The day of a new moon is the start of a month (Beijing time which is UT+8:00). A year has 12 months which we can number 1 to 12. To construct a Chinese calendar, find two consecutive December solstices around date of interest. The new moon on or before solstice 1 date is month 11 of year 1, and the new moon on or before solstice 2 date is month 11 of year 2. To determine the numbering of the other months in between, count the number of new moons in between (possible values are 11 and 12). If the number is 11 then number the month as expected. Otherwise (12 months) the first month without a major solar term is a leap month and has the same number as the previous month. A major solar term is date of apparent solar longitude of either 0, 30, 60, 90, 120, …, 270, 300, 330 degrees. Chinese New Year is day 1 of month 1.
And you’re done! What you need to know (Beijing time):
- Dates of the relevant consecutive December solstices.
- Dates of the new moons in the range.
- If there is no leap month then that’s all you need. Otherwise you’ll also need the dates of the major solar terms.
- What kind of accuracy do you need? The demand for accuracy is unlimited, especially if an astronomical event occurs around midnight. For example, if a new moon occurs slightly before midnight, today is a new month; if it occurs slightly after midnight, the start of a new month is tomorrow.
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- The Chinese calendar is a lunisolar calendar based on astronomical events related to the movement of the Earth and the moon in the solar system. This is in contrast to the normal Gregorian calendar, which is algorithmically based. The use of astronomical events for the Chinese calendar may lead to problems in constructing the calendar for dates far in the future. This is because astronomical events cannot be predicted or calculated accurately for too far in the future; beside positional uncertainty, a major stumbling block is the uncertainty in calculating delta T, the difference between universal time (used in essentially all civil life) that is changing and dynamical time that is unchanging. This accuracy is critical when an astronomical event (important for the calendar) occurs around the boundary of the current day and the next day; this will be discussed further below.
- Time used for the calendar is UT + Beijing time zone. Currently this is UT + 8 hours. Before 1929 Beijing local mean time was used, which is approximately UT + 1397/180 hours.
- Day starts at midnight (time 0:00:00).
- Month starts at the day of a new moon. That is, if a new moon occurs from 0:00:00 to 23:59:59.99999* of a particular day, that day is the start of a new month.
Note that if a new moon occurs very close around midnight, this could lead to a prediction problem; in this case, the predicted/calculated start of a calendar month may be off by +/- one day and may affect other months (see below).
- Beside the astronomical new moon event, 24 solar terms are also defined, split into 12 major solar terms and 12 minor solar terms. The 12 major solar terms refer to the apparent solar longitude of 0, 30, 60, 90, 120, …, 270, 300, 330 degrees. The 0, 90, 180, 270 degrees longitude are also known as the March equinox, June solstice, September equinox, and December solstice. The 12 minor solar terms refer to the apparent solar longitude of 15, 45, 75, 105, …, 285, 315, 345 degrees. The construction of the calendar months especially requires knowledge of the major solar terms.
- A month is said to contain a particular solar term if the solar term happens in that month; that is, from time 0:00:00 of day 1 of the month, to 23:59:59.99999* of the last day of the month.
- Notice that by virtue of the above rules, if a new moon occurs at 12:57 of a particular day, that day is the start of a new month m; if a solar term occurs at 8:25 of the same day that solar term is deemed to have occurred in month m, even though the solar term occurs before the new moon (8:25 is before 12:57).
- The make-up of the months in the calendar is constructed so that the December solstice (apparent solar longitude of 270 degrees) occurs in the eleventh month. This is the major/strict rule of the Chinese calendar; the other rules revolve around this major rule to force its consistency. This also means that the December solstice can be used as the reference point for the construction of the Chinese calendar. More specifically, the new moon closest (on the day or before) to the December solstice is the eleventh month of the Chinese calendar; that is, if the December solstice occurs anytime (0:00:00 to 23:59:59.99999*) of the day d, then we find the closest new moon on or before time 23:59:59.99999* of day d.
Notice that if the new moon or December solstice occurs around midnight at each other’s boundaries, then a predicted eleventh month may be off by +/- one month and may affect other months.
- As the December solstice is the only reference point we have for the calendar, the construction of the calendar revolves around a December-solstice-to-December-solstice period, which we will simply call a solstice period.
- The first step is to determine how many new moons there are (or will be) in a solstice period. For this purpose, count the number of new moon starting from the day after December solstice 1, up to and including the day of December solstice 2. Obviously, the closest new moon (on the day or before) to December solstice 2 will be the next month 11 (as per the above rule). All that needs to be done now is to number the intermediate months.
For the current era and foreseeable future, there can be either 12 or 13 new moons in a solstice period.
In the case of 12 new moons in a solstice period, the calendar month can be constructed as per the above rules, starting from the eleventh month identified earlier, so we have 11, 12, 1, 2, 3, …, 9, 10, 11.
To force consistency in the “winter-solstice-in-the-eleventh-month” rule, when there are 13 new moons in a solstice period, one of the month is considered a “leap” month, and the other 12 a “normal” month. The leap month is the first month in the solstice period that does not have any major solar term. The leap month has the same “numbering” as the previous normal month; for example, if the month following the normal eleventh month (containing the December solstice) has no major solar term, then it is a leap month 11, the next month is 12, and the next is month 1 (start of a new Chinese year). This rule ensures that the next month 11 contains the December solstice. As a sidenote, when people refer to a certain month (e.g. seventh month of the Chinese calendar), they usually refer to the normal seventh month. Most notably, the traditional Chinese holidays are observed in the non-leap months.
Notice that there are exactly 12 major solar terms in a solstice period, and either 12 or 13 new moons. As such, in a leap solstice period with 13 months, there will always be at least one month that has no major solar term, for which the first one (in the solstice period) is taken as the leap month.
Note that in a non-leap solstice period there can be zero, one, or more months without a major solar term. In a leap solstice period there can be one or more months without a major solar term. This is caused by one or more month having more than one major solar term. In the present era a month can have either zero, one, or two major solar terms.
Notice that in determining the leap month, if a new moon or major solar term occurs very close around midnight at the boundary of each other, then a predicted month number can be off by +/- one month and may affect other months.
- Chinese New Year is the first day of month 1.
- The Chinese calendar uses a 60-year naming cycle for the years of the calendar. This consists of 10 heavenly stems and 12 earthly branches that cycles independently, resulting in a 10-year cycle for the stems and 12-year cycle for the branches, and together they form a 60-year naming cycle (lowest common multiple of 10 and 12). In recent years only the 12 branches remain in common use.
In English (note that none of these are translations) the ten stems are usually labelled:
{Male Wood, Female Wood, Male Fire, Female Fire, Male Earth, Female Earth, Male Metal, Female Metal, Male Water, Female Water}
{甲, 乙, 丙, 丁, 戊, 己, 庚, 辛, 壬, 癸}
{jiǎ, yǐ, bǐng, dīng, wù, jǐ, gēng, xīn, rén, guǐ}
The twelve branches are usually labelled as animals:
{Rat, Ox, Tiger, Rabbit, Dragon, Snake, Horse, Goat, Monkey, Chicken, Dog, Pig}
{子, 丑, 寅, 卯, 辰, 巳, 午, 未, 申, 酉, 戌, 亥}
{zǐ, chǒu, yín, mǎo, chén, sì, wǔ, wèi, shēn, yǒu, xū, hài}
The combining of the stems and branches for a year name results in {Rat, Tiger, Dragon, Horse, Monkey, Dog} matching to only the Male form of the stems, and {Ox, Rabbit, Snake, Goat, Chicken, Pig} matching to only the Female form of the stems (but again, the Male and Female form are not translations).
- For a particular Gregorian year, to get the cycle name of the current Chinese year (after the Chinese New Year around January-February) do the following, where Mod is the division remainder operator (e.g. 5 Mod 2 = 1).
Stem = (Gregorian year - 4) Mod 10; 0 refers to Male Wood, 9 refers to Female Water.
Branch = (Gregorian year - 4) Mod 12; 0 refers to Rat, 11 refers to Pig.
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| Calendar and Astronomical Data |
Click here for a yearly calendar with Chinese calendar dates such as Chinese New Year, Lantern festival, Dragon Boat festival, Mid-Autumn festival, Mid-Winter festival, to name a few.
Click here for times of the lunar phases as well as the solar longitudes, from year 1600 to 2200. These times are essential for anyone interested in the Chinese calendar, as well as the Japanese, Korean, and Vietnamese calendar.
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