Century leap year (Gregorian rule)

Rule and simple test

The rule for leap years in the Gregorian calendar can be stated succinctly: a year is a leap year if it is divisible by 4, except that years divisible by 100 are not leap years unless they are also divisible by 400. This makes century years (those divisible by 100) leap years only when divisible by 400. Equivalently, to test a century year: divide it by 400 — if there is no remainder, it is a century leap year; if there is a remainder, it is a common year.

Examples and a short list

Historical and near-future examples illustrate the concept: 1600 and 2000 were century leap years, while 1700, 1800 and 1900 were not. Similarly, 2100 (2100), 2200 and 2300 will be common years despite being divisible by 4; the next century leap year will be 2400. A compact list:

• Century leap years: 1600, 2000, 2400…
• Century common years: 1700, 1800, 1900, 2100, 2200, 2300…

Historical origin and purpose

The 400-year exception is part of the Gregorian reform introduced in 1582 to correct a mismatch in the older Julian calendar. The Julian rule — every fourth year a leap year without exception — produced an average year length slightly longer than the actual solar year. Over centuries that produced a measurable drift of calendar dates relative to the seasons. By omitting three leap days every 400 years (the century years not divisible by 400), the Gregorian calendar reduces that drift and more closely aligns the calendar year with the Earth's orbit.

Weekday patterns and notable calendar facts

Century years show consistent weekday behavior in the Gregorian system. Century leap years always begin on a Saturday, and their extra day, February 29, always falls on a Tuesday. Exceptional century common years follow a pattern determined by their residue modulo 400: a century year with remainder 100 begins on a Friday, remainder 200 begins on a Wednesday, and remainder 300 begins on a Monday. These regularities help calendar designers, historians and software developers predict dates far in the past or future.

Importance, examples of use and adoption differences

The century-leap-year rule is significant for civil timekeeping, astronomy and chronology because it keeps annual dates tied to the seasons over long spans. Adoption of the Gregorian rules occurred at different times in different countries, so local civil calendars in the transition era used different leap rules until they switched. For practical use today—date validation, calendaring software, legal deadlines and historical research—implementing the divisible-by-400 check is the standard way to determine whether a century year is a leap year.

For further reference see: Gregorian calendar overview, leap year rules, February 29, common year, examples like 1600 and 2000, historical non-leap centuries 1700, 1800, 1900, future non-leap 2100, weekday facts start-day pattern and February 29 weekday, and background on the Julian calendar.