The calculations related to Tibetan calendars are often based on the ideas presented in the Kalachakra Tantra. In this case, some interpretations may differ, which then changes the very structure of the calendar and the methods of calculation. If in the usual Tibetan calendar the 33rd month of each cycle is inserted, then in the Tsurphu calendar the correspondence 67 average lunar months=65 average solar months is used. At the same time it should be taken into account that from the point of view of classical astronomy it will still lead to some errors in calculations, as the synodic period of the Moon's revolution is 29.530588 days. Accordingly, further as constant values (which is also some error that can be accumulated in Tibetan calendars due to the peculiarities of mathematics and approach) the synodic period of the Moon's revolution will be used.

     For convenience in determining the number of past lunar months, we will also use data on Julian dates, which may allow to some extent to increase the accuracy of calculations for determining the number of lunar months and some dates. The second main problem to consider is the need to determine the starting point of the calculations. Since the Tsurphu calendar has been changed several times, if history is to be believed, the date of July 26, 1854 (the sixth lunar month) will be taken as the starting point of the calculation. This is due to the fact that on this day begins the first day of the lunar month after the actual appearance of an additional month.

     About correspondence of lunar and solar months a little was written above. However it is also necessary to take into account, when in this case lunar months are added, but it does not happen every year. So the second lunar additional month will be at the end of the period, that is it will have number 67. Accordingly, the first lunar additional month will be the 33rd month in this cycle of 67 months.

     So, further on the example of several years (2003, 2004, 2023, 2024, 2025) we will show calculations, allowing to determine the date of occurrence of Losars. The date from which the calculations will be made will be taken arbitrarily, so that such date does not coincide with a possible losar (new year). The first of March of each of the specified years will be used as such date. Also, to demonstrate the situation when there will be a different value in paragraph 6.3, a date for calculations will be added: September 1, 2025

 

     So, the sequence of actions is as follows:
1. determine the Julian date of the base date. To determine the Julian date there are many different services on the web and descriptions in astronomy collections, so the sequence will not be described here.
     For July 26, 1854 the Julian day number will be 2398425
2- Determine the Julian dates (Julian day number) for the given years

August 1, 2003	2452852
August 1,2004	2453218
August 1,2023	2460157
August 1,2024	2460523
August 1,2025	2460888
Sept. 1, 2025	2460919
August 1,2033	2463810

 

3. determine the number of days that have passed from the base date

August 1, 2003	2452852-2398425	54427
August 1, 2004	2453218-2398425	54793
August 1, 2023	2460157-2398425	61732
August 1, 2024	2460523-2398425	62098
August 1, 2025	2460888-2398425	62463
Sept. 1, 2025	2460919-2398425	62494
August 1, 2033	2463810-2398425	65385

4. Determine the number of lunar months that have passed since the base date. And allocate the whole part

August 1, 2003	54427/29,530588	1843
August 1, 2004	54793/29,530588	1855
August 1, 2023	61732/29,530588	2090
August 1, 2024	62098/29,530588	2102
August 1, 2025	62463/29,530588	2115
Sept. 1, 2025	62494/29,530588	2116
August 1, 2033	65385/29,530588	2214

5. Determine the number of double lunar months that have passed since the beginning of the base date by dividing by 67 and separating the whole part and the remainder. One must be added to the remainder to get rid of the zero month error and inaccuracy in determining the last month of the cycle

August 1, 2003	1843/67	27	35
August 1, 2004	1855/67	27	47
August 1, 2023	2090/67	31	14
August 1, 2024	2102/67	31	26
August 1, 2025	2115/67	31	39
Sept. 1, 2025	2116/67	31	40
August 1, 2033	2214/67	33	4

6. To reduce to the 1-12 dimension, we need to perform several operations. 
6.1 We remove data on pairs of double months by subtracting the posterior number of past cycles of 67 months each

August 1, 2003	1843-27*2	1789
August 1, 2004	1855-27*2	1801
August 1, 2023	2090-31*2	2028
August 1, 2024	2102-31*2	2040
August 1, 2025	2115-31*2	2053
Sept. 1, 2025	2116-31*2	2054
August 1, 2033	2214-33*2	2148

 

6.2 Subtract the data for the only additional month. This is done when the remainder of the division by 67 (with an additional unit) is not equal to 33 or 67. In this case, it is better to take another date for calculations with an offset of one and a half months in one or the other direction
If the remainder is less than 33, there is no need to subtract one month. If it is more than 32 - subtract one month

August 1, 2003	1789	(34)	1	1788
August 1, 2004	1801	(46)	1	1800
August 1, 2023	2028	(13)	0	2028
August 1, 2024	2040	(25)	0	2040
August 1, 2025	2053	(38)	1	2052
Sept. 1, 2025	2054	(39)	1	2053
August 1, 2033	2148	(4)	0	2148

6.3 Divide the result by 12 and subtract only the remainder

August 1, 2003	1788/12	0
August 1, 2004	1800/12	0
August 1, 2023	2028/12	0
August 1, 2024	2040/12	0
August 1, 2025	2052/12	0
Sept. 1, 2025	2053/12	1
August 1, 2033	2148/12	0

6.4 Recall that the primary date was the sixth month, so we need to add 6 to the result we get

August 1, 2003	6
August 1, 2004	6
August 1, 2023	6
August 1, 2024	6
August 1, 2025	6
1 сентября 2025	7
August 1, 2033	6

 

7. To determine the date of Losar celebration in the specified years, we need to do the following: analyze the possibility of additional months between the specified month and the beginning of the year. To do this, we need to analyze the remainder of point 5.

August 1, 2003	6 л.м.	34
August 1, 2004	6 л.м.	46
August 1, 2023	6 л.м.	13
August 1, 2024	6 л.м.	25
August 1, 2025	6 л.м.	38
Sept. 1, 2025	7 л.м.	39
August 1, 2033	6 л.м	4

 

8. If the remainder is less than the month number, it means that there was an additional month and the additional unit must be subtracted when determining the new month number for Losar

August 1, 2003	6 л.м	нет	0
August 1, 2004	6 л.м.	нет	0
August 1, 2023	6 л.м.	нет	0
August 1, 2024	6 л.м.	нет	0
August 1, 2025	6 л.м.	нет	0
Sept. 1, 2025	7 л.м.	нет	0
August 1, 2033	6 л.м.	да	-1

9. If there is a probability of crossing the number 33 in the remainder or the result is 33 when subtracting the number of the month, you must subtract an additional unit

August 1, 2003	6 л.м.	да	34	-1
August 1, 2004	6 л.м.	нет	46	0
August 1, 2023	6 л.м.	нет	13	0
August 1, 2024	6 л.м.	нет	25	0
August 1, 2025	6 л.м.	да	38	-1
Sept. 1, 2025	7 л.м.	да	39	-1
August 1, 2033	6 л.м.	нет	4	0

 

10. Then we determine the actual month number taking into account items 4, 7, 8, 9 and adding the correction factor 1 (there is no zero month).

August 1, 2003	54427/29,530588	1+1843-6+0-1	1837
August 1, 2004	54793/29,530588	1+1855-6+0	1850
August 1, 2023	61732/29,530588	1+2090-6+0	2085
August 1, 2024	62098/29,530588	1+2102-6+0	2097
August 1, 2025	62463/29,530588	1+2115-6+0-1	2109
(Sept. 1, 2025)	62494/29,530588	1+2116-7+0-1	2109
August 1, 2033	65385/29,530588	1+2214-6-1	2208

 

11. determine the Julian day number for the beginning of the month plus a five-day offset by multiplying the result by the Moon's synodic period of revolution and adding the base date number

(August 1, 2003)	1837*29,530588+2398425+5	2452677,69	(Feb. 6, 2003)
(August 1,2004)	1850*29,530588+2398425+5	2453061,588	(Feb. 25, 2004)
(August 1,2023)	2085*29,530588+2398425+5	2460001,276	(Feb. 25, 2023)
(August 1,2024)	2097*29,530588+2398425+5	2460355,643	(Feb. 14, 2024)
(August 1,2025)	2109*29,530588+2398425+5	2460710,01	(Feb. 3, 2025)
(Sept. 1, 2025)	2109*29,530588+2398425+5	2460710,01	(Feb. 3, 2025)
(August 1,2033)	2208*29,530588+2398425+5	2463633,538	(Feb. 4, 2033)

 

Use calendars and online directories to determine the nearest new moons (the date should be smaller)

(August 1, 2003)	(Feb. 6, 2003)	Feb. 01, 2003
(August 1, 2004)	(Feb. 25, 2004)	January 22, 2004
(August 1, 2023)	(Feb. 25, 2023)	February 20, 2023
(August 1, 2024)	(Feb. 14, 2024)	February 10, 2024
(August 1,2025)	(Feb. 3, 2025)	Jan. 29, 2025
(Sept. 1, 2025)	(Feb. 3, 2025)	Jan. 29, 2025
(August 1, 2033)	(Feb. 4, 2033)	Jan. 31, 2033

 

     And further we determine according to time of new moon and beginning of day according to the Tibetan calendar.