The 29^{th} of February is an incredibly special day. As you are all likely aware, once every 4 years, this extra day is added to February. However, What is the mathematical reason for having another day in February?

A year is the time it takes to do one full orbit around the Sun. Using this calculation, we discover that a year is actually *close to* 365.25 days. When the Julian calendar was invented, a leap year was scheduled once every 4 years, and added another day to February, which is sometimes dubbed the “Leap Day”. This system creates a net average of 365.25 days in a year. Thereby creating Leap Years, and keeping the seasons in line with the calendar.

However, this was the old Julian system, so what *actually *changed when we invented the Gregorian calendar commonly used today?

Earlier, I mentioned that a year is **close **to 365.25. A rough estimate is actually 365.2422 days in a year. This makes sense, as why would the time it took the Earth to rotate on its axis, and the time it takes the Earth to orbit the sun be related at all. By this logic, surely there has to be a leap day removed at some point?

That’s correct, and exactly what the Gregorian calendar system did. Originally, the attempt was to make every 4 years a leap year, **except **a century. However, this would cause a small issue, our calendar would drift at an approximate rate of 1 day over 323.6 years, which would quickly build up and cause significant misalignment. Although it was far less than the Julian calendars 133 years to drift a day, it still wasn’t good enough for Pope Gregory XIII!

That’s exactly how we came to our modern solution, where we remove a leap year every century, except for if the year is divisible by 400. The US Naval Observatory states “the years 1700, 1800 and 1900 are not leap years but 2000 is.” This lowers our drift so we only lose one day every 3236 years. This is much more effective, however issues may still pile up in many thousands of years.

Unless you’re here in 2100, this is likely something you won’t have to remember the rule of, which is exactly why many believe that we still follow the simple Julian Calendar style for Leap Years.