H034

Is every fourth year a leap year?

Most of us learned the rule as "every four years." But 1900 had no February 29, and neither will 2100. The year 2000 was the exception to the exception.

Earth's year
365.2422 days
one trip around the Sun, measured season to season
"Every 4 years" gives
365.25 days
about 11 minutes too long, every year
Skip 3 leap days per 400 years
365.2425 days
off by about 1 day every 3,000+ years

Which century years get a February 29?

The Gregorian calendar, adopted in 1582, drops three leap days every 400 years

1600 Leap 1700 No 1800 No 1900 No divisible by 4,still skipped 2000 Leap you livedthrough this 2100 No divisible by 4,still skipped 2200 No 2300 No 2400 Leap Century years are leap years only when divisible by 400

A leap day every four years overshoots, so the calendar quietly skips three of them every 400 years. A year is about 365.2422 days, not 365.25. Adding a day every four years makes the calendar run about 11 minutes long each year, and those minutes pile up to a full day roughly every 128 years. The fix: century years are leap years only if they divide evenly by 400. So 2000 was a leap year, but 1700, 1800, 1900, and 2100 are not.

Simple rules people repeat are often the first step of a longer rule. Before relying on one, ask whether it has exceptions that only show up rarely, like once a century.

Try it somewhere else

Your phone, your bank, and your calendar app all have to decide whether February 29, 2100 exists.

If a program used the simple "every four years" rule, what would go wrong, and when?

Why the calendar had to be fixed in 1582

The older Julian calendar used the simple every-four-years rule. By the 1500s it had drifted about 10 days away from the seasons, pushing the spring equinox, and the date of Easter that depends on it, earlier and earlier. Pope Gregory XIII's 1582 reform jumped the calendar ahead 10 days (October 4 was followed by October 15) and added the century rule. Britain and its colonies did not switch until 1752, when they had to skip 11 days.

Related exhibits

Sources: Length of the tropical year and the Gregorian leap-year rule: U.S. Naval Observatory; Royal Museums Greenwich. Calendar reform of 1582 and Britain's 1752 change: Encyclopaedia Britannica.