28-year cycle
Calendar Cycle Calculator
Where a year sits in the Gregorian weekday cycle and the next matching years.
Calendar cycle
Enter a year. Century non-leap years break a naive 28-year shortcut — this page checks leap status too.
The calendar cycle calculator explains where a year sits in the Gregorian weekday cycle and lists nearby years that match its layout, with an explicit warning that the popular 28-year shortcut fails at century years that are not leap years. The 28-year figure comes from 28 × 365.25 days aligning weekdays in a stretch of regular leap years. When a century skips February 29, that alignment slips by a day and plus-28 no longer reprints the same January–December grid.
What the 28-year shortcut assumes
In a long run of leap years every four years, the weekday of January 1 repeats every 28 years for a given leap/common pattern. People therefore print add-28 on classroom posters. The shortcut is a teaching approximation, not a theorem of the full Gregorian system. Gregorian centuries are leap years only if divisible by 400, so 1900-type years insert a missing leap day that the 28-year story did not budget.
The same calendar years matcher lists years that share leap status and January 1 weekday. This cycle page is the explainer: why those matches are spaced as they are, when +6 or +11 appears for common years, and why +28 can lie. Use the matcher for a list; use this page for the mechanism.
How to read the cycle position
Enter a year. The result should state leap status, January 1 weekday, and matching years checked with real leap status rather than a blind +28 table. If a naive +28 year is a century non-leap, it will not appear as a true match. That omission is the lesson.
Reuse of last year’s wall print is a narrower yes/no on calendar reuse. Cycle math can say two years match even when they are not consecutive. Reuse asks only about the printed year versus the following year.
Common-year gaps of 6 and 11
Common years often repeat after 6 or 11 years because leftover weekdays accumulate until both leap status and January 1 weekday align again. Leap years wait longer. Tables that only show 28-year columns hide those shorter common-year repeats. This page should surface the actual next matches, not only year+28.
Do not confuse those gaps with ISO 53-week spacing or with retail 53-week years. Cycle talk here is civil January–December grids only.
Worked examples
A museum exhibit claims calendars repeat every 28 years. Staff enter a century non-leap year, then the year 28 years later, and show that one is common and the other is leap, so the grids disagree after February. The exhibit caption is then rewritten to mention century exceptions.
A designer in 2026 wants to know why last year’s file does not match even though 28 years ago a similar file did. They enter 2026 here, see the true matches, and stop using a +28 spreadsheet that crossed a century skip.
Dominical letters and year types
Publishers sometimes code a year by dominical letter or by a pair (leap flag, start weekday). The cycle is the walk through those types as leap days insert extra weekday steps. Two letters in a leap year (one for January–February, one after February 29) are why leap years are a different type even when January 1 matches a common year.
This site does not require you to memorize letters. The calculator checks leap status and January 1. Letters are optional vocabulary for readers who meet them in older almanacs.
Proleptic Gregorian and history
The tool uses the same Gregorian rules as the rest of the site, including years before a country adopted the Gregorian calendar. Historical Easter or Julian dates are out of scope. For leap-year lists under Gregorian rules, see leap years list.
Skipped days at Gregorian adoption in particular countries are not modeled on this cycle page. Treat outputs as Gregorian civil planning.
What the cycle page does not replace
It does not generate a 12-month grid; use the calendar generator. It does not mark holidays. It does not compute ISO weeks. It teaches spacing of identical civil year layouts and flags the century trap.
Pair with 2026 yearly calendars when you already know 2026’s type and want the picture rather than the cycle lecture.
Classroom demonstration
Show a common year, jump six or eleven years, and confirm January 1 weekday plus leap status. Then show a leap year and a +28 candidate that crosses a non-leap century, and confirm the candidate fails. The two demos together beat a poster that only says twenty-eight. 2026 can be the starting year for the first demo if it is common or leap as needed.
Students who then want a reusable wall print for next year should leave this lecture and use the reuse calculator. Cycle class is not a print shop.
Software that adds twenty-eight
Scripts that compute match years as year+28, year+56, and so on without testing leap status will emit false matches around century skips. Replace those scripts with a check of leap flag and January 1 weekday, which is what the same-calendar-years matcher already does. This page exists so those scripts get retired with an explanation, not only with a new list.
Frequently asked questions
Why does the 28-year calendar shortcut sometimes fail?
The shortcut assumes leap days arrive every four years. Gregorian century years are leap years only when divisible by 400, so a 1900-type year skips February 29. That missing day shifts weekdays, and year plus 28 no longer shares both leap status and January 1 weekday. This page checks real leap status instead of adding 28 blindly.
How is this different from same calendar years?
Same calendar years lists other years whose full January–December layout matches the year you enter. This cycle calculator explains the spacing, including 6- and 11-year common-year repeats and the century trap. Use the list when you need matching years; use this page when you need to know why adding 28 can lie.
When do common years repeat after 6 or 11 years?
Leftover weekdays accumulate until a later common year again shares January 1’s weekday. The wait is often 6 or 11 years, not 28. Leap years insert an extra step and usually wait longer. The calculator lists actual next matches rather than a single 28-year column.
What should be used to reuse last year’s wall calendar?
Use the calendar reuse calculator, which answers yes or no for the printed year versus the following year. Cycle math can match years that are not consecutive. Reuse is the consecutive-print question; this page is the Gregorian cycle explanation, including why adding 28 years can fail at century non-leaps.
Is a century year always a leap year in this check?
No. A century year is a Gregorian leap year only when divisible by 400. A century that skips February 29 compared with a leap year 28 years later shows why a naive reprint fails after February. Leap centuries divisible by 400 do not insert that skip.
Is the weekday cycle based on Julian leap rules?
No. Outputs follow proleptic Gregorian leap rules used elsewhere on the site. Julian leap every four years without the 400-year exception would keep a cleaner 28-year rhythm. Historical adoption skips in particular countries are not modeled as dropped days here. Treat results as Gregorian civil planning only.