In our lifetime, every four years is a leap year

I wonder how many people know what a leap year is, when they occur, and why. Everybody knows the poem "Thirty days hath September...", and from that poem, everybody "knows" that every fourth year is a leap year (1992, 1996, 2000, 2004, 2008, 2012, ...). That's what I "knew" too, until my first year of university.

As an aside, I didn't know how our state and federal elections worked (i.e. preferential and proportional voting) until my third year of university, studying Computer Science...

But it's not true, at least not anymore. From the first century to the 16th century every fourth year was a leap year, but that calendar – the Julian Calendar – was too fast: the calendar date gradually lost its synchronisation with the natural seasons (the equinoxes), the lunar cycles, and most importantly Easter. Now Easter may not be that important to you or me, but it was important to the Catholic church, and Pope Gregory XIII initiated calendar reform to solve this problem.

With a leap year every four years, there are 365.25 calendar days per year, on average. However, a solar year (the amount to time the Earth spends completing one revolution of the sun) is 365.24219 days, to five decimal places. The difference between 365.25 days and 365.24219 days is 0.00781 days. Thus the Julian calendar "gains" 0.00781 days per year, which means it gains one whole day every 128.0409 years.

Julius Caesar introduced the Julian Calendar in 46BC. Thus by 1500AD, approximately 12 days had been gained. What effect did this have? Well, as mentioned earlier, it meant that Easter (and solstices and equinoxes) were not being celebrated at the correct time according to the position of the sun and the stars in the sky. While it's impossible to create a human calendar that perfectly matches the Earth's movement around the Sun, when you're celebrating Easter 12 days early, it's probably time to review your calendar.

And that's why we don't have a leap year every four years anymore. Although he didn't design it, Pope Gregory XIII introduced the Gregorian Calendar in 1582, and various countries adopted it at different times, from Italy/France/Spain/others in 1582 through England in 1752 to Russia in 1918, making it difficult to compare dates between certain countries during that 336-year period.

The rule governing leap years in the Gregorian Calendar is this: every fourth year is a leap year, but every hundredth one is not, but every four-hundredth one is. Thus, 1900 wasn't a leap year; nor was 1800 or 1700. But 2000 was. And 2100, 2200 and 2300 won't be. But 2400 will be. And so on.

I think it's unfortunate that 2000 was a leap year, because it meant that we'll never experience an exception to the rule "every fourth year is a leap year" unless we live to 2100, which means that many people will remain ignorant of their own calendar.

See the Wikipedia page on the Gregorian Calendar for a lot more fascinating information.

So if a Julian year is on average 265.25 days, how long is a Gregorian year? Well, the Gregorian Calendar repeats every 400 years, so we'll need to average it out over that period of time. Instead of 100 leap years, there are only 97, so the number of days in 400 Gregorian years is 365 × 400 + 97 = 146097, making an average of 146097 ÷ 400 = 365.2425 days per year. And how long is a solar year? 365.24219 days. So it's close, but still one calendar day will be gained every 3225.8 years. Sir John Herschel proposed in the 18th century that one leap year in 4000 years should be cancelled so the calendar would be even more accurate, but this wasn't adopted.