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Every four years, falling alongside the US presidential election and the Summer Olympics, we get an extra day in our calendar (perhaps to keep up with all that’s happening). Leap years add Feb. 29 to the normally 28-day month of February, extending our yearly total to 366 days.

But have you ever stopped to wonder why and how we ended up with an extra day? Here’s a little background:

The Earth actually takes a bit more than 365 days to go around the sun

That’s right: Our planet actually takes nearly six hours more than that to complete one orbit of the sun, according to NASA. The Earth’s orbit roughly equals 365.25 days, meaning that every four years, we have an extra day on our hands.

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Rather than have each year be an incomplete number of days, modern calendars rely on leap years once every four years to make the average year equal 365.25 days. So, 2017, 2018, and 2019 were 365 days apiece, while 2020 is a leap year with 366 days. Add those days together and divide by four and you have an average year of 365.25 days.

So 2020 is a leap year with a Feb. 29, as were 2016, 2012, 2008, and so on.

Another twist — which requires some math

This modern standard was set in 1582 by Pope Gregory (well before US elections and the modern Summer Olympics were around — their alignment is a coincidence), and is based on the Roman calendar established in 46 B.C.E. by Julius Caesar.

But, there’s actually a further twist courtesy of Pope Gregory, who developed what we’ve come to know as the Gregorian calendar. The Earth actually takes 365.2425 days (that’s 365 days, 5 hours, 48 minutes, and 46 seconds by NASA’s watch) to orbit the sun, which means every four years, there’s an additional .01 of a year unaccounted for.

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To solve that problem, the pope prohibited century years (such as 1700, 1800, or 1900) from serving as leap years, unless they were divisible by 400, like the year 2000.

That’s because it takes 400 years to observe the difference between 365.25 days and 365.2425 days. So making 1700, 1800, and 1900 normal years but adding one day in the leap year 2000 kept us on track, removing the three extra days that would have been recorded during that stretch. Multiply 365.25 times 400 and multiply 365.2425 times 400 and the difference between the two resulting numbers is three. (146,100-146,097=3.)

So holding back on extra days in 1700, 1800, and 1900 meant that by the time we reached 2000, we had taken care of that three-day difference.

Is that enough math for you? It can always be more rigorous, as the Encyclopaedia Britannica points out, “for still more precise reckoning, every year evenly divisible by 4,000 (i.e., 16,000, 24,000, etc.) may be a common (not leap) year.”

So, look out for the year 4000. Your descendants won’t know what to do without that extra day.


Peter Bailey-Wells can be reached at peter.bailey-wells@globe.com. Follow him on Twitter @pbaileywells.