Interconverting Chinese and Western Years by Peter Meyer First published on this website on 2003-04-25 CE Online Chinese/Western Year ConverterA Chinese year is uniquely determined by an element name, an animal name and a cycle number. Thus each Chinese year may be represented as an ordered triple (e,a,k), where e and a are the numerals given below corresponding to the five element names and the twelve animal names and k is the number of the 60-year cycle in which the year occurs. The first year of the Chinese chronology (2697 BCE, the first year of the reign of the Yellow Emperor, Huang Di) is represented as (0,0,1) and the metal-dragon year of the present cycle is represented as (3,4,79).
Given the Chinese year (e,a,k) the corresponding Western year may be determined as follows. (e,a,k) is the mth year of the cycle, where m = 12e - 5a + j, and
Wood Fire Earth Metal Water 0 1 2 3 4
Rat Ox Tiger Rabbit Dragon Snake Horse Sheep Monkey Rooster Dog Pig 0 1 2 3 4 5 6 7 8 9 10 11
j = 1 if a is even and a <= 2e 61 if a is even and a > 2e 7 if a is odd and a <= 2e + 1 67 if a is odd and a > 2e + 1
and the corresponding Western year is m + 60k - 2757. Thus the Western year n corresponding to the Chinese year (e,a,k) is given by the formula
n = 12e - 5a + j + 60k - 2757
where j is determined as above.
The value of m for any given Chinese year in the cycle may be obtained directly from the following table:
Wood Fire Earth Metal Water Rat 1 13 25 37 49 Ox 2 14 26 38 50 Tiger 51 3 15 27 39 Rabbit 52 4 16 28 40 Dragon 41 53 5 17 29 Snake 42 54 6 18 30 Horse 31 43 55 7 19 Sheep 32 44 56 8 20 Monkey 21 33 45 57 9 Rooster 22 34 46 58 10 Dog 11 23 35 47 59 Pig 12 24 36 48 60
Having found the value of m corresponding to a given Chinese year in the kth cycle, the corresponding European year is m + 60k - 2757.
For converting Western years into Chinese, for any positive integers x and y, let rem(x,y) denote the remainder on dividing x by y (i.e., rem(x,y) = x mod y). Then given a Western year n, the Chinese year (e,a,k) may be determined as follows: Let i = rem(n+6,10) if n is even, rem(n+6,10) - 1 otherwise. Then e = ½ i. (Note that rem(n+6,10) is simply the last digit of n+6.) a = rem(n+8,12), and k is the largest integer k' such that 60k' <= n + 2756 (provided that n >= -2696). Having determined e and a by these means, the element name and the animal name are obtained from the above correspondence.
It should be noted that Chinese years do not coincide exactly with Western years, because Chinese years begin sometime in January or February. (Actually, according to Prof. Helmer Aslaksen, they always begin between January 21st and February 21st inclusive.) Thus when we say here that Western year n corresponds to Chinese year m this should be understood as saying that Chinese year m begins in January or February of Western year n.
One other point to note is that we have here taken the year (0,0,1) to correspond to -2696 (a.k.a. 2697 BCE) so that the 79th 60-year cycle began in 1984 CE. Some prefer to have (0,0,1) correspond to -2636,in which case 1984 corresponds to the beginning of the 78th cycle.
To illustrate this conversion algorithm, consider the Western year 1996. Then i = 2002 mod 10 = 2, so e = 1. a = 2004 mod 12 = 0. Since 60.79 = 4740 < 4752 = 1996 + 2756, k = 79. Thus 1996 corresponds to the fire-rat year in the 79th cycle.
Converting back from (1,0,79), we have e = 1 and a = 0, so a <= 2e so j = 1, so m = 13, so the corresponding Western year is 13 + 60.79 - 2757 = 1996.
For the Western year 2000 we have i = 6 so e = 3. a = 2008 mod 12 = 4 and k is the same so the corresponding Chinese year is the metal-dragon year in the 79th cycle.
For the Western year 1983 i = 1989 mod 10 - 1 = 8, so e = 4. a = 1991 mod 12 = 11. Since 60.78 = 4680 < 4739 = 1983 + 2756, k = 78. Thus 1983 corresponds to the water-pig year in the 78th cycle.
What Western year corresponds to the fire-dog year in the 78th cycle? In this case e = 1 and a = 10, so a is even and a > 2e so j = 61. Thus m = 12 - 50 + 61 = 23 and so the corresponding Western year is 23 + 78*60 - 2757 = 1946.
Online Chinese/Western Year Converter
This conversion algorithm has been implemented by the author as an online converter. This allows you to display:
- (i) all years, (ii) all years of a certain element-animal combination (e.g., wood-rooster), (iii) all years of for a specific element (e.g., fire) or for a specific animal (e.g., dragon) or (iv) all years at a certain position (1-60) in the Chinese 60-year cycle
- (i) in a certain range of years in the Common Era Calendar (e.g. -100 through 200) or (ii) in a certain range of Chinese 60-year cycles (e.g. 75 through 80).
For just one year or one cycle leave the second input box blank.
If you were born on or after February 21st in some year then to find the Chinese year corresponding to your birth year select Show all years in the range Common Era years birth-year. If you were born before January 21st then use the year immediately preceding your birth year. For other dates you must know when Chinese New Year occurred in the year of your birth, and use your birth year if you were born on or after Chinese New Year, otherwise the preceeding year.
The "epoch", i.e. the year corresponding to (0,0,1), may be set either to -2696 CE or to -2636 CE. This does not effect the element-animal combination of the Chinese year corresponding to a particular Western year.
This converter handles all years in the Chinese cycles 1 through 100, corresponding to the range of years CE from the epoch through the epoch + 5999 (which, if the epoch is -2696 CE, is -2696 CE through 3303 CE).
Chinese Calendar Date Conversion Software
For software useful in a scholarly study of the Chinese Calendar see Chinese Calendrics Software.
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