Why do we have leap year?

Robert Egler, senior lecturer in physics and director of instructional labs at N.C. State, explains why we have that extra day this month. Questions and answers have been edited.

Q: Why is a leap year necessary?

The actual time it takes the Earth to complete one orbit of the sun - called a "tropical year" - is 365.2422 days. Thus a standard calendar year of 365 days is 0.2422 days, or 5 hours, 48 minutes, 46 seconds short of the actual year. If this isn't corrected, the calendar year will lose one day in relation to the actual year about every 4.4 years. At this rate, the start of the calendar year will be about 24 days early in 100 years. Since this is approximately one day in four years, every four years (with exceptions) we add one extra day to the calendar year to bring it back in line with the actual year.

A leap year every four years is equal to an average length of the calendar year of 365.2500 days, known as the "Julian year." Better than 365 days, but still not the same as the actual year of 365.2422 days. An average year of 365.2500 days still is wrong by 11 minutes and 14 seconds each year. This doesn't seem like much, but over time it adds up: 1 day in 128 years. If we make a slight change by saying that century years - 1700, 1800, 1900, 2000, etc. - are not leap years, unless they are evenly divisible by 400, we get an average year of 365.2425 days, which is only wrong by 26 seconds a year.

Q: Who invented leap year?

The leap year was invented by the Romans in 46 BC, credited officially to Julius Caesar, but actually derived by the astronomer Sosigenes at the request of Caesar. By 46 BC, the date of the spring equinox had slowly shifted about 81 days out of place in the Roman calendar, so Caesar added 81 days to reset the year to the correct date, and introduced the leap year to help it stay in the right place. The Roman leap year was every four years without exception. This version, called the Julian calendar in honor of Julius Caesar, has the average year as 365.2500 days.

By AD 1582 the error between the calendar year of 365.2500 days and the actual year of 365.2422 days had once again accumulated to about 10 days, which was messing up the date of Easter. So in February 1582, Pope Gregory XIII issued an order, known as the Inter Gravissimas, that reset the start of the year by dropping 10 days out of the calendar that year. The Gregorian calendar is the calendar we follow today.

Q: How far off would our seasons be if leap years were never invented?

If Caesar had never reset the calendar and instituted the leap year, the accumulated error today would be about 580 days. In other words, we would have lost one entire year and an additional 214 days, and today mid-winter would actually be in June. January would be the height of summer vacation season.