History of Leap Year

Leap Year Day

The Leap Day, February 29, depicts a day that occurs only once every four years, every Leap Year or intercalary year when an extra day is inserted. But not every fourth year, if that year ends in “00” like 1900, then it is not a Leap Year. Except if that year ending in 00 is also divisible by 400 then it is a Leap Year. Unless it is a Tuesday and it is dark. OK, I made up that last rule. So, years like 2008 are Leap Years, being divisible by 4. 1900 is not a Leap Year as it ends in 00. In the year 2000, you’ll remember, the famous Y2K, when computer programmers only obeyed the first two rules and assumed that it wasn’t a Leap Year so that all the computers failed and the world came to an end? That was a Leap Year, as it was divisible by 4, and though it ended in 00, it was divisible by 400 (indeed, it’s divisible five times, if you’re still with me.)

Calculation Correction

How did we get into this calculation conundrum? It has to do with a cumulative rounding error in trying to reconcile the Julian calendar with the tropical or astronomical calendar. The Julian calendar, established by Julius Caesar in 46 B.C. lasted from 45 B.C. until A.D. 1582 and stipulated that the year should be 365 days for 3 years in a row, with every 4th year having 366 days. This meant that an average year was 365.25 days. But according to the tropical calendar, the year has 365.24219 days.

Tropical Year

A Leap Second is the fraction 1/31,556,925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time. But that was determined back in 1960. Since then, the second has been defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the Cesium 133 atom… due, of course, to the interaction of the state of the nucleus and the state of the electron clouds. Perhaps that’s intuitively obvious to the most casual observer of the Newtonian dynamical theory of motion.

It Adds Up


Gregorian vs Julian Calendar

Gregory XIII

In A.D. 1582 this accumulated error was estimated at 10 days, and Pope Gregory XIII decreed that the day following Oct. 4 would be Oct. 15, pretty handy if you had a library book due during that time. This Gregorian calendar was adopted throughout much of the Catholic world, but not everywhere. Uncivilized parts of the British Empire, like America, didn’t make the change until 1752 when September 2 was followed by September 14 and New Year’s Day was changed from 25 March to 1 January.

Ultimately, to make future adjustments for the error, which amounts to about three days every 400 years, it was decided that years ending in “00” would be normal years rather than Leap Years, with the exception of those divisible by 400. Unless it is a Tuesday and it is dark.

Bill Petro, your friendly neighborhood historian

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About billpetro

Bill Petro has been a technology sales enablement executive with extensive experience in Cloud Computing, Automation, Data Center, Information Storage, Big Data/Analytics, Mobile, and Social technologies.


  1. A leap second is not that fraction of the tropical year for 1900; it is exactly one second of TAI. The length of the atomic second was initially chosen to match that fraction of the tropical year, but the uncertainty was 2 parts in 10 to the 9, and the rate of TAI was adjusted by 1 part in 10 to the 12 at the beginning of 1977.

  2. Well Steve, apparently I’ve oversimplified to the point of error! Thanks for the comment.

  3. Hey Bill, another quick note. Unfortunately the earth’s rotation is slowing down at a rate of .005 seconds per year. So, if you extrapolate the math out … carry the 2 … divide by 3.14 … In about 2,000,000,000 we will need to add another leap year to keep us in sync.

    • Thanks Austin. I only update this article every 4 years, but I’ll put this in my To Do list to update the article when the cumulative rotational deterioration reaches a threshold of notice.

  4. Thank you for sharing.

  5. But till now i couldn’t get the correct answer of ending 00 is not leap year why, tell me briefly as possible

    • The time it takes for the Earth to orbit the sun is actually 365.242199 days. Adding one extra day to every fourth year (leap year), we get an average of 365.25 days per year, which is fairly close to the actual number. To get closer still, adding a leap year every 400 years on the century mark brings the average length of the year to 365.2425 days.


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