or ($isoM($to) = $isoM($from) and $isoD($to) < $isoD($from));\n    $beforeAnniversary ? $y - 1 : $y\n  ) };\n\n  /* Whole completed months between two ISO dates, same convention. */\n  $monthsBetween := function($from, $to) { (\n    $m := ($isoY($to) - $isoY($from)) * 12 + ($isoM($to) - $isoM($from));\n    $isoD($to) < $isoD($from) ? $m - 1 : $m\n  ) };\n\n  /* Inclusive count of days between two ISO dates — both endpoints counted, because a leave year\n     runs from its first day to its last and an employee present on both is present for both.\n     Pro-rata accrual is then $proRataDays(a, b) / $proRataDays(yearStart, yearEnd). */\n  $proRataDays := function($from, $to) {\n    ($toMillis($to) - $toMillis($from)) / 86400000 + 1\n  };\n\n  /* Progressive charge across bands. `$bands` is ordered lowest-first, each {\"upTo\": n, \"rate\": r};\n     the final band's `upTo` is omitted or null to mean \"no ceiling\". Each band's rate applies ONLY\n     to the slice of the amount inside it — the single most common error in a hand-written bracket\n     walk is applying the top rate to the whole amount. Returns 0 for a non-positive amount. */\n  $bandedCharge := function($amount, $bands) { (\n    $a := $n($amount);\n    $a <= 0 ? 0 : $reduce($bands, function($acc, $band) { (\n      $ceiling := $exists($band.upTo) and $band.upTo != null ? $band.upTo : $a;\n      $top := $ceiling < $a ? $ceiling : $a;\n      $slice := $top - $acc.floor;\n      {\n        \"floor\": $top > $acc.floor ? $top : $acc.floor,\n        \"charge\": $acc.charge + ($slice > 0 ? $slice * $n($band.rate) : 0)\n      }\n    ) }, {\"floor\": 0, \"charge\": 0}).charge\n  ) };\n\n  /* Clamp into [floor, cap]. Either bound may be omitted (null) to leave that side open — a benefit\n     with a cap and no floor is as common as one with both. */\n  $clampFloorCap := function($value, $floor, $cap) { (\n    $v := $n($value);\n    $withFloor := $exists($floor) and $floor != null and $v < $floor ? $floor : $v;\n    $exists($cap) and $cap != null and $withFloor > $cap ? $cap : $withFloor\n  ) };\n\n  /* Level annuity payment for a principal over `$months` at `$annualRatePct` nominal, compounded\n     monthly. Falls back to straight-line division at a zero rate, where the standard formula\n     divides by zero. */\n  $annuityPayment := function($principal, $annualRatePct, $months) { (\n    $p := $n($principal);\n    $m := $n($months);\n    $i := $n($annualRatePct) / 1200;\n    $m <= 0 ? 0 : ($i = 0 ? $p / $m : $p * $i * $power(1 + $i, $m) / ($power(1 + $i, $m) - 1))\n  ) };\n\n  /* Amortisation schedule: one row per month until the balance clears or `$months` is reached.\n     Returns {\"payment\", \"months\", \"totalInterest\", \"schedule\": [{month, interest, principal,\n     balance}]}. `$extra` is an optional monthly overpayment.\n\n     A real month-by-month fold rather than a closed form, because an overpayment changes every\n     later row — the same reason debt-payoff simulates. Bounded by `$months`, so it always\n     terminates. */\n  $amortize := function($principal, $annualRatePct, $months, $extra) { (\n    $i := $n($annualRatePct) / 1200;\n    $pay := $annuityPayment($principal, $annualRatePct, $months) + $n($extra);\n    $r := $reduce([1..$n($months)], function($acc, $month) {\n      $acc.balance <= 0 ? $acc : (\n        /* The running balance is kept UNROUNDED and only the emitted row is rounded. Rounding the\n           balance each month instead accumulates drift: at 200,000 over 360 months it left 2.83\n           still owing in the final row, which would break the \"final balance is zero\" invariant\n           (§7.3) and look to a reader like the schedule does not pay the loan off. Lenders compute\n           on the exact balance and adjust the last payment, which is what this does. */\n        $interest := $acc.balance * $i;\n        $due := $acc.balance + $interest < $pay ? $acc.balance + $interest : $pay;\n        $principalPart := $due - $interest;\n        $balance := $acc.balance - $principalPart;\n        {\n          \"balance\": $balance,\n          \"totalInterest\": $acc.totalInterest + $interest,\n          \"schedule\": $append($acc.schedule, [{\n            \"month\": $month,\n            \"interest\": $round($interest, 2),\n            \"principal\": $round($principalPart, 2),\n            \"balance\": $round($balance, 2)\n          }])\n        }\n      )\n    }, {\"balance\": $n($principal), \"totalInterest\": 0, \"schedule\": []});\n    {\n      \"payment\": $round($pay, 2),\n      \"months\": $count($r.schedule),\n      \"totalInterest\": $round($r.totalInterest, 2),\n      \"schedule\": [$r.schedule]\n    }\n  ) };\n\n  [\"n\", \"isoY\", \"isoM\", \"isoD\", \"yearsBetween\", \"monthsBetween\", \"proRataDays\",\n   \"bandedCharge\", \"clampFloorCap\", \"annuityPayment\", \"amortize\"]\n)\n"
        }
      ]
    },
    "defaultValues": [
      {
        "path": "$",
        "expr": "{ 'monthsWorked': 12, 'daysTaken': 0 }"
      }
    ],
    "derivations": [
      {
        "path": "$.daysEntitled",
        "expr": "($m := $clampFloorCap($floor($n(monthsWorked)), 0, $const.monthsPerYear); $round($const.annualWorkingDays * $m / $const.monthsPerYear, 1))"
      },
      {
        "path": "$.monthsUntilTakeable",
        "expr": "($r := $const.qualifyingMonths - $n(monthsWorked); $r < 0 ? 0 : $round($r, 1))"
      },
      {
        "path": "$.daysRemaining",
        "expr": "($r := daysEntitled - $n(daysTaken); $r < 0 ? 0 : $round($r, 1))"
      }
    ],
    "constraints": [],
    "viewDefinition": {
      "renderer": "builtin",
      "defaultView": "main",
      "views": [
        {
          "id": "main",
          "label": "Congé annuel",
          "layout": "vertical",
          "components": [
            {
              "id": "note",
              "type": "staticText",
              "text": "Guichet.lu: “La durée du congé annuel est fixée à 26 jours ouvrables par année, indépendamment de l’âge du salarié.” Twenty-six working days is the second-largest real entitlement in this comparison after the UK’s 28 — and the ITM records how it got there: “L’article L. 233-4 du Code du travail prévoit une augmentation du congé payé légal minimum de 25 à 26 jours par année”, in force since 1 January 2019."
            },
            {
              "id": "inputs",
              "type": "fieldSet",
              "label": "Vos données",
              "components": [
                {
                  "id": "monthsWorked",
                  "type": "numericField",
                  "label": "Full months worked this year",
                  "bind": "$.monthsWorked",
                  "helperText": "“Le congé de la première année est dû à raison d’un douzième par mois de travail entier” — a twelfth per FULL month, so a part month does not count."
                },
                {
                  "id": "daysTaken",
                  "type": "numericField",
                  "label": "Days already taken",
                  "bind": "$.daysTaken"
                }
              ]
            },
            {
              "id": "sep",
              "type": "separatorLine"
            },
            {
              "id": "entitledTile",
              "type": "statTile",
              "label": "Working days entitled",
              "value": "$.daysEntitled"
            },
            {
              "id": "remainingTile",
              "type": "statTile",
              "label": "Working days remaining",
              "value": "$.daysRemaining"
            },
            {
              "id": "breakdown",
              "type": "keyValueList",
              "label": "Before you can take it",
              "items": [
                {
                  "label": "Months still to run before leave may be taken",
                  "value": "$.monthsUntilTakeable"
                }
              ]
            },
            {
              "id": "assumptions",
              "type": "staticText",
              "text": "The three-month rule is about TAKING the leave, not earning it: “le salarié ne peut prendre son congé qu’après 3 mois de travail ininterrompu auprès d’un même employeur”, and it applies to fixed-term and permanent contracts alike. So the accrued days are shown in full and the waiting period is reported beside them rather than deducted. The entitlement covers every employee, apprentices included, whatever their schedule; the ITM publishes a separate table of the leave HOURS owed to part-time employees, which this page does not reproduce. Leave requested by the employee must be fixed at least a month in advance. Parental leave suspends accrual when taken full-time and is pro-rated against weekly hours when part-time; maternity leave does not suspend it. Public holidays are separate, and collective agreements commonly give more than 26 days."
            },
            {
              "id": "sources",
              "type": "sourceList",
              "label": "Sources",
              "layers": 1,
              "exempt": [
                "monthsPerYear"
              ],
              "items": [
                {
                  "label": "Guichet.lu, Demander un congé légal annuel — guichet.public.lu (26 jours ouvrables a year regardless of age; a twelfth per full month in the first year; three months before the leave may be taken)",
                  "url": "https://guichet.public.lu/fr/citoyens/travail/conges-jours-feries/annuel/conge-legal-annuel.html",
                  "date": "2026-10-11",
                  "covers": [
                    "annualWorkingDays",
                    "qualifyingMonths"
                  ]
                },
                {
                  "label": "Inspection du travail et des mines, D8a1 — itm.public.lu (the 26 days in force since 1 January 2019, raised from 25 by art. L. 233-4 of the Code du travail)",
                  "url": "https://itm.public.lu/fr/questions-reponses/droit-travail/conges/a/a1.html",
                  "date": "2026-10-11",
                  "covers": []
                }
              ]
            }
          ]
        }
      ]
    },
    "tests": [
      {
        "description": "N1 a full year is 26 working days",
        "given": {
          "$.monthsWorked": 12,
          "$.daysTaken": 0
        },
        "expect": {
          "$.daysEntitled": 26,
          "$.monthsUntilTakeable": 0
        }
      },
      {
        "description": "N2 six full months accrue half",
        "given": {
          "$.monthsWorked": 6,
          "$.daysTaken": 0
        },
        "expect": {
          "$.daysEntitled": 13
        }
      },
      {
        "description": "N3 a twelfth per month, so one month is 2,2 days",
        "given": {
          "$.monthsWorked": 1,
          "$.daysTaken": 0
        },
        "expect": {
          "$.daysEntitled": 2.2
        }
      },
      {
        "description": "N4 a part month does not count — 1,9 months is one full month",
        "given": {
          "$.monthsWorked": 1.9,
          "$.daysTaken": 0
        },
        "expect": {
          "$.daysEntitled": 2.2
        }
      },
      {
        "description": "N5 at two months the leave has accrued but cannot be taken for another month",
        "given": {
          "$.monthsWorked": 2,
          "$.daysTaken": 0
        },
        "expect": {
          "$.daysEntitled": 4.3,
          "$.monthsUntilTakeable": 1
        }
      },
      {
        "description": "N6 at three months the waiting period is over",
        "given": {
          "$.monthsWorked": 3,
          "$.daysTaken": 0
        },
        "expect": {
          "$.daysEntitled": 6.5,
          "$.monthsUntilTakeable": 0
        }
      },
      {
        "description": "N7 no full month earns nothing",
        "given": {
          "$.monthsWorked": 0,
          "$.daysTaken": 0
        },
        "expect": {
          "$.daysEntitled": 0
        }
      },
      {
        "description": "N8 days already taken come off the remainder",
        "given": {
          "$.monthsWorked": 12,
          "$.daysTaken": 10
        },
        "expect": {
          "$.daysRemaining": 16
        }
      },
      {
        "description": "N9 taking more than the entitlement never goes negative",
        "given": {
          "$.monthsWorked": 12,
          "$.daysTaken": 40
        },
        "expect": {
          "$.daysRemaining": 0
        }
      }
    ]
  }
}