Solar cycle (calendar)

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The solar cycle (calendar) is the pattern of how calendars align with weekdays because of leap years. In the old Julian calendar, every 4 years is a leap year, adding February 29. This makes the weekday pattern repeat about every 28 years. To find a year’s place in this 28-year cycle, you can use: (year + 8) mod 28, then add 1. For example, 2026 gives 19.

In the Gregorian calendar, leap years are chosen differently: century years aren’t leap years unless divisible by 400. This breaks the 28-year cycle. However, 400 years contain exactly 146,097 days (20,871 weeks), so the calendar pattern repeats every 400 years.

The cycle is also linked to Dominical letters, which mark Sundays in a year. In the Julian system the 28-year cycle lines up with these letters, but in the Gregorian system the alignment only holds for some centuries due to the leap-year rule. For instance, the year 1500 sits at position 25 in the cycle, and its Dominical letter is ED.