Derge Kangyur/Tengyur e-text, Esukhia/Barom edition — public domain (mechanical reproduction)
This technical manual provides specific mathematical instructions for calculating astronomical and temporal data within the Kālacakra system. The text outlines a procedural methodology for converting elapsed years from the birth of the Void into smaller temporal units, employing a series of multiplications and divisions to determine padas, ghaṭī, pala, and śvāsa. By detailing the handling of remainders and the application of specific numerical constants, the work commits the reader to a rigorous computational framework used to track the positions and functions of planets, lunar dates, and asterisms. The text functions as a practical guide for practitioners to synchronize chronological time with cosmic cycles, asserting that the correct application of these calculations is essential for understanding the movements of celestial bodies and their corresponding functions.
Provenance
About this text
A technical guide for astronomical calculation, the Śrīkālacakragaṇanopadeśa belongs to the Non-dual Tantra collection. The work is attributed to the Indian author Śākyaśrībhadra. Preserved in the Tengyur, volume པ, the text appears in the classical Tibetan language under the title dpal dus kyi 'khor lo'i rtsis kyi man ngag and extends over four pages. The work enacts a rigorous computational methodology for determining temporal data, beginning with the birth of the Void. It provides specific instructions for converting elapsed years into months and further subdividing these into padas, ghaṭī, pala, and śvāsa through a series of multiplications, divisions, and the management of remainders. By applying specific numerical constants and adjusting for even or odd quotients, the text establishes a framework for synchronizing chronological time with cosmic cycles. A scholar or serious reader consults this manual today to understand the precise mathematical procedures used to track the movements of celestial bodies and the corresponding functions of the Kālacakra system.
Cite thisAnuvāda, “Personal Instructions on the Calculations in the Glorious Kālacakra” (Toh 1384), machine draft, 2026.https://naxiai.com/tibetan/works/toh1384
Summary & commentary
Significance
The work is significant as it demonstrates the integration of advanced Indian mathematical astronomy into the Tibetan Buddhist Kālacakra tradition. For the modern reader, it provides primary evidence of how precise temporal calculations were utilized to support the complex cosmological and ritual requirements of the system.
Structure
Passages
Section
Description
1-3
Calculation Procedures
Instructions for converting elapsed years into smaller units of time through division and multiplication.
4
Application and Scope
Definition of the components of calculation, including planets, lunar dates, and asterisms.
Themes
Temporal Conversion (1-3)
Astronomical Parameters (4)
Summary, significance and provenance note generated by gemma4:31b from the translation and the catalogue record.
AnuvādaPersonal Instructions on the Calculations in the Glorious Kālacakra·
In the language of India: Śrī-kālacakra-gaṇitopadeśa-nāma. In the language of Tibet: dpal dus kyi ’khor lo’i rtsis kyi man ngag ces bya ba. Homage to the glorious Kālacakra!
Starting from the birth of the Void, the years are purified by adding the elapsed years. Multiplying by twelve converts them into months. Add the elapsed months of the middle winter month and so forth.
In two places, multiply the lower by two. Divide by seventy-five and add one; by adding this to the upper, the purified months are obtained. In the three places of the purified months, multiply the middle by thirty and add two. Divide the lower by six and subtract from the middle. To the remainder, add zero; from the middle, subtract one. Bring it down to the lower and multiply by sixty. Add zero and subtract; the remainder is in finger-widths (chu srang). Divide the middle by sixty; the quotient is added to the upper, and the remainder is in the place of water-measures (chu tshod). Divide that by seven; the remainder is in the place of the planets (gza’).
In the two places, add eight and two to the lower. Divide by two; the remainder is in the place of fractions (cha shas). Add seven and one to the wealth (nor). Multiply the upper by two and add it. Divide by eight and two; the remainder is in the place of whole numbers. Add the hood (gdengs ka) to the purified months.
In the three places, multiply the middle by eleven. The lower is multiplied by nine and three. Subtract the quotient from the middle; the remainder is multiplied by zero and time (0×60). The quotient and the remainder multiplied by six are subtracted from the middle and brought down to the lower. The remainder remains in finger-widths and breaths (dbugs). The remainder of dividing the middle by sixty is the water-measures; to the quotient, add one. Add the multiplied remainder to the upper. The remainder of such a division is in the place of the lunar mansions (skar ma). Add the lunar days (tshes) to the planets and subtract from the danda (dbyu gu).
Give the whole [value] as a gift;
The remainder, divided by the moon,
Should be taken as the padas. If there is no remainder,
Take that very [value]. If the quotient is even, add; if odd, subtract.
Multiply the parts by the previously held padas:
Five, five, five, and four;
Three, two, and one moon.
For the subsequent [half], reverse those very [values].
Thus should the lunar padas be known.
Multiply by the first [value] if the pada has not been held.
Divide that by six and twelve;
The quotient is the ghaṭīs.
Multiply the remainder by sixty;
The quotient by the aforementioned divisor
Is the vighaṭīs; for the remainder,
Multiply by six and the quotient is the śvāsas.
With those values thus obtained,
Add to the previously eaten pada,
And subtract from the not-yet-eaten subsequent [pada].
In the place of the planet's movement,
Add or subtract as known by the previous signs.
Multiply the two places of the lunar day by four;
Add a third of the lower [value] to the upper.
Divide that by forty; the quotients
Should be added to the place of the asterisms.
The remainder is mixed into the place of the ghaṭīs.
Multiply the lower remainder by twenty;
It should be inserted into the place of the vighaṭīs.
In those two places, in one of them,
Subtract six from the asterism place
And forty-five from the ghaṭī place.
If, by subtracting, there is more than half a cycle, subtract it.
If not, add half a cycle and then subtract.
Multiply the remainder of the subtraction by sixty;
Take the lower ghaṭīs upward.
The quotient by five and three is the solar pada.
Six, two, and one moon; reverse that for the latter.
Thus should the solar padas be known.
By the previously held pada,
Multiply the asterism place and so forth.
In that regard, divide by the moon’s [mean] value; the quotient is the ghaṭī. Multiply the remainder by sixty and bring up the pala from below; the quotient from that is the pala. Multiply the remainder by six and bring up the śvāsa from below; the quotient from that is the śvāsa. Add those obtained values to the previously consumed solar pāda; subtract them from the [solar pāda] not yet consumed. To the [mean] positions of the planet and the sun, they are to be added or subtracted: they are added during the sun’s northward course and subtracted when it moves south. That itself is the [mean] position of the planet and the sun. Add the lunar date (tithi) to the sun’s asterism (nakṣatra). Below that, multiply the date by six and mix it with the planet’s position. Divide that by sixty; the quotient is to be subtracted from the asterism place. Subtract the remainder from the ghaṭī and so forth. The remainder after subtraction is the moon’s asterism. The sum of the sun and moon becomes the yoga. Multiply the date by two, subtract one, and divide by seven; the remainder is the karana. If there is no remainder, know that it is that very [karana]. Divide the planet’s place by seven; the remainder is the weekday. If there is no remainder, that itself is the weekday. Its ghaṭī, pala, and śvāsa should be known as the future [position] for that date. If the same weekday occurs twice, two dates are omitted in that day. If that weekday is skipped, that same date occurs twice. By that, the omission or addition of dates is known. Divide the asterism place by twenty-seven; the remainder is the asterism. If there is no remainder, that itself is [the asterism].
The application is also similar to that. The number is asserted to be the lower one. One should understand the elapsed hours, minutes, and so forth of the asterisms and the applications. Thus, the planets, the lunar dates, the asterisms, the applications, and the functions constitute the calculation of the five branches. This concludes the Instruction on the Calculation of the Glorious Kālacakra, composed by the great Paṇḍita Śākyaśrībhadra.