Leap year

# Leap year

## What is a Leap Year?

A year whose numerical value is exactly divisible by 4 is called a leap year. But if the last two digits of the year is zero, then it must be divisible by 400.

For example, 2004, 2012, 2016, etc. are leap year because these are divisible by 4, but 2100, 2200, 2300 are not leap years even they are divisible by 4 because they are not divisible by 400.

## Why do we have a leap year?

Leap days align our modern-day Gregorian calendar with the Earth's orbit around the Sun. It takes the Earth about 365.242189 days, or 365 days, 5 hours, 48 ​​minutes and 45 seconds to revolve around the Sun. It is called the Tropical Year, and it begins on the March equinox.
However, the Gregorian calendar has only 365 days in a year. If we do not add a leap day on February approximately every four years, then each calendar year will begin 6 hours before the completion of its revolution around the Sun.

As a result, our time calculations will gradually diverge from the tropical year and rapidly fall out of sync with the seasons. With a deviation of about 6 hours per year, the weather will change to about 24 calendar days within 100 years. Let it be for some time, and residents of the Northern Hemisphere will be seen celebrating Christmas in the middle of summer in just a few centuries.

Leap days fix that error by giving the Earth extra time to complete a full cycle around the Sun.

## Why don't we add a leap day every 4 years?

If the tropical year was 6 hours longer than a calendar year with 365 days, we can use the Julian calendar, which without exception adds one leap day every 4 years. The deviation will increase for exactly 24 hours in 4 years, and will require exactly one day to hold the Earth in its orbit to the position where it was 4 years ago.

However, the deviation between the normal year and the tropical year is slightly less than 6 hours. The Gregorian calendar employs a slightly more complex set of rules to determine which years are leap years. This is still not true, but the resulting deviation is very small.

## Why we add a leap year after every 4 years and 400 years?

For the Gregorian calendar, the average length of the calendar year (the mean year) across the complete leap cycle of 400 years is 365.2425 days.

365.2425 days = 365 days + 0.24 day + 0.0025 day

Or 365.2425 days = 365 days + 0.25 day – 0.01 day + 0.0025 day             …………….  (i)

We take 365 days in a year.

0.25 day makes 1 day in 4 years, because 0.25 × 4 = 1 day.

So, we add this 1 day in the leap year after every 4 years.

Again, 0.01 day × 100 = 1 day

In equation (i), we can see that 0.01 is with minus sign and it makes 1 day after 100 years.

So, we subtract 1 day after 100 years. And miss a leap year after every 100 years.

For example, 2088, 2092, 2096 will be a leap year but 2100 will not be a leap year. 2104, 2108, etc. will again be a leap year.

Now, we see in equation (i), 0.0025 is with plus sign.

0.0025 day × 400 = 1 day

So, we add this 1 day after 400 years.

Thus, the year 2400 will be a leap year.

Conclusion

If a year number is a multiple of 4, it is a leap year. But if the year number is a multiple of 4 and contains 2 zeroes at the end like 2100, 2200, 2300, etc., then it should be a multiple of 400 to be a leap year.