What is a leap year?

1.1 Overview

The calendar year used by most of the modern world, the Gregorian calendar, consists of 365 days. However, the time required for the Earth to complete one full orbit around the Sun, known as a tropical year or solar year, is approximately 365.2422 days. This means that a standard calendar year is roughly six hours shorter than a solar year.

If this fractional difference were ignored, the calendar would drift away from the natural seasons by about one day every four years. Over the span of a century, the calendar would shift by approximately 24 days, causing seasonal events such as the spring equinox to occur much earlier in the calendar year. To mitigate this discrepancy, an extra day is periodically added to the month of February, extending it from 28 to 29 days.^{[1]2월이 다른 달보다 짧은 이유는 로마 교황이나 황제가 자기 이름의 달을 길게 만드느라 2월에서 며칠을 뺏어갔다는 루머가 널리 퍼져 있으나, 실제로는 율리우스 력 제정 당시부터 2월이 평년 28일, 윤년 29일로 정해져 있었다.} A year containing this extra day is known as a leap year, while a standard 365-day year is referred to as a common year.

1.2 Calculation and Rules

In the Gregorian calendar, determining whether a given year is a leap year follows a specific set of mathematical rules to account for the precise length of the tropical year.

• The Four-Year Rule: Every year that is evenly divisible by four is designated as a leap year.
• The Century Exception: Years that are evenly divisible by 100 are not leap years, despite being divisible by four.
• The Four-Century Exception: Years that are evenly divisible by 400 are leap years, overriding the century exception.

Under these criteria, the years 1996 and 2004 were leap years because they are divisible by four. The year 1900 was a common year because it is divisible by 100 but not by 400. Conversely, the year 2000 was a leap year because it is divisible by 400. This three-part rule ensures an average calendar year length of 365.2425 days, closely matching the actual astronomical year.

1.3 Historical Evolution

The concept of inserting extra days to balance timekeeping dates back to antiquity. Early civilizations recognized the mismatch between lunar cycles and solar seasons, often adding intercalary months to their calendars on an ad-hoc basis.

1.4 Solar vs. Lunisolar Calendars

While modern international standards rely on the solar-based Gregorian leap day, other traditional calendar systems utilize different mechanisms for temporal correction.

• Solar Calendars: Systems such as the Coptic or Ethiopian calendars also add a leap day every four years, creating an intercalary mini-month at the end of the year rather than extending an existing month.
• Lunisolar Calendars: Systems like the traditional Chinese calendar, the Hebrew calendar, and the Korean traditional calendar track both lunar phases and the solar year. Because twelve lunar months equal approximately 354 days—roughly 11 days short of a solar year—these calendars periodically insert an entire leap month rather than a single day to realign with the solar cycles.

1.5 Cultural and Social Impact

The presence of an extra day in leap years has generated unique societal phenomena, traditions, and administrative considerations.

2.1 The Julian Calendar and the Alexandrian Computation

The concept of inserting an intercalary day every four years was formally systematized under the dictatorship of Julius Caesar in 45 BCE. Guided by the Alexandrian astronomer Sosigenes, the Roman state transitioned from a lunar-solar alignment to a strict solar calendar of 365.25 days. To correct centuries of accumulated seasonal drift, the year 46 BCE—known historically as the *Annus Confusionis* ("Year of Confusion")—was extended to 445 days via the manual insertion of two extra months between November and December, alongside the standard intercalary month.^{[3]https://www.britannica.com/topic/Julian-calendar — 당시 누적된 오차 90일을 한 번에 바로잡기 위해 력 사이에 두 달을 강제로 쑤셔 넣는 바람에 46 BCE는 인류 역사상 가장 긴 445일짜리 해가 되었다.}

2.2 The Gregorian Intercalation Rule

While the Julian model assumed an orbital period of exactly 365.25 days, the actual tropical year is approximately 365.2422 days. This discrepancy of roughly 11 minutes per year results in a drift of one full day every 128 years. By the 16th century, the vernal equinox had shifted by ten days, disrupting the ecclesiastical calculation of Easter. In 1582, Pope Gregory XIII issued the papal bull *Inter gravissimas*, introducing a refined century-based exception rule: year numbers divisible by 100 are omitted from leap status unless they are also uniformly divisible by 400.^{[4]https://www.vaticanobservatory.org/resources/history-of-astronomy/inter-gravissimas — 교황 그레고리오 13세가 선포한 교서 이름 'Inter gravissimas'는 라틴어로 '가장 중대한 임무 중에서'라는 뜻이다.} This modification reduced the mean calendar year length to 365.2425 days, shifting the error margin to just one day every 3,030 years.

2.3 The Bissextile Naming Convention

In classic Roman chronology, days were not numbered sequentially from the first of the month; instead, they were counted backward from fixed reference points (Kalends, Nones, and Ides). The leap day was not added to the end of February (February 29), but was inserted by repeating the sixth day before the Kalends of March (*Ante diem sextum Kalendas Martias*). The duplicated day was termed *bis sextum* ("the second sixth"), which serves as the etymological root for the term for leap year in various Romance languages, such as *année bissextile* in French and *año bissextile* in Spanish.

2.4 The Gregorian Transition Anomalies

The adoption of the Gregorian calendar occurred non-uniformly across sovereign states, creating severe chronological discrepancies during international record-keeping:

• The British Empire (1752): The Calendar (New Style) Act 1750 mandated the realignment of the calendar. Eleven days were dropped from September 1752 (September 2 was followed immediately by September 14), triggering localized civil protests regarding contractual obligations and lease terms.
• Sweden (1700–1712): Sweden attempted a gradual transition by omitting leap days from 1700 to 1740. However, due to the outbreak of the Great Northern War, the rule was applied inconsistently. To re-align with the Julian calendar, Sweden added *two* leap days to the year 1712, creating the historically unique date of February 30, 1712.^{[5]스웨덴은 율리우스력에서 그레고리오력으로 천천히 넘어가려다 전쟁 때문에 잊어버리고 윤년을 누락하여 날짜가 꼬이자, 결국 율리우스력으로 복귀하기 위해 2월 30일을 임시로 만드는 기묘한 해프닝을 겪었다.}
• The Soviet Union (1930–1931): Following the introduction of the Soviet Revolutionary Calendar (which utilized five-day work weeks), February 30 was temporarily used in official planning cycles during 1930 and 1931 to ensure uniform month lengths, before the state reverted to the traditional calendar structure.

2.5 Leap Seconds vs. Intercalary Days

Leap days address the orbital period of the Earth around the Sun (the tropical year), whereas leap seconds compensate for variations in Earth's rotational speed on its own axis. Because tidal dissipation and core-mantle liquid interactions cause irregular decelerations in rotational velocity, Coordinated Universal Time (UTC) periodically inserts or subtracts a "leap second" at the end of June 30 or December 31. Unlike the deterministic, mathematically predictable occurrence of leap years, leap seconds are designated dynamically by the International Earth Rotation and Reference Systems Service (IERS) with only six months' advance notice.

2.6 Statutory and legal status of February 29

Under classic English Common Law, the extra day of a leap year and the day preceding it were treated in legal contexts as a single continuous 48-hour unit (*nondum quasi incrementum*), established by the statute *De Anno et Die Bissextili* of 1236. In modern legislation, age of majority calculations for individuals born on February 29 differ by jurisdiction:

• Under the laws of the United Kingdom and Taiwan, a person born on February 29 legally reaches their anniversary of birth on March 1 in non-leap years.
• Under legal precedents in parts of the United States and New Zealand, the statutory recognition of legal adulthood defaults to February 28 in non-leap years.

2.7 Non-Earth Planetary Intercalation

The dynamic requirement for leap intercalations extends to any planetary calendar tied to a celestial body whose rotational period is not an integer fraction of its orbital period:

• Mars: The Martian solar day (sol) is approximately 24 hours, 39 minutes, and 35 seconds long, while the Martian year comprises approximately 668.599 sol. Proposed Martian calendars (such as the Darian calendar) incorporate a systematic leap cycle consisting of six leap years of 669 sols per 10-year period to stabilize seasonal markers.^{[6]화성의 1년은 지구 기준으로 약 687일이며, 화성 하루(sol)가 지구보다 약 39분 길기 때문에 화성용 달력 계산은 지구보다 훨씬 복잡하다.}