This note was found in January 2000 among the author's papers. It has not been published before. It was written c. 1977 in India and is presumably based upon the author's study of Tibetan calendars published there. It is reproduced here without change.

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Since a Tibetan year is uniquely determined by an element name, an animal name and a number, each Tibetan year may be represented as an ordered triple (e,a,k), where e and a are the numerals given below corresponding to the element name and the animal name of the year, and k is the number of the cycle in which the year occurs. For example, the wood-hare year of the present [c. 1977 (- Ed.)] cycle is (4,0,16), and the first year of the Tibetan chronology is represented as (0,0,1).

Fire	Earth	Iron	Water	Wood
0	1	2	3	4

Hare	Dragon	Snake	Horse	Sheep	Monkey	Bird	Dog	Pig	Mouse	Ox	Tiger
0	1	2	3	4	5	6	7	8	9	10	11

Given the Tibetan 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

j =	1	if 2e >= a and a is even
	61	if 2e < a and a is even
	-5	if 2e > a and a is odd
	115	if e = 0 and a = 11
	55	otherwise

and the corresponding Western year is m + 60k + 966. Thus the Western year n corresponding to the Tibetan year (e,a,k) is given by the formula

n = 12e - 5a + j + 60k + 966

where j is determined as above.

The value of m for any given Tibetan year in the cycle may be obtained directly from the following table:

	Fire	Earth	Iron	Water	Wood
Hare	1	13	25	37	49
Dragon	50	2	14	26	38
Snake	51	3	15	27	39
Horse	40	52	4	16	28
Sheep	41	53	5	17	29
Monkey	30	42	54	6	18
Bird	31	43	55	7	19
Dog	20	32	44	56	8
Pig	21	33	45	57	9
Mouse	10	22	34	46	58
Ox	11	23	35	47	59
Tiger	60	12	24	36	48

Having found the value of m corresponding to a given Tibetan year in the kth cycle, the corresponding European year is m + 60k + 966.

For converting Western years into Tibetan, for any positive integers x and y, let rem(x,y) denote the remainder on dividing x by y. [That is, rem(x,y) = x mod y (- Ed.)] Then given a Western year n, the Tibetan year (e,a,k) may be determined as follows: Let i = rem(n+4,10) if n is even, rem(n+4,10) - 1 otherwise. Then e = ½ i. (Note that rem(n+4,10) is simply the last digit of n+4.) a = rem(n+5,12), and k is the largest integer k' such that 60k' <= n - 967 (provided that n >= 1027). Having determined e and a by these means, the element name and the animal name are obtained from the above correspondence.

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Added January 2000:

To illustrate this conversion, consider the Western year 1996. Then i = 2000 mod 10 = 0, so e = 0. Since 60.17 = 1020 < 1029 = 1996 - 967, k = 17. a = 2001 mod 12 = 9. Thus 1996 corresponds to the fire-mouse year in the 17th cycle.

Converting back from (0,9,17), we have e = 0 and a = 9, so j = 55, so m = 10, so the corresponding Western year is 10 + 60.17 + 966 = 1996.

For the Western year 2000 we have i = 4 so e = 2. k is the same and a = 2005 mod 12 = 1, so the corresponding Tibetan year is the iron-dragon year in the 17th cycle.

Finally, for the first year in the Tibetan Calendar (0,0,1) we have m = j = 1 so the corresponding Western year is 1 + 60 + 966 = 1027.

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Added April 2003:

The above algorithm for converting Tibetan calendar years into their Western equivalents has been implemented as an online calculator at Tibetan Calendar Converter.

Interconverting Chinese and Western Years
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