Science

Why we have leap years, and why some are skipped

A year is not a whole number of days. Every calendar rule since has been an attempt to manage the remainder without letting the seasons drift.

By 3 min read
An illustrated calendar page for the month of February, with a starling.
A February calendar page. Image by Theo van Hoytema, Public domain, via Wikimedia Commons.

Key takeaways

  • The tropical year is about 365.2422 days, not 365.25 and certainly not 365.
  • Adding a day every four years assumes 365.25, which is slightly too long.
  • That error accumulated to about ten days by the late sixteenth century.
  • The Gregorian rule drops the leap day in century years unless divisible by 400.
  • The result, 365.2425 days, is accurate to about a day in three thousand years.

The Earth’s orbit and the Earth’s rotation are unrelated processes, so there is no reason for one to divide neatly into the other, and it does not. A year is about 365.2422 days. Every calendar humans have used is a scheme for handling that awkward fraction, and leap years are the current scheme.

What happens if you ignore the fraction

Run a 365-day calendar and you finish each year about a quarter of a day before the Earth has finished its orbit. That sounds negligible and it compounds quickly.

After four years you are a day early. After a century, roughly 24 days. After twelve centuries the calendar has slid by a full season, and the month you call June is happening in what used to be spring. Ancient calendars that drifted this way had to be corrected by decree from time to time, which is as unsatisfactory as it sounds.

The Julian fix, and the error inside it

The Julian calendar added a day every fourth year. Four years of 365 plus one extra day averages 365.25 days per year, which is very close.

Close, but slightly too long. The real figure is 365.2422, so the Julian year overshoots by about 0.0078 days, roughly eleven minutes.

Eleven minutes a year is a day every 128 years or so. It is a much smaller error than before, and it runs in the opposite direction, but it is still an error and it still accumulates. By the late sixteenth century the calendar had drifted about ten days out of step with the seasons, and the spring equinox was arriving well before the date the church had fixed it at.

The Gregorian rule

The 1582 reform did two things. It removed the accumulated ten days in a single jump, and it changed the rule so the error would not build up again.

The new rule has three parts:

  • A year divisible by 4 is a leap year.
  • Unless it is divisible by 100, in which case it is not.
  • Unless it is also divisible by 400, in which case it is after all.

So 1700, 1800 and 1900 were ordinary years. 1600 and 2000 were leap years. 2100 will not be.

Dropping three leap days every four centuries removes exactly the excess the Julian rule was adding. The average becomes 365.2425 days, which is within about half a minute a year of the truth: a day of error in roughly three thousand years.

Countries changed at different times

The reform was not adopted everywhere at once, and for a long period different countries were running different calendars, which makes historical dates genuinely ambiguous.

Britain and its colonies held out until 1752, by which point the discrepancy had grown to eleven days, and they were removed in one step: the 2nd of September was followed by the 14th. Some countries did not change until the twentieth century, which is why the October Revolution in Russia is dated to November elsewhere.

Leap seconds are a different problem

Worth separating, because the two get confused. Leap days reconcile the day with the year. Leap seconds reconcile clock time with the Earth’s rotation, which is very slightly irregular and gradually slowing.

Unlike leap days, leap seconds cannot be scheduled by a rule, because the slowing is not perfectly predictable. They are announced when needed, which is exactly why they cause so much difficulty for computer systems.

More timekeeping and orbits

For a place where the difference between solar time and clock time is built into stone, the instruments at Jantar Mantar. For another consequence of orbital mechanics, why the Moon shows us one face.

Sources

  1. Tropical year
  2. Gregorian calendar
  3. Julian calendar

Frequently asked questions

Yes. It is the exception people find counterintuitive. Century years are normally skipped, but 2000 is divisible by 400, so it kept its leap day. 1700, 1800 and 1900 did not, and 2100 will not either. Anyone whose intuition about the rule was formed around the year 2000 learned the exception rather than the rule.

When the Gregorian calendar was introduced, the accumulated drift had to be removed in one step, so ten dates were simply skipped: in the countries that adopted it immediately, the 4th of October was followed by the 15th. Other countries adopted it much later and had to drop more days. Britain and its colonies changed in 1752 and skipped eleven.

Chiefly because the date of Easter is calculated from the spring equinox, and the drift was steadily moving the calendar equinox away from the astronomical one. A calendar that slips a day every century eventually has its seasons in the wrong months, which matters for agriculture as well as for the church.

HRITU Editorial Desk is the byline for pieces produced in-house by the HRITU editorial team. We write about cooking, travel, science and everyday knowledge, and we explain the reasoning behind what we publish rather than just stating conclusions. Every article is checked against primary or reference sources before it goes out, dated on publication, and updated in the open when we learn something is wrong. Corrections and questions are welcome at info@hritu.com.

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