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What is a 4-4-5 calendar? The 4-5-4 and 5-4-4 variants, the 53rd week, and the 2026 period table

Translated from the canonical Japanese page recipes/4-4-5-calendar.md.

A 4-4-5 calendar is a fiscal calendar that divides the year into four 13-week quarters and each quarter into three periods of 4, 4 and 5 weeks (52 weeks, 364 days in total). Every period ends on the same weekday, so periods carry the same number of weeks and weekends and year-over-year comparisons line up — which is why retailers, restaurants and manufacturers report on it. The 4-5-4 variant (the NRF retail calendar in the US) and 5-4-4 only move the five-week period. Because 52 weeks are 364 days, a 53rd week has to be added every five or six years, and which period absorbs it is where implementations have always diverged.

This page gives (1) the 2026 period table, then (2) the definition that produced it. The table is the literal output of the definition (a Kairos expression), executed and checked by the reference implementation.

The 2026 period table (ISO-week based; a 53-week year)

Period	Start (Mon)	End (Sun)	Weeks	ISO weeks
P1	2025-12-29	2026-01-25	4	W01–W04
P2	2026-01-26	2026-02-22	4	W05–W08
P3	2026-02-23	2026-03-29	5	W09–W13
P4	2026-03-30	2026-04-26	4	W14–W17
P5	2026-04-27	2026-05-24	4	W18–W21
P6	2026-05-25	2026-06-28	5	W22–W26
P7	2026-06-29	2026-07-26	4	W27–W30
P8	2026-07-27	2026-08-23	4	W31–W34
P9	2026-08-24	2026-09-27	5	W35–W39
P10	2026-09-28	2026-10-25	4	W40–W43
P11	2026-10-26	2026-11-22	4	W44–W47
P12	2026-11-23	2027-01-03	6	W48–W53

• The year starts on the Monday of ISO week W01 (2025-12-29). 2026 has 53 ISO weeks; the 53rd week is absorbed by the last period, so P12 alone is six weeks long.
• Select the table in your browser and copy it — it pastes into Excel cell by cell.
• The NRF retail calendar starts the fiscal year on the Sunday nearest February 1 — a different year-start convention. It can be written with the same vocabulary but is outside this page (a separate recipe if there is demand).

What happens elsewhere

• cron’s and RRULE’s month/week fields are fixed to Gregorian months and cannot refer to 4-4-5 “periods”.
• In practice, accounting SaaS products implement it as a dedicated feature — solved outside the scheduling language.
• In ISO years with 53 weeks (such as 2026), you additionally need a carry rule for which period absorbs week 53 — a classic source of divergence between implementations.

Writing it in Kairos — the carry rule falls out of the definition

Take the period heads — “Mondays of ISO weeks 1, 5, 9, 14, …, 48” — as a marker stream and cut periods with segmentBy, deriving from the standard ISOWeek premise. The example premise US445 is US Eastern time (the calendar is date-only, so the time zone does not change the result — it is aligned with the Playground’s display zone). Weeks are ISO weeks (Monday start), hence wkst: Mon:

# eval: 2025-12-01..2027-03-01 tz: America/New_York
premise R445 = ISOWeek with {
  periodStart = isoWeekStart |> filter(d =>
    ((isoWeekNo(d) - 1) mod 13 == 0 or (isoWeekNo(d) - 1) mod 13 == 4 or (isoWeekNo(d) - 1) mod 13 == 8)
    and isoWeekNo(d) <= 48)
  period = day |> segmentBy(periodStart, edges: clip, empties: error)
}
premise US445 { calendar-system: R445; tz: "America/New_York"; wkst: Mon }

@US445
everyDay |> within(period) |> first
#=> 2025-12-29 2026-01-26 2026-02-23 2026-03-30 2026-04-27 2026-05-25
#=> 2026-06-29 2026-07-27 2026-08-24 2026-09-28 2026-10-26 2026-11-23
#=> 2027-01-04 2027-02-01

ISO year 2026 has 53 weeks — the final period P12 automatically stretches to six weeks (11/23 through 2027-01-03, absorbing W49–W53), and the next year restarts normally from W01 (2027-01-04). The carry rule (NRF’s “add it to the last period”) is nowhere in the code — it falls out of the shape of the definition, “period heads only up to W48”. Instead of enumerating rules, you define the structure of the calendar and the correct edges emerge.

Period ends (the “End” column of the table above) come from the same definition:

# eval: 2025-12-29..2027-01-04 tz: America/New_York
premise R445 = ISOWeek with {
  periodStart = isoWeekStart |> filter(d =>
    ((isoWeekNo(d) - 1) mod 13 == 0 or (isoWeekNo(d) - 1) mod 13 == 4 or (isoWeekNo(d) - 1) mod 13 == 8)
    and isoWeekNo(d) <= 48)
  period = day |> segmentBy(periodStart, edges: clip, empties: error)
}
premise US445 { calendar-system: R445; tz: "America/New_York"; wkst: Mon }

@US445
everyDay |> within(period) |> last
#=> 2026-01-25 2026-02-22 2026-03-29 2026-04-26 2026-05-24 2026-06-28
#=> 2026-07-26 2026-08-23 2026-09-27 2026-10-25 2026-11-22 2027-01-03

Once the periods exist, “3 business days before period-end” and “first business day of the period” use exactly the same vocabulary as Gregorian months (within(period), roll, shift).

Try it in your browser

Run it in the Playground (period starts) · period ends — change mod 13 == 0/4/8 and you get the 4-5-4 and 5-4-4 variants.

Related

• Fiscal years (April start etc.) are the standard premise Fiscal: stdlib
• Window-cutting vocabulary: segmentBy · split (regular equal partitions are canonically split; each page notes how this recipe’s form relates)
• Head office and branches on different calendars (the same expression yielding different dates): study 11 and premise derivation

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