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The Sanskrit word Kalpa has several distinct meanings in the context of Indian religious tradition: first, it can refer to a measurement of time in the cosmic cycles of creation and dissolution of the universe; or second, it can refer to one of the six disciplines of Vedanga (meaning "limbs of the Veda") in Hinduism that focuses on ritual. The Vedanga are six auxiliary disciplines for the understanding and tradition of the Vedas comprising of the following topics:

  1. Shiksha (śikṣā): phonetics and phonology
  2. Vyakarana (vyākaraṇa): grammar
  3. Nirukta (nirukta): etymology
  4. Jyotisha (jyotiṣa): astrology and astronomy, dealing particularly with the auspicious days for performing sacrifices.
  5. Kalpa (kalpa): ritual

The Vedangas are first mentioned in the Mundaka Upanishad as topics to be observed by students of the Vedas. Later, they developed into independent disciplines, each with its own corpus of Sutras.

Finally, the word "Kalpa" can also be used in the religious context of Jainism to refer to the Kalpasutras.

Kalpa as a unit of time

A kalpa is a Sanskrit word meaning an aeon, or a vast period of time in Hindu and Buddhist cosmology.

In Hinduism, a kalpa is equal to 4.32 billion years, a "day (day only) of Brahma" or one thousand mahayugas, measuring the duration of the world. Each kalpa is divided into 14 manvantara (each lasting 306,720,000 years). Two kalpas constitute a day and night of Brahma. A "month of Brahma" is supposed to contain thirty such days (including nights), or 259.2 billion years. According to the Mahabharata, 12 months of Brahma constitute his year, and 100 such years the life cycle of the universe. Fifty years of Brahma are supposed to have elapsed, and we are now in the shvetavaraha-kalpa of the fifty-first; at the end of a Kalpa the world is annihilated.

In Buddhism, there are four different lengths of kalpas. A regular kalpa is approximately 16 million years long, and a small kalpa is 1000 regular kalpas, or 16 billion years. Further, a medium kalpa is 320 billion years, the equivalent of 20 small kalpas. A great kalpa is four medium kalpas, or 1.28 trillion years.[1]

Kalpa as a branch of Vedanga

Hinduism contains a branch of Vedic science (Vedanga) that seeks to elucidate the rituals associated with sacrificial practice (yajna). This branch of study gave rise to a large number of systematic sutras for the several classes of priests. The most important of these works have come down to us, and they occupy by far the most prominent place among the literary productions of the sutra-period.

The Kalpa-sutras, or rules of ceremonial, are of two kinds: (1) the Shrautasutra's, which are based on the shruti, and teach the performance of the great sacrifices, requiring three sacrificial fires; and (2) the Smrtasutra's, or rules based on the smrti or tradition. The latter class again includes two kinds of treatises: (1) the Grhyasutra's, or domestic rules, treating of ordinary family rites, such as marriage, birth, namegiving, etc., connected with simple offerings in the domestic fire; and (2) the Dharmasutra's, which treat of customs and temporal duties, and are supposed to have formed the chief sources of the later law-books. Besides, the Shrauta-sutras of the Yajurveda have usually attached to them a set of so-called Shulva-sutras, i.e. rules of the cord, which treat of the measurement by means of cords, and the construction, of different kinds of altars required for sacrifices. These treatises are of special interest as supplying important information regarding the earliest geometrical operations in India. Along with the Sutras may be classed a large number of supplementary treatises, usually called Parishishta, on various subjects connected with the sacred texts and Vedic religion generally.

Shrauta Sutras

The Shrautasutras (śrautasūtra) form a part of the corpus of Sanskrit Sutra literature. Their topic is the interpretation of the shruti corpus and instructions relating to kalpa, the correct performance of ritual sacrifice. The bulk of the Shrautasutras are roughly contemporary to the Grhya corpus of domestic sutras, their language being late Vedic Sanskrit, dating maybe to roughly the sixth century B.C.E. (the century predating Panini).

Veda Śrautasûtra[2]
R̥gveda Āśvalāyana Śrautasûtra
Sāṅkhāyana Śrautasûtra
Sāmaveda Lātyāyana Śrautasûtra
Drāhayana Śrautasûtra
Jaiminiya Śrautasûtra
Kr̥sna Yajurveda Baudhāyana Śrautasûtra
Mānava Śrautasûtra
Bharadvāja Śrautasûtra
Āpastamba Śrautasûtra
Hiraṅyakeśi Śrautasûtra
Vārāha Śrautasûtra
Vaikhānasa Śrautasûtra
Śukla Yajurveda Kātyāyana Śrautasûtra
Atharvaveda Vaitāna Śrautasûtra

Shulba Sutras

The verses 1-2 of Baudhayana Shulba Sutra state that the squares of any rectangle's width and length add up to the square of its diagonal. This is one of the earliest descriptions of Pythagorean theorem, appearing many centuries before Pythagoras.

The Shulba Sutras ( Śulbasûtra) dealing with altar deal with the mathematical methodology to construct altar geometries for the Vedic rituals.[3] The Sanskrit word "Shulba" means cord, and these texts are "rules of the cord."[4] They provide, what in modern mathematical terminology would be called "area preserving transformations of plane figures," tersely describing geometric formulae and constants.

Five Shulba Sutras texts have survived through history, of which the oldest surviving is likely the Baudhayana Shulba Sutra (800-500 B.C.E.), while the one by Katyayana may be chronologically the youngest (~300 B.C.E.).[4]

Veda Śulbasûtra[2]
Kr̥sna Yajurveda Baudhāyana Śulbasûtra
Mānava Śulbasûtra
Āpastamba Śulbasûtra
Śukla Yajurveda Kātyāyana Śulbasûtra

Grhya Sutras

The Grhya Sutras "domestic sutras" are a category of Sanskrit texts in the tradition of the Brahmanas, commenting on Vedic ritual. Their language is late Vedic Sanskrit, and they date to around roughly 500 B.C.E., contemporary with the Shrautasutras. They are named after Vedic shakhas.

Veda Gr̥hyasûtra
R̥gveda Âśvalâyana-Grhyasûtra
Sâmaveda Gobhila-Grhyasûtra
Khâdira-Grhyasûtra (Drâhyâyana-Grhyasûtra)
Kr̥sna Yajurveda Baudhâyana-Grhyasûtra
Hiraṇyakeśi-Grhyasūtra (Satyâsâdha-Grhyasûtra) (Laugâksi-Grhyasûtra)
Kapisthala-Katha Grhyasûtra (unpublished)
Śukla Yajurveda Kâtyâyana Grhyasûtra (different from Pâraskara-Grhyasûtra)
Atharvaveda Kauśika Grhyasûtra

Dharma Sutras

The Dharmasutras are Sanskrit texts dealing with law and rituals. They include the four surviving written works of the ancient Indian tradition on the subject of dharma, or the rules of behavior recognized by a community. Unlike the later Dharmashastra, the dharmasutras are composed in prose. The oldest Dharmasutra is generally believed to have been that of Apastamba, followed by the dharmasutras of Gautama, Baudhayana, and Vasishtha. It is difficult to determine exact dates for these texts, but the dates between 500-300 B.C.E. have been suggested for the oldest Dharmasutras. Later Dharmasutras include those of Kasyapa, Brhaspati, and Ushanas.

Veda Dharmasûtra
R̥gveda Vasishtha Dharmasûtra
Sāmaveda Gautama Dharmasûtra
Kr̥sna Yajurveda Baudhāyana Dharmasûtra
Āpastamba Dharmasûtra


  1. Ronald B. Epstein. Buddhism A to Z (Burlingame, CA: The Buddhist Text Translation Society, 2003, ISBN 0881393533).
  2. 2.0 2.1 Rajesh Kochar, Vedic People:Their History and Geography (Orient Longman, New Delhi, 2000, ISBN 8125010807).
  3. Pradip Kumar Sengupta, History of Science and Philosophy of Science (Pearson Education, 2010, ISBN 978-8131719305).
  4. 4.0 4.1 Kim Plofker, Mathematics in India (Princeton University Press, 2009, ISBN 0691120676).

ISBN links support NWE through referral fees

  • Dhallapiccola, Anna. Dictionary of Hindu Lore and Legend. Thames & Hudson, 2004. ISBN 0500510881
  • Epstein, Ronald. Buddhism A to Z. Burlingame, CA: Buddhist Text Translation Society, 2003. ISBN 0881393533
  • Klostermaier, Klaus. A Survey of Hinduism. Albany, NY: State University of New York Press, 1989. ISBN 0887068073
  • Kochar, Rajesh. Vedic People: Their History and Geography. Orient Longman, New Delhi, 2000. ISBN 8125010807
  • Plofker, Kim. Mathematics in India. Princeton University Press, 2009. ISBN 0691120676
  • Sengupta, Pradip Kumar. History of Science and Philosophy of Science. Pearson Education, 2010. ISBN 978-8131719305

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