The Leap Year as Explained by Neil deGrasse Tyson | StarTalk

Lee: Piers, no, they don't happen all the time. But neither do presidential elections. But people don't freak out with it. Well, it's a presidential election year. It's rare—notes every four years. Chill out!

We, on Earth, as we orbit the Sun, we know how to calculate a year; it's how long it takes to come back to where you were. That's a year. But it turns out if you cut the number of days we live into the year, it doesn't divide evenly. So there's not an even number of days in the time it takes Earth to go around the Sun. It takes like 365 and a quarter days to go around the Sun.

So we just ignore that quarter day—just sweep it under the rug. For three years, the fourth year—how many quarters have you added up? Four quarters! So there's a whole day now that you've saved up. In the fourth year, you put that day back in the calendar, and you give it to the neediest month, February.

And so this is the origin of the leap day, and this is as it was conceived in the Julian calendar, the calendar that preceded the current calendar, the Gregorian calendar. Most people don't know that this one every four-year rule overcorrects the leap day. It's not actually 365 and a quarter days; it's a little bit less than a quarter.

So you wait four years and put in a whole day. You put in too much; so you have to wait until you put in a whole day too much, then you take out a leap day that would have otherwise appeared. So every hundred years, you have overcorrected by a leap day, by an entire day.

So every hundred years—100 years are divisible by four, aren't they? Every hundred years, you take out the leap day that would have otherwise been there. So 1900 was not a leap year. 1800 was not a leap year. 1700 was not a leap year—for this reason, okay?

So now, by taking out that day, now you have overcorrected in the opposite direction, and now there's a day that you have to put back in. It turns out every 400 years—so every 400 years, in the century year that would have not had a leap day, on the century rule, gets a leap day put back in on the 400-year rule.

This sounds complicated, but it has profound implications. In the year 2000, it's a century year that wouldn't normally get a leap day, but it's a century year divisible by 400, so you put the leap day back in. So when everyone experienced the leap day in the year 2000, they're saying to themselves, “Of course, it's a leap year; it's divisible by four.” It's like, “No, it's a leap year because it's a century year divisible by 400.”

Therein is the Gregorian calendar as it was established in 1582. That's the story of the calendar you asked! Okay, I was sitting here minding my own business, and you had to ask about the calendar and the leap day.