# Reason We Have Leap Years

## What Is a Leap Year

A leap year is a year in which February has 29 days. Sometimes this is also known as an intercalary year.

Typically February will have 28 days. However about every four years, February will instead have 29 days. For instance, the years 2000, 2004, 2008, 2012 are leap years in which February has this extra day. This is unique to February. All the other months have the same number of days every year.

Therefore a leap year will have 366 days instead of the typical 365. the extra day of February 29 is known as the leap day.

## Leap year to synchronize calendar with Earth's orbit

The reason why we have to add an extra day to February in certain years is to keep the calendar in sync with Earth's orbit around the sun.

Originally, people used the calendar to track this seasons, so they know when crops will bloom and when to plant seeds. Since the seasons are caused by Earth's orbit around the sun, we have to keep the calendar in sync with the Earth's orbit in order to properly track the seasons.

It takes one year for the Earth to go around the sun. One calendar year corresponds to this this one orbit around the sun.

It takes about 365.25 days for the Earth to go around the sun. That is 365 days plus a quarter of a day. But since calendars can not have a quarter day, calendars are made with just 365 days, which is close enough for most purposes.

Over year after year, this quarter day that we had tossed out in our calender every year will start to accumulate and make a difference. In fact, after four years, our calendar will be short one whole day. Therefore every four years, we put in that extra leap day into our calendars.

Why we put that extra day into February instead of any other month is anyone's guess. But perhaps it is because February has the least numbers of days to begin with.

## How to Determine If a Year is Leap Year

Here is how to determine if a year is a leap year or not. (Aside from flipping to February and seeing if it has 29 days).

If a year is evenly divisible by 400, then it is a leap year for sure. Year 2000 is a leap year because 2000 is evenly divisible by 400.

If a year is not divisible by 400, but is evenly divisible by 100, then it is definitely not a leap year. Year 1900 is not a leap year because it is not divisible by 400, but is divisible by 100.

If a year is not divisible by 400 nor by 100, but is evenly divisible by 4, then it is a leap year. Year 2008 is neither divisible by 400 nor by 100. But it is divisible by 4. So it is a leap year.

If a year is not divisible by 400 nor by 100, nor by 4, then it is not a leap year. Year 2009 is an example.

By determining the answers to the above questions, one can determine precisely if a year is leap or not.

## Flow Chart to Determine Leap Year

## Another Way to Look at Leap Year

Starting at year 2000 which is a leap year, every four years from then, you get a leap year unless the year is a "century year". The exception is that if the year is divisible by 400, then it is always a leap year.

## Not Really Every Four Years

Some people will note that leap years typically occur every four years. And so if we know one leap year, we can determine the other leap years by counting every four. This is correct most of the time, but not always.

Since we know year 2000 is a leap year, then 2004, 2008, 2012, 2016, 2020, ..., 2096 would be leap years. It seems like leap year occurs every four years -- but not always.

This four-year pattern only works up to 2096. Because 2100 is NOT a leap year; it is not divisible by 400, but is divisible by 100. By our rule above it is not a leap year. The next leap year after 2096 is 2104. So here we jump EIGHT whole years before encountering another leap year. So year 2100 is when a leap year has skipped. Year 2100 would typically have been a leap year, but it is not.

Why don't we want to add the extra day to year 2100? The reason for the skipped leap year is because the Earth does not go around the sun in EXACTLY 365.25 days. It actually goes around the sun in 365.242374 days. Just a tad short of 365 and a quarter. Adding a day every four years would be a tad too much.

Therefore, if we keep adding a day every four years, that tad would accumulate and throw off our calendars again. So every so often, we skip adding that extra day. Year 2100 happens to be the year when we skip adding the leap day for that particular year.

## Steps for Determining Leap Year

If you are into algorithms, here is one provided by Wikipedia for determining leap year.

if year modulo 400 is 0

then is_leap_year

else if year modulo 100 is 0

then not_leap_year

else if year modulo 4 is 0

then is_leap_year

else

not_leap_year

"if year modulo 400 is 0" means "if year is evenly divisible by 400".

The algorithm indicates for us to do this ...

Step 1: Is the year evenly divisible by 400? If yes, then is leap year. Done. If no, go to step 2.

Step 2: Is the year evenly divisible by 100? If yes, then is not leap year. Done. If no, go to step 3.

Step 3: Is the year evenly divisible by 4? If yes, then is leap year. If no, then not leap year. That's it. You got your answer.