Leap Day

A leap year (also known as an intercalary year or a bissextile year) is a year containing one additional day (or, in the case of lunisolar calendars, a month) added to keep the calendar year synchronized with the astronomical or seasonal year. Because seasons and astronomical events do not repeat in a whole number of days, calendars that have the same number of days in each year drift over time with respect to the event that the year is supposed to track. By inserting (also called intercalating) an additional day or month into the year, the drift can be corrected. A year that is not a leap year is called a common year.

For example, in the Gregorian calendar, each leap year has 366 days instead of the usual 365, by extending February to 29 days rather than the common 28. Similarly, in the lunisolar Hebrew calendar, Adar Aleph, a 13th lunar month, is added seven times every 19 years to the twelve lunar months in its common years to keep its calendar year from drifting through the seasons. In the Baha’i Calendar, a leap day is added when needed to ensure that the following year begins on the vernal equinox.

The name “leap year” comes from the fact that while a fixed date in the Gregorian calendar normally advances one day of the week from one year to the next, the day of the week in the 12 months following the leap day (from March 1 through February 28 of the following year) will advance two days due to the extra day (thus “leaping over” one of the days in the week). For example, Christmas fell on Tuesday in 2001, Wednesday in 2002, and Thursday in 2003 but then “leapt” over Friday to fall on a Saturday in 2004

February 29, also known as leap day in the Gregorian calendar, is a date that occurs in most years that are divisible by 4, such as 2008, 2012, 2016, 2020, and 2024. Years that are divisible by 100, but not by 400, do not contain a leap day. Thus, 1700, 1800, and 1900 did not contain a leap day, 2100, 2200, and 2300 will not contain a leap day, while 1600 and 2000 did, and 2400 will. Years containing a leap day are called leap years. February 29 is the 60th day of the Gregorian calendar in such a year, with 306 days remaining until the end of the year. In the Chinese calendar, this day will only occur in years of the monkey, dragon, and Rat. Although most modern calendar years have 365 days, a complete revolution around the Sun (one solar year) takes approximately 365 days and 6 hours. An extra 24 hours thus accumulates every four years, requiring that an extra calendar day be added to align the calendar with the Sun’s apparent position. Without the added day, in future years the seasons would occur later in the calendar, eventually leading to confusion about when to undertake activities dependent on weather, ecology, or hours of daylight.

A solar year is actually slightly shorter than 365 days and 6 hours (365.25 days). The Earth completes its orbit around the Sun in 365 days, 5 hours, 49 minutes, and 16 seconds (365.2425 days). The currently accepted figure is 365 days, 5 hours, 48 minutes, 45 seconds. Thus adding a calendar day every four years is an excess of around 44 minutes each time, or about 3 days every 400 years. To compensate for this, three days are removed every 400 years. The Gregorian calendar reform implements this adjustment by making an exception to the general rule that there is a leap year every four years. Instead, a year divisible by 100 is not a leap year unless that year was also exactly divisible by 400. This means that the years 1600, 2000, and 2400 are leap years, while the years 1700, 1800, 1900, 2100, 2200, 2300, and 2500 are not leap years. The Gregorian calendar repeats itself every 400 years, which is exactly 20,871 weeks including 97 leap days. Over this period, February 29 falls on Sunday, Tuesday, and Thursday 13 times each; 14 times each on Friday and Saturday; and 15 times each on Monday and Wednesday. The order of the leap days is: Thursday, Tuesday, Sunday, Friday, Wednesday, Monday, and Saturday.

Adding a leap day  shifts the commemorations in the 1962 Roman Missal. The calendar of the Roman king Numa Pompilius had only 355 days (even though it was not a lunar calendar) which meant that it would quickly become unsynchronized with the solar year. An earlier Roman solution to this problem was to lengthen the calendar periodically by adding extra days to February, the last month of the year. February consisted of two parts, each with an odd number of days. The first part ended with the Terminalia on the 23rd, which was considered the end of the religious year, and the five remaining days formed the second part. To keep the calendar year roughly aligned with the solar year, a leap month, called Mensis Intercalaris (“intercalary month”), was added from time to time between these two parts of February. The (usual) second part of February was incorporated in the intercalary month as its last five days, with no change either in their dates or the festivals observed on them. This followed naturally, because the days after the Ides (13th) of February (in an ordinary year) or the Ides of Intercalaris (in an intercalary year) both counted down to the Kalends of March (i.e. they were known as “the nth day before the Kalends of March”). The Nones (5th) and Ides of Intercalaris occupied their normal positions. When it was thought necessary to add (every two years) an intercalary month of 22 or 23 days, so that the civil year corresponded to the natural (solar) year, this intercalation was made in February, between Terminalia [23rd] and Regifugium [24th].

The leap day was introduced in Rome as part of the Julian reform in the 1st century BC. As before, the intercalation was made after February 23. The day following the Terminalia (February 23) was doubled, forming the “bis sextum”—literally ‘twice sixth’, since February 24 was ‘the sixth day before the Kalends of March’ using Roman inclusive counting (March 1 was the Kalends of March and was also the first day of the calendar year). Although there were exceptions, the first day of the bis sextum (February 24) was usually regarded as the intercalated or “bissextile” day since the 3rd century AD. February 29 came to be regarded as the leap day when the Roman system of numbering days was replaced by sequential numbering in the late Middle Ages. The concepts of the leap year and leap day are distinct from the leap second, which results from changes in the Earth’s rotational speed. But the basic problem is the same: the quotient of the larger measure of time by the smaller is a non-integer. There is no way to perfectly fit a whole number of days/months into a year, nor is there a way to perfectly fit a whole number of seconds into a day. Leap seconds and leap years are used to correct the resulting drift.