The math of leap years: Why Feb 29 does not come once every four years

We know 2024 is a leap year because 24 is divisible by 4, the same reason that 2020, 2016, 2012, 2008, 2004 and 2000, too, were leap years.

In 1924, months before the Gateway of India was inaugurated in December, our counterparts a century older would have reasoned along similar lines, but with a key difference. They knew 1924 was a leap year, as were 1920, 1916, 1912, 1908 and 1904.

The difference was 1900 which, unlike 2000, was a non-leap year.

The year 1800 wasn't leap either, nor was 1700, but 1600 was leap. Going ahead, 2100, 2200 and 2300 will not be leap years, but 2400 will be.

So, what is going on here? Years ending in 00 are not always leap, even though they are all divisible by 4. They are leap years only if the two digits preceding the 00 form a multiple of 4; hence 1600, 2000 and 2400 are leap. To put it simply, a leap year does not come exactly once every four years; the actual frequency is 97 times every 400 years.

This is something that is perhaps less widely known than the idea of leap years and February 29 at its most basic level. To be sure, many people eventually get to know about this rule when they come across the non-leap 00 year during their lifetimes. On the other hand, many of the people living today will have missed the point when they found that 2000 was a leap year, like all other multiples of 4. And many of these same people will never get to see the next exception, in 2100, unless they are very young today and blessed with a long life.

The first time anyone learns about the rule, the obvious question that pops up is: Why? There is mathematics, astronomy and history at play here, and the explanation must begin with why we have leap years in the first place.

The early leaps