2100 will not be a leap year while 2400 will be.

Leap years can be confusing sometimes. But, why were they formed?

So the task was to form a calendar which matches with astronomical year ( i.e earth’s rotation and revolution) without any error for millions of years.

To do that, we consider every fourth year as leap year. In other words, any year divisible by four, will be a leap year. So why 2100 is not a leap year?

That’s because we want to be very precise.

Here is the actual rule: The year must be evenly divisible by 4;

If the year can also be evenly divided by 100, it is not a leap year;

unless…

The year is also evenly divisible by 400. Then it is a leap year.

Let’s start from the basics. You can skip to why not 2100?

So here’s the defination we made:

1 day: 1 rotation of earth around its axis.

1 year: 1 complete revolution of earth around the sun.

Let’s invite some numbers now.

Earth completes one revolution around the earth in 365.242375 days

So physically, 1 year = 365.242375 days

But in calendar, we consider 1 year = 365 day

To compensate that extra ¼ day each year, we decided to have one extra day every four year.

So in every 4 year cycle, 3 years would have 365 days and one leap year will have 366 days.

Thus, number of days passed in four year, according to calendar would sync with earth’s revolution.

why not 2100?

But story didn’t end there. When we calculate number of days passed in 100 years according to calendar and according to earth’s revolution, error arises.

As we decided earlier that, every fourth year would would be leap year i.e 366 days. So, in a span of 100 years there would be 25 leap years (having 366 days) and 75 normal years (having 365 days).

Let’s do very simple calculation:

Calendar vs. Earth’s revolution

100 years = 25 (366) + 75 (365) = 36525

100 years = 100 (365.24) = 36524

Oops! According to our previous thumb rule, our calendar will have one extra day.

So, what to do now? We made another rule.

To settle that one extra day, we decided that every 100th year in calendar would not be a leap year i.e it will have 365 days only.

100 years = 24(366) + 76 (365) = 36524 days.

100 years = 100 (365.242375) = 36524.23 days.

Account settled! Every 100th year like 1800, 1900, 2100, 2200 are not considered as leap years.

Do you think story ends there? No.

When we calculate number of days passed in 400 years according to calendar and according to earth’s revolution, error arises again.

We made the rule that every fourth year would be leap year expect every 100th year.

So in span of 400 years, there would be 96 leap years and 304 normal years.

400 years = 96(366) + 304 (365) days = 146096

400 years = 400(365.242375) = 146096.95 = 146097

So, now in our calendar we have one day less.

Again to compensate, we decided, every 400th year would be a leap year.

So 2400, 2800, 3200… are leap years

Whereas 2100, 2200, 2300, 2500 … are not leap years

So here’s the final rule :

The year must be evenly divisible by 4;

If the year can also be evenly divided by 100, it is not a leap year;

unless…

The year is also evenly divisible by 400. Then it is a leap year.