A lot of the major holidays in East Asia are based on the lunar calendar. Additionally, older generation of East Asians celebrate their birthdays according to the lunar calendar. Thus, a conversion a necessary.
You can use this tool to pick a day and display what the equivalent lunar calendar day is!
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The origins of the Chinese Lunar Calendar is often attributed to Huang-ti, the Yellow Emperor in 2697 B.C. The calendar consists of twelve cycles of the moon, from a full moon to a new moon. The lunar calendar does not coincide exactly with the solar calendar, hence complex calculations are necessary to convert from one to another.
The information from this site is gathered from the Hong Kong Observatory