Why Do We Have Leap Days?

The leap day, February 29, is approaching. This day only comes once every four years, and we’ll explore the reasons behind that in today’s article.

To understand why leap days exist, we first need to understand what days and years exactly are. While you might have heard that a day is a rotation of the Earth, that is the sidereal day. But the day we use on a calendar is a solar day, which is precisely 24 hours (give or take a second in very special cases), but the rotation period of the Earth is actually about four minutes less than that. That’s because you need to take the Earth’s orbit within a rotation into account. A solar day is the time it takes from one noon to the next on a particular place. And the Earth actually rotates a little more than 360 degrees in one solar day because it has moved a little bit every day in its orbit.

Meanwhile, one year is the orbital period of the Earth. It takes exactly one year, on average, for Earth to orbit once around the Sun. This is also the period of the cycle of the seasons. Earth has seasons because of its axial tilt, and as the rotational axis of the Earth is stable, the Earth is tilted the same way today than it was one year ago. It might be a little bit difficult to understand with plain text, but we’ll illustrate it to you with a diagram.

We might have heard that one year is 365 days, but when you calculate the orbital period, it actually comes out to about 365.25 days. And that 0.25 days per year is what the leap day is trying to solve.

If we used a plain 365-day schedule for one year, that would mean one year would be six hours less than one revolution of the Earth around the Sun. And while that might not seem like much, if we don’t correct the error, it would gradually expand over the years. For example, January 1 is winter in the northern hemisphere and summer in the southern hemisphere. But if we stop having leap days once every four years, the Earth would actually travel slightly less than 360 degrees around the Sun after one calendar year. That day would become summer in the northern hemisphere and winter in the southern hemisphere in about 730 years’ time. This would stop the calendar from telling which season it is based on the day of the year.

And since it was decided that it would be more convenient for the calendar to keep track of the seasons, people have modified the calendar to correct for the extra 0.25 days per year. That comes out to one day every four years, and that is how the leap day, on February 29, works.

But the relationship isn’t that simple. If you look closer into the Earth’s orbital period, it’s not exactly 365.25 days. It’s actually around 365.242 days. That means, even with the leap day once every four years, the year would still deviate from the Earth’s actual orbit.

Therefore, there is a more precise method to correct for the extra part of the day in a year. Specifically, in a period of 400 years, instead of having 100 leap days, we only have 97. Most of the time, if the year is divisible by 4 (like in 2024), there is one leap day in the year. But if the year is divisible by 100, but not by 400, no leap day occurs. This is seen most recently in the years 1900 and 1800, and will be seen again in the year 2100.

But if you know anything about real numbers, almost all of them are irrational. They cannot be expressed as fractions of integers. And since the ratio between Earth’s orbital period and rotational period is probably irrational (it even changes over time as the Earth’s orbit evolves), we don’t have a precise, finitely repeating way to add leap days to keep the year perfectly in sync with the actual orbital period of the Earth. That means on-demand leap days are necessary outside of the current leap-day schedule. But the current calendar is good enough that we don’t need these additions in the foreseeable future.

In this article, we discussed why there is a leap day once every four years, or rather, 97 times every 400 years. This is because one year is 365 days plus about 6 hours, and we need to account for that extra 6 hours per year to keep it from falling out of sync with the seasons.

1. (n.d.). Earth Fact Sheet. Retrieved February 28, 2024, from https://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html