EOY

Why leap years exist, and why February gets the extra day

The calendar says 365 days; the Earth takes about 365.2422 days to go round the Sun. Leap years are the bookkeeping that stops the two drifting apart.

The fraction that will not go away

A tropical year — the time from one spring equinox to the next — is approximately 365.2422 days. If every calendar year had exactly 365 days, the calendar would run ahead of the seasons by almost a quarter of a day each year: about one day every four years, a month every 120 years. Any calendar that wants New Year to stay in the same season has to put that quarter day back somewhere.

Caesar's fix: one day every four years

The Julian calendar, which took effect in 45 BC under Julius Caesar, used the simplest possible rule: add a leap day every four years, making the average year 365.25 days. That is very close to 365.2422, but not equal — the Julian year is about 11 minutes too long. Over centuries the minutes add up: roughly three days every four hundred years.

Gregory's correction: skip three leap days in four centuries

By the late sixteenth century the Julian calendar had drifted about ten days from the equinoxes. The reform promulgated by Pope Gregory XIII in 1582 — designed chiefly by Aloysius Lilius and Christopher Clavius — kept Caesar's rule but removed three leap days every 400 years. The rule most of the world uses today reads:

Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100, but these centurial years are leap years if they are exactly divisible by 400.

So 1900 was not a leap year, 2000 was, and 2100 will not be. The average Gregorian year is 365.2425 days — within about 27 seconds of the tropical year, an error of roughly one day in three thousand years. To realign the calendar with the seasons, the reform also skipped ten days outright: Thursday 4 October 1582 was followed by Friday 15 October 1582. Countries adopted the change at very different times; Great Britain and its colonies waited until 1752 and had to drop eleven days from that September.

A pleasing consequence of the 400-year rule: a full cycle is 146,097 days, which is exactly 20,871 weeks — so the Gregorian calendar repeats itself, weekdays included, every four centuries.

Why February

In the Roman calendar, all months except February had an odd number of days — 29 or 31 — because even numbers were considered unlucky. February, already the odd one out and the month where the Romans made their intercalary adjustments, kept that role when Caesar reformed the calendar, and it has kept it ever since. The leap day is 29 February for no astronomical reason at all; it is a two-thousand-year-old habit.

What this means for the countdown

The board does not count calendar days and then guess. It measures the exact time to midnight on 1 January in the selected zone, so in a leap year the extra day is simply there: on 1 January of a leap year the board reads 366 days, and the progress bar along the bottom is scaled to the real length of the year, with the month marks placed where the months actually begin. See how many days are left in the year for the month-by-month table.

Sources

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