{
  "$comment": "Machine-readable companion to https://valem.run/calculators/germany/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/germany/holiday-entitlement",
  "dataUrl": "https://valem.run/calculators/germany/holiday-entitlement.json",
  "license": {
    "name": "CC BY 4.0",
    "url": "https://creativecommons.org/licenses/by/4.0/",
    "attribution": "Germany urlaubsanspruch model by Valem (https://valem.run/calculators/germany/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/germany/holiday-entitlement/verify",
  "country": "germany",
  "countryName": "Germany",
  "formula": "holiday-entitlement",
  "formulaName": "Urlaubsanspruch",
  "title": "Urlaubsanspruch Berechnen 2026 — German Statutory Leave",
  "answer": "German law gives at least 24 Werktage of paid leave a year, but § 3(2) BUrlG counts a Werktag as any day that is not a Sunday or a public holiday — a six-day week — so an employee working the usual five days is entitled to 20 days.",
  "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": "2026-10-09"
  },
  "sources": [
    {
      "label": "§ 3 BUrlG — Dauer des Urlaubs (24 Werktage; Werktag = any day that is not a Sunday or a public holiday)",
      "url": "https://www.gesetze-im-internet.de/burlg/__3.html",
      "checked": "2026-10-09"
    }
  ],
  "terminalOutput": "daysRemaining",
  "headlineOutput": "daysEntitled",
  "inputs": [
    {
      "name": "leaveYearStart",
      "type": "string",
      "label": "Leave year starts (YYYY-MM-DD)"
    },
    {
      "name": "leaveYearEnd",
      "type": "string",
      "label": "Leave year ends (YYYY-MM-DD)"
    },
    {
      "name": "workStart",
      "type": "string",
      "label": "First day worked in it (YYYY-MM-DD)"
    },
    {
      "name": "workEnd",
      "type": "string",
      "label": "Last day worked in it (YYYY-MM-DD)"
    },
    {
      "name": "daysPerWeek",
      "type": "number",
      "label": "Days you work per week",
      "minimum": 1,
      "maximum": 6
    },
    {
      "name": "daysTaken",
      "type": "number",
      "label": "Days already taken",
      "minimum": 0
    }
  ],
  "outputs": [
    {
      "name": "weeksEntitlement",
      "type": "number",
      "formula": "$const.statutoryDays / $const.statutoryBasisDays"
    },
    {
      "name": "fullYearDays",
      "type": "number",
      "formula": "weeksEntitlement * daysPerWeek"
    },
    {
      "name": "yearLengthDays",
      "type": "number",
      "formula": "$proRataDays(leaveYearStart, leaveYearEnd)"
    },
    {
      "name": "presentDays",
      "type": "number",
      "formula": "$proRataDays(workStart, workEnd)"
    },
    {
      "name": "accrualFraction",
      "type": "number",
      "formula": "($f := presentDays / yearLengthDays; $f > 1 ? 1 : $f)"
    },
    {
      "name": "daysEntitled",
      "type": "number",
      "formula": "$round(fullYearDays * accrualFraction, 1)"
    },
    {
      "name": "daysRemaining",
      "type": "number",
      "formula": "($r := daysEntitled - $n(daysTaken); $r < 0 ? 0 : $round($r, 1))"
    }
  ],
  "testCases": [
    {
      "description": "B1 a five-day week gets 20 days, NOT the statute’s 24",
      "given": {
        "leaveYearStart": "2026-01-01",
        "leaveYearEnd": "2026-12-31",
        "workStart": "2026-01-01",
        "workEnd": "2026-12-31",
        "daysPerWeek": 5,
        "daysTaken": 0
      },
      "expect": {
        "weeksEntitlement": 4,
        "daysEntitled": 20
      }
    },
    {
      "description": "B2 a six-day week gets the statutory 24 exactly",
      "given": {
        "leaveYearStart": "2026-01-01",
        "leaveYearEnd": "2026-12-31",
        "workStart": "2026-01-01",
        "workEnd": "2026-12-31",
        "daysPerWeek": 6,
        "daysTaken": 0
      },
      "expect": {
        "daysEntitled": 24
      }
    },
    {
      "description": "B3 three days a week",
      "given": {
        "leaveYearStart": "2026-01-01",
        "leaveYearEnd": "2026-12-31",
        "workStart": "2026-01-01",
        "workEnd": "2026-12-31",
        "daysPerWeek": 3,
        "daysTaken": 0
      },
      "expect": {
        "daysEntitled": 12
      }
    },
    {
      "description": "B4 half a leave year on a five-day week",
      "given": {
        "leaveYearStart": "2026-01-01",
        "leaveYearEnd": "2026-12-31",
        "workStart": "2026-01-01",
        "workEnd": "2026-06-30",
        "daysPerWeek": 5,
        "daysTaken": 0
      },
      "expect": {
        "daysEntitled": 9.9
      }
    },
    {
      "description": "B5 no cap applies, unlike the UK",
      "given": {
        "leaveYearStart": "2026-01-01",
        "leaveYearEnd": "2026-12-31",
        "workStart": "2026-01-01",
        "workEnd": "2026-12-31",
        "daysPerWeek": 6,
        "daysTaken": 4
      },
      "expect": {
        "daysRemaining": 20
      }
    },
    {
      "description": "B6 joining partway through the leave year",
      "given": {
        "leaveYearStart": "2026-01-01",
        "leaveYearEnd": "2026-12-31",
        "workStart": "2026-10-01",
        "workEnd": "2026-12-31",
        "daysPerWeek": 5,
        "daysTaken": 0
      },
      "expect": {
        "presentDays": 92,
        "daysEntitled": 5
      }
    }
  ],
  "spec": {
    "id": "holiday-entitlement-germany",
    "version": "1.0.0",
    "schema": {
      "type": "object",
      "properties": {
        "leaveYearStart": {
          "type": "string"
        },
        "leaveYearEnd": {
          "type": "string"
        },
        "workStart": {
          "type": "string"
        },
        "workEnd": {
          "type": "string"
        },
        "daysPerWeek": {
          "type": "number",
          "minimum": 1,
          "maximum": 6
        },
        "daysTaken": {
          "type": "number",
          "minimum": 0
        },
        "weeksEntitlement": {
          "type": "number",
          "readOnly": true
        },
        "fullYearDays": {
          "type": "number",
          "readOnly": true
        },
        "yearLengthDays": {
          "type": "number",
          "readOnly": true
        },
        "presentDays": {
          "type": "number",
          "readOnly": true
        },
        "accrualFraction": {
          "type": "number",
          "readOnly": true
        },
        "daysEntitled": {
          "type": "number",
          "readOnly": true
        },
        "daysRemaining": {
          "type": "number",
          "readOnly": true
        }
      }
    },
    "constants": {
      "statutoryDays": 24,
      "statutoryBasisDays": 6
    },
    "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": "{ 'leaveYearStart': '2026-01-01', 'leaveYearEnd': '2026-12-31', 'workStart': '2026-01-01', 'workEnd': '2026-12-31', 'daysPerWeek': 5, 'daysTaken': 0 }"
      }
    ],
    "derivations": [
      {
        "path": "$.yearLengthDays",
        "expr": "$proRataDays(leaveYearStart, leaveYearEnd)"
      },
      {
        "path": "$.presentDays",
        "expr": "$proRataDays(workStart, workEnd)"
      },
      {
        "path": "$.accrualFraction",
        "expr": "($f := presentDays / yearLengthDays; $f > 1 ? 1 : $f)"
      },
      {
        "path": "$.weeksEntitlement",
        "expr": "$const.statutoryDays / $const.statutoryBasisDays"
      },
      {
        "path": "$.fullYearDays",
        "expr": "weeksEntitlement * daysPerWeek"
      },
      {
        "path": "$.daysEntitled",
        "expr": "$round(fullYearDays * accrualFraction, 1)"
      },
      {
        "path": "$.daysRemaining",
        "expr": "($r := daysEntitled - $n(daysTaken); $r < 0 ? 0 : $round($r, 1))"
      }
    ],
    "constraints": [],
    "viewDefinition": {
      "renderer": "builtin",
      "defaultView": "main",
      "views": [
        {
          "id": "main",
          "label": "Holiday entitlement",
          "layout": "vertical",
          "components": [
            {
              "id": "note",
              "type": "staticText",
              "text": "§ 3 BUrlG says 24 WERKTAGE, and § 3(2) defines a Werktag as any calendar day that is not a Sunday or a public holiday — so Saturday counts and the 24 is measured on a SIX-day week. A normal five-day employee is therefore entitled to 20 days, not 24. \"Germany gives 24 days\" is true of the statute and false of almost every employee, which makes it the most misquoted figure in this family. Twenty days is four weeks, the same floor the EU Working Time Directive sets; many German contracts give more, and this page computes the legal minimum rather than what your contract says."
            },
            {
              "id": "inputs",
              "type": "fieldSet",
              "label": "Your details",
              "components": [
                {
                  "id": "daysPerWeek",
                  "type": "numericField",
                  "label": "Days you work per week",
                  "bind": "$.daysPerWeek",
                  "helperText": "Your own working week. The statute counts in its own — 6 days — and this page converts between the two."
                },
                {
                  "id": "leaveYearStart",
                  "type": "textField",
                  "label": "Leave year starts (YYYY-MM-DD)",
                  "bind": "$.leaveYearStart",
                  "placeholder": "YYYY-MM-DD"
                },
                {
                  "id": "leaveYearEnd",
                  "type": "textField",
                  "label": "Leave year ends (YYYY-MM-DD)",
                  "bind": "$.leaveYearEnd",
                  "placeholder": "YYYY-MM-DD"
                },
                {
                  "id": "workStart",
                  "type": "textField",
                  "label": "First day worked in it (YYYY-MM-DD)",
                  "bind": "$.workStart",
                  "placeholder": "YYYY-MM-DD",
                  "helperText": "Leave this as the leave year start unless you joined partway through."
                },
                {
                  "id": "workEnd",
                  "type": "textField",
                  "label": "Last day worked in it (YYYY-MM-DD)",
                  "bind": "$.workEnd",
                  "placeholder": "YYYY-MM-DD",
                  "helperText": "Leave this as the leave year end unless you are leaving partway through."
                },
                {
                  "id": "daysTaken",
                  "type": "numericField",
                  "label": "Days already taken",
                  "bind": "$.daysTaken"
                }
              ]
            },
            {
              "id": "sep",
              "type": "separatorLine"
            },
            {
              "id": "entitledTile",
              "type": "statTile",
              "label": "Days entitled",
              "value": "$.daysEntitled"
            },
            {
              "id": "remainingTile",
              "type": "statTile",
              "label": "Days remaining",
              "value": "$.daysRemaining"
            },
            {
              "id": "breakdown",
              "type": "keyValueList",
              "label": "How that is worked out",
              "items": [
                {
                  "label": "Statutory weeks",
                  "value": "$.weeksEntitlement"
                },
                {
                  "label": "Full-year days for your week",
                  "value": "$.fullYearDays"
                },
                {
                  "label": "Days in the leave year",
                  "value": "$.yearLengthDays"
                },
                {
                  "label": "Days worked in it",
                  "value": "$.presentDays"
                }
              ]
            },
            {
              "id": "holidaysNote",
              "type": "staticText",
              "text": "§ 3(2) puts public holidays OUTSIDE the Werktage the 24 is counted in, so they cannot be set against your entitlement — the opposite of the UK position, where an employer may count bank holidays towards the minimum."
            },
            {
              "id": "sources",
              "type": "sourceList",
              "label": "Sources",
              "layers": 1,
              "items": [
                {
                  "label": "§ 3 BUrlG — Dauer des Urlaubs (24 Werktage; Werktag = any day that is not a Sunday or a public holiday)",
                  "url": "https://www.gesetze-im-internet.de/burlg/__3.html",
                  "date": "2026-10-09",
                  "covers": [
                    "statutoryDays",
                    "statutoryBasisDays"
                  ]
                }
              ]
            }
          ]
        }
      ]
    },
    "tests": [
      {
        "description": "B1 a five-day week gets 20 days, NOT the statute’s 24",
        "given": {
          "$.leaveYearStart": "2026-01-01",
          "$.leaveYearEnd": "2026-12-31",
          "$.workStart": "2026-01-01",
          "$.workEnd": "2026-12-31",
          "$.daysPerWeek": 5,
          "$.daysTaken": 0
        },
        "expect": {
          "$.weeksEntitlement": 4,
          "$.daysEntitled": 20
        }
      },
      {
        "description": "B2 a six-day week gets the statutory 24 exactly",
        "given": {
          "$.leaveYearStart": "2026-01-01",
          "$.leaveYearEnd": "2026-12-31",
          "$.workStart": "2026-01-01",
          "$.workEnd": "2026-12-31",
          "$.daysPerWeek": 6,
          "$.daysTaken": 0
        },
        "expect": {
          "$.daysEntitled": 24
        }
      },
      {
        "description": "B3 three days a week",
        "given": {
          "$.leaveYearStart": "2026-01-01",
          "$.leaveYearEnd": "2026-12-31",
          "$.workStart": "2026-01-01",
          "$.workEnd": "2026-12-31",
          "$.daysPerWeek": 3,
          "$.daysTaken": 0
        },
        "expect": {
          "$.daysEntitled": 12
        }
      },
      {
        "description": "B4 half a leave year on a five-day week",
        "given": {
          "$.leaveYearStart": "2026-01-01",
          "$.leaveYearEnd": "2026-12-31",
          "$.workStart": "2026-01-01",
          "$.workEnd": "2026-06-30",
          "$.daysPerWeek": 5,
          "$.daysTaken": 0
        },
        "expect": {
          "$.daysEntitled": 9.9
        }
      },
      {
        "description": "B5 no cap applies, unlike the UK",
        "given": {
          "$.leaveYearStart": "2026-01-01",
          "$.leaveYearEnd": "2026-12-31",
          "$.workStart": "2026-01-01",
          "$.workEnd": "2026-12-31",
          "$.daysPerWeek": 6,
          "$.daysTaken": 4
        },
        "expect": {
          "$.daysRemaining": 20
        }
      },
      {
        "description": "B6 joining partway through the leave year",
        "given": {
          "$.leaveYearStart": "2026-01-01",
          "$.leaveYearEnd": "2026-12-31",
          "$.workStart": "2026-10-01",
          "$.workEnd": "2026-12-31",
          "$.daysPerWeek": 5,
          "$.daysTaken": 0
        },
        "expect": {
          "$.presentDays": 92,
          "$.daysEntitled": 5
        }
      }
    ]
  }
}