Chinese Lunar Calendar: The Calculation of the New Year's Date

What day does a Chinese lunar calendar new year's date fall on?  The answer can be quite complex.

Here are a few rules of thumb:

1) All calculations must be based on longitude 120d east, which corresponds to the east coast of China.

2) The new year's date falls on the second new moon after the winter solstice (which occurs around December 22nd).

3) The new year's date falls between January 21st and February 21st.

4) The new year's date falls on the new moon that is closest to the start of spring (Lập Xuân, 立春, which occurs around February 4th).

Rules 2-4 may fail once in a while.  However, taken all together, we will arrive at the Chinese new year's date.