In addition to the Xia or Chinese Solar Calendar the Chinese have a Chinese Lunar Calendar. It is based on the moon’s rotation around the earth which takes approximately 29.53059days.
The ancient Chinese felt the need to synchronize the Chinese lunar calendar with the Chinese solar calendar. Unfortunately this is not an easy task. Twelve lunar months add up to 354.36708 days and is not equal to one solar year of 365.242199 days!
To solve this problem, the Chinese added an addition month in 7 out of every 19 years. The additional month takes the name of the month before and is known as a leap month. Due to this addition month, the 1st day of the 1st month (also known as Chinese New Year) varies from year to year between the months of January and February. This can be very confusing but it works.
The first lunar month is not called January. Instead it is simply called the 1st Month. The second month is called the 2nd Month and so on until the 12th Month!
Each lunar month can have either 29 or 30 days. When the month has 29 days, it is considered to be small and when it has 30 days it is considered to be big.
Hence a lunar 1st Month that has 30 days is called 1st Month Big while a 6th Month that has 29 days is called 6th Month Small.
The lunar year is name after the 12 Earthly Branches with names like Zi, Chou, Yin, Mao and so on. To make it easy for the general population, they associate an animal with each of the Branch. For example Zi is Rat, Chou is Ox, Yin is Tiger, Mao is rabbit etc. This cycle is repeated every 12 years. For example 1960 is the year of Zi or the Rat and so is 1972, 1984, 1996 and so on.
To find out the Chinese lunar calendar equivalent of any western date you can use this conversion calendar.
Most traditional Chinese festivals such a the Chinese New Year, Lantern Festival, All Souls Day, Mid-Autumn (Moon Cake) festival are based on the Chinese Lunar Calendar.