How often do leap years occur? Leap year calculation method.

Typically, a year has 365 days, but some years, known as leap years, have 366 days. Let's explore how often leap years occur and the method to calculate them.

What is a leap year? Frequency of leap years.

A leap year is a year with more days and months than a standard year, specifically:

- Lunar Leap Year is a year that includes an additional month. For instance, certain Asian countries like Vietnam, Japan, China incorporate an extra lunar month in leap years, such as 2017 having two lunar June months, and 2020 having two lunar April months.

- Solar Leap Year is a year that totals 366 days. The leap day falls on February 29th, and the majority of countries worldwide recognize and utilize this day.

In the Gregorian calendar, leap years occur every 4 years, while in the Lunar calendar, leap years occur every 3 years. Detailed explanation and calculation methods for leap years are provided in the following section.

2. Leap Year Calculation

2.1. Calculation of Gregorian Leap Year

Gregorian Calendar is based on the Earth's orbit around the Sun. Earth completes its orbit around the Sun in 365 days and 6 hours, which is considered a cycle and called a Gregorian year. There is an extra 6 hours each year, and every 4 years, these hours accumulate to 24 hours (one day), and the fourth year of the cycle adds an extra day in February (29th), known as a leap year.
There is a trick to calculate the Gregorian leap year: divide the number of years to be calculated by 4. If it is divisible by 4, then it's a leap year; otherwise, it's not.

Example:

- Years 2016 and 2020 are leap years because they are divisible by 4.

- Years 2018 and 2021 are not leap years because they are not divisible by 4.

Additionally, for years ending with two zeros (centuries), we divide the year by 400 to determine leap years. If it is divisible by 400, then it's a leap year; otherwise, it's not.

Example:

- Years 1600 and 2000 are leap years because they are divisible by 400.

- Years 1800 and 2200 are not leap years because they are not divisible by 400.

2.2. Calculation of Lunar Leap Year

Lunar Calendar is based on the Moon's orbit around the Earth. The Moon completes its orbit around the Earth in 29.53 days (known as one cycle), and a lunar year consists of 354 days (11 days less than the solar year). With this calculation method, lunar years are 33 days shorter (more than a month) than solar years.

To synchronize lunar phases with the seasons, an extra month is added every 3 lunar years to ensure alignment with the solar calendar. Even so, the lunar calendar still falls behind the solar calendar. To reconcile the lunar-solar calendar, every 19 years, an additional month is added twice within the span of 2 years.

Within 19 Gregorian years, there are 228 months, while within 19 lunar years, there are 235 months, resulting in a 7-month difference between the lunar and solar calendars. Within these 7 differential months, leap months are added in the 3rd, 6th, 9th, 11th, 14th, 17th, and 19th years of the 19-year lunar cycle.

To calculate the lunar leap year, one would divide the corresponding Gregorian year by 19. If the result is divisible by 19 or yields remainders of 3, 6, 9, 11, 14, or 17, then that year will have a leap month.

Example:

- Year 2017 in the lunar calendar is a leap year because when divided by 19, 2017 yields a remainder of 3, meaning 2017 has 1 leap month.

- 2021 Lunar year isn't a leap year due to a remainder of 7 when divided by 19.

Determining leap months after identifying leap years can be complex and involves astronomy. For ease, refer to the leap year and leap month chart from 1995 to 2031.

This article's insights help you grasp leap year calculations and the intriguing aspects of this method. Best of luck!