Understanding Leap Year

Introduction

A leap year is a year with an extra day, so it’s longer than a normal year. Every 4 years, we have a leap year, and it adds an extra day to February. So February has 29 days in a leap year, instead of the usual 28. So, in a leap year, there are 366 days compared to the usual 365 days in a normal year. But, you might be wondering why we add a day every 4 years. To understand this, let’s look at the two most famous calendar systems: the Julian calendar and the Gregorian calendar.

The Julian Calendar vs. The Gregorian Calendar

In reality, an astronomical year is actually a little less than 365.25 days. The Julian calendar system says that every year has 365 days, except for every 4th year, which has 366 days. This is to account for that extra 0.25 days that we wouldn’t otherwise include in the calculation of the days in a normal year. By not including 0.25 days every normal year, we get 1 day every 4th year, and this is why every 4th year is considered a leap year with 366 days.

According to the Julian calendar system, there are approximately 365.25 days in a year, and hence it is reasonable to add 1 day every 4 years to account for that extra 0.25 days every year. 

As I said, an astronomical year is actually a little less than 365.25 days. To be precise, it’s 365.2422 days. This means that the Julian calendar isn’t quite accurate. That’s where the Gregorian calendar comes in. It’s the calendar that’s used all over the world. The Gregorian calendar is a little more accurate than the Julian calendar. It uses 365.2425 days in a year, which is very close to 365.2422 days.

The Gregorian calendar system states that “a year that is exactly divisible by 4 is a leap year, except for years that are exactly divisible by 100. But if a year is exactly divisible by 400, then it is a leap year.”

For example, 1700, 1800, and 1900 aren’t leap years, but 2000 is because it’s exactly divisible by 400. But why is that the case?

Remember when I said that the Gregorian calendar considers each year to
have 365.2425 days? Let’s do some math to understand why we shouldn’t consider
years like 1700 as leap years:

To simplify the calculations a bit, let’s start from year one. Every year, there are extra 0.2425 days as we are considering that a normal year has 365 days. This means that after every 4 years, there are 0.2425 * 4 = 0.97 days which is nearly equal to 1 day. So, we add 1 day every 4 years, but this is not accurate. We should have added 0.97 days, but we decided to add 1 day. This means that 0.03 days (1 – 0.97 = 0.03) are added extra every 4 years. By the time 100th year comes, we have added 0.75 days (0.03 * 25 = 0.75) extra. Let’s consider the approximate value which is 1 day. So, we need to subtract 1 day every centurial year. This is the reason why every centurial year in the Gregorian calendar is not leap years. But, remember that the actual number was 0.75 days and we considered it as 1 day. This means we subtracted 0.25 days each centurial year. Therefore, every 400 years, we should consider adding 1 day (0.25 * 4 = 1 day) to account for this difference. This is the reason why if a year is divisible by 400 it should be considered a leap year according to the Gregorian calendar. So, in this way, we can accurately calculate each year as 365.2425 days. 

Summary

The Gregorian calendar is more accurate than the Julian calendar because it closely approximates the number of days in an astronomical year. Every fourth year is a leap year, except for years that are exactly divisible by 100. However, if a year that is divisible by 100 is also divisible by 400, then it is a leap year.