# Leap Years

### The Rule:

According to the **Gregorian calendar**, which is the civil
calendar in use
today, years evenly divisible by 4 are leap years, with the exception of
centurial years that are not evenly divisible by 400. Therefore, the years
1700, 1800, 1900 and 2100 are not leap years, but 1600, 2000, and 2400
are leap years.

### Background:

The Gregorian calendar year is intended to be of the same length as
the cycle of the seasons. However, the cycle of the seasons, technically
known as the **tropical year**, is approximately 365.2422 days. Since
a calendar year consists of an integral number of whole days, a calendar year
cannot exactly match the tropical year. If the calendar year always consisted
of 365 days, it would be short of the tropical year by about 0.2422 days every
year. Over a century, the calendar and
the seasons would depart by about 24 days, so that the beginning of Spring
in the northern hemisphere would shift from March 20 to April 13.

To synchronize the calendar and tropical years, leap days are periodically
added to the calendar, forming leap years. If a leap day is added every
fourth year, the average length of the calendar year is 365.25 days. This
was the basis of the **Julian calendar**, introduced by Julius Caesar in
46 B.C. In this case the calendar year is longer than the tropical year by
about 0.0078 days. Over a century this difference accumulates to a little over
three quarters of a day. From the time of Julius Caesar to the sixteenth
century A.D., the beginning of Spring shifted from March 23 to March 11.

When Pope Gregory XIII instituted the Gregorian calendar in 1582, the calendar was shifted to make the beginning of Spring fall on March 21 and a new system of leap days was introduced. Instead of intercalating a leap day every fourth year, 97 leap days would be introduced every 400 years, according to the rule given above. Thus, the average Gregorian calendar year is 365.2425 days in length. This agrees to within a half a minute of the length of the tropical year. It will take about 3300 years before the Gregorian calendar is as much as one day out of step with the seasons.