How to Make a Better Leap Year With Math

Roman emperors, popes, and stand-up comedians have all tried to make a more efficient leap year.


Leap year, lest you forget, is not only significant because it’s the title of a terrible movie and allowed the birth of American rapper Ja Rule (#LeapyearRule). It means we get an extra day every four years — unless that year is divisible by 100 — so we can stay in sync with the Earth’s rotation around the sun. It’s a fine system, but math nerds over the years, including YouTube comic Matt Parker, have argued that we could do a lot better.

While time may just be an illusion, our calendar is made of 365 days. The problem is, it actually takes Earth about 365.24219 days to circle around the sun — which is about an extra five hours, 48 minutes, 45 seconds and 138 milliseconds. All of this spare time needed to be accounted for.

Julius Caesar tried to fix this problem in 45 B.C. with his Julian calendar, and Pope Gregory XIII instigated the creation of the Gregorian calendar in 1582 A.D., which we still use today.

But, as Parker points out in his video, the Gregorian calendar is not quite perfect — in about 3,216 years the system will be off by a day — so he proposes that we make a switch to one of two alternative systems.

The first option is to adjust the Gregorian calendar by taking out three leap year days every 10,000 years. If the first two digits of any four-digit century (for example, the 20 in 2016) happens to be a multiple of 28, then we don’t have a leap year. With this 2,800-year rule, the calendar would only drift one day every 91,743 years.

Matt Parker breaks down the math.


“The easy way to remember this is if you’re in a year the year ‘blah blah blah’ and it ends with 2,800 or 5,600 or 8,400 — in any of those cases you don’t have a leap year,” Parker explains in a new video on his channel Standup Maths. “Otherwise, carry on with the Gregorian calendar as intended.”

While Parker came up with this system on his own, he does acknowledge that British mathematician Adam Goucher had suggested the idea before. (Spacetime know-it-all Neil deGrasse Tyson, naturally, did not skip his chance to chime in.)

Still, 91,743 years is mathematically ugly, so Parker suggests a second alternative — that we go back to the Julian calendar, but adjust it so that we skip one leap day every 128 years. This system would have it so that the calendar would only be off by a day every 625,000 years; essentially, humankind would go half a million years before we drifted a day.

Admittedly, calculating what year makes for every 128 years isn’t the easiest, so Parker takes it one step further, suggesting we just write all our years in binary. If the last seven digits of a binary year are zeros, then we skip the leap year. This year is 11111100000 in binary, so we’re good.

An astronomical clock created in the Middle Ages.

Andreas Rentz/Getty Images

If living in a mathematically sound society is a priority, then sure, we have multiple alternatives for adjusting the way leap years work now. The alternative? Say fuck it and let our descendants figure it out in 3,000 years.

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