Where leap years come from: from Julius Caesar to the century rule
The seasonal year lasts about 365.2422 days, so the calendar needs an extra day to keep up. Here is how the Julian calendar and the 1582 Gregorian reform produced today's rule.
Every four years, February gains a 29th day. Almost always, but not always: 1900 was not a leap year, 2000 was, and 2100 will not be. That odd rule is the result of two thousand years of tweaks to keep the calendar from drifting away from the seasons.
A year that doesn't add up
The year that matters for the seasons is the tropical year: the time between two March equinoxes, for example. It lasts about 365.2422 days, or roughly 365 days, 5 hours, 48 minutes and 46 seconds. A calendar of exactly 365 days would fall almost a quarter of a day behind every year. According to the US Naval Observatory, that would add up to about 24 days per century, and the start of spring in the Northern Hemisphere would slide from March 20 to mid-April within a hundred years.
Julius Caesar and the 445-day year
By the 1st century BC, the Roman calendar was such a mess that it was about three months out of step with the Sun. Julius Caesar decided to fix it once and for all. To realign the dates, the year 46 BC was stretched to 445 days, the longest in the history of the Western calendar. From 45 BC, the Julian calendar took effect, with advice from the astronomer Sosigenes of Alexandria: 365-day years plus an extra day every four years, for an average of 365.25 days.
That is where the word bissextile comes from. The Romans counted days backward from the kalends, the first day of the month. The extra day was added by repeating the sixth day before the kalends of March, which then occurred twice: bis sextus, the doubled sixth. The rollout also stumbled at first: because of counting mistakes, the calendar only worked as intended from around AD 8.
A tiny error that grew to ten days
The Julian year of 365.25 days is about 11 minutes and 14 seconds longer than the tropical year. That sounds trivial, but it adds up to almost a full day every 128 years. By the 16th century, the March equinox was falling around the 11th, about ten days before its reference date of March 21. That worried the Church, because the date of Easter is calculated from the equinox.
The fix came with the papal bull Inter gravissimas, signed by Pope Gregory XIII on February 24, 1582. The core proposal came from the physician and astronomer Aloysius Lilius and was developed by the mathematician Christopher Clavius. To make up the lag, ten dates were simply skipped: in several Catholic countries, Thursday, October 4, 1582, was followed by Friday, October 15. The sequence of weekdays was left untouched.
The century rule
- Years divisible by 4 are leap years.
- Exception: years divisible by 100 are not leap years.
- Exception to the exception: years divisible by 400 are leap years again.
With this rule there are 97 leap years every 400 years, and the average year becomes 365.2425 days, very close to the tropical year's 365.2422. The remaining gap is about half a minute per year. Sources differ on when it will add up to a full day: about 3,030 years, according to calculations based on the mean tropical year, or about 3,300 years, according to the US Naval Observatory. The gap comes from different definitions of the year.
Not everyone switched in 1582
The reform came from the pope, and Protestant and Orthodox countries were slow to accept it. The later a country switched, the bigger the jump, because every non-leap century year added another day of difference.
| Country or region | Year adopted | Dates skipped |
|---|---|---|
| Spain, Portugal and their empires, Italy, Poland | 1582 | 10 |
| France | 1582 (December) | 10 |
| Protestant German states | 1700 | 11 |
| Great Britain and colonies | 1752 | 11 |
| Sweden | 1753 | 11 |
| Japan | 1873 | switched from another calendar |
| Russia | 1918 | 13 |
| Greece | 1923 | 13 |
Spanish and Portuguese colonies in the Americas, including Brazil, followed the reform of their mother countries, in some places with a delay while the news crossed the ocean. In Great Britain, September 2, 1752, was followed by September 14. In Russia, the change came after the revolution, and many Orthodox churches still use the Julian calendar for religious feasts, which is why Orthodox Christmas falls on January 7.
In short, leap years exist because Earth does not complete its orbit around the Sun in a whole number of days. Caesar solved most of the problem, Gregory XIII refined the rule, and the result is a calendar that will not need another fix for thousands of years. When in doubt about a year, apply the three rules above.
