Hindu units of time

Hindu units of time are described in Hindu texts ranging from microseconds to trillions of years, including cycles of cosmic time that repeat general events in Hindu cosmology.[1][2] Time (kāla) is described as eternal.[3] Various fragments of time are described in the Vedas, Bhagavata Purana, Vishnu Purana, Mahabharata, Surya Siddhanta etc.

"Srishti" redirects here. For the 1976 Indian Malayalam film, see Srishti (film).

Sidereal metrics
Hindu measurements in logarithmic scale based on seconds
UnitDefinitionRelation to SI units
Trutiत्रुटि Base unit≈ 0.30 µs
Renuरेणु 60 Truti≈ 18 µs
Lavaलव 60 Renu≈ 1080 µs
Līkṣakaलीक्षक 60 Lava≈ 64.8 ms
Liptaलिप्ता 64.8 Leekshaka≈ 4.2 s
Vipalaविपल
Palaपल 60 Lipta≈ 30 s
Vighaṭiविघटि
Vinādīविनाडी
Ghaṭiघटि 31 Vighaṭi≈ 1.86 ks
Nādīनाडी
Dandaदण्ड
Muhūrtaमुहूर्त 2 Ghaṭi≈ 3.72 ks
Nakṣhatra Ahorātram
(sidereal day)		नक्षत्र अहोरात्रम्62 Ghaṭī≈ 86.4 ks
32 Muhūrta≈ 86.4 ks

According to Sūrya Siddhānta[4]

UnitDefinitionRelation to SI units
Truti Base unit≈ 29.6 µs
Tatpara 100 Truti≈ 2.96 ms
Nimesha 30 Tatpara≈ 88.9 ms
Kāṣṭhā 18 Nimesha≈ 1.6 s
Kalā 30 Kāṣṭhā≈ 48 s
Ghatika 30 Kalā≈ 1.44 ks
Muhūrta 2 Ghatika≈ 2.88 ks
Ahorātram
(sidereal day)		 30 Muhūrta≈ 86.4 ks

Small units of time used in the Vedas:

UnitDefinitionRelation to SI units
ParamāṇuBase unit≈ 25 µs
Aṇu2 Paramāṇu≈ 50 µs
Trasareṇu3 Aṇu≈ 151 µs
Truṭi3 Trasareṇu≈ 454 µs
Vedha100 Truṭi≈ 45 ms
Lava3 Vedha≈ 0.14 s
Nimeṣa3 Lava≈ 0.4 s
Kṣaṇa3 Nimesha≈ 1.22 s
Kāṣṭhā5 Kṣaṇa≈ 6 s
Laghu15 Kāṣṭhā≈ 92 s
Danda15 Laghu≈ 1.38 ks
Muhūrta2 Danda≈ 2.76 ks
Ahorātram31 Muhūrta≈ 86.4 ks
Masa (month)30 Ahorātram≈ 2592 ks
Ritu (season)2 Masa≈ 5184 ks
Ayana3 Ritu≈ 15552 ks
Samvatsara (year) 2 Ayana≈ 31104 ks[5]
Ahorātram of Deva

Lunar metrics

Consists of the following:[6]

  • A Tithi or lunar day is defined as the time it takes for the longitudinal angle between the Moon and the Sun to increase by 12°. Tithis begin at varying times of day and vary in duration from approximately 19 to approximately 26 hours.[7]
  • A Paksa (also Pakṣa) or lunar fortnight consists of 15 tithes.
  • A Māsa or lunar month (30 days) is divided into 2 Pakṣas: the one between new moon and full moon (waxing) is called gaura or (bright) or Śukla Pakṣa; the one between full moon and new moon (waning) Kṛiṣhṇa (dark) paksha.
  • A Ṛitu (or season) is 2 Māsa.
  • An Ayana is 3 Ṛitus.
  • A year is two Ayanas.

Tropical metrics

Consists of the following:[8]

  • A Yāma = ​1⁄4 of a day (light) or night = ​7 1⁄2 Ghatis (घटि) = ​3 3⁄4 Muhurtas = 3 Horas (होरा)tely 24 hours.
  • Eight Yāmas make a full day (day + night)
  • An Ahorātra is a tropical day (Note: A day is considered to begin and end at sunrise, not midnight.)
NameDefinitionEquivalence
Yamaयाम​1⁄4 of a day (light) or night≈ 3 hours
Sāvana Ahorātramसावन अहोरात्रम्8 Yamas1 Solar day

Cosmic metrics

The below table contains calculations of cosmic units of time and the time dilation experienced by different entities. Calculations use a traditional 360-day year (twelve 30-day months) and a standard 24-hour day for all entities.

Unit[lower-alpha 1] Definition Human Pitri Deva Manu Brahma
Mahā-kalpa 36,000 Kalpa & Pralaya 311,040,000,000,000 yr 10,368,000,000,000 yr 864,000,000,000 yr ~101,408,450.70 yr 100 yr
Mahā-pralaya Mahā-kalpa length
Parārdha ​1⁄2 Mahā-kalpa 155,520,000,000,000 yr 5,184,000,000,000 yr 432,000,000,000 yr ~50,704,225.35 yr 50 yr
Kalpa 1,000 CY; 14 M + 15 MS 4,320,000,000 yr 144,000,000 yr 12,000,000 yr ~1,408.45 yr 12 hr
Pralaya Kalpa length
Manvantara [M] 71 Catur-yuga 306,720,000 yr 10,224,000 yr 852,000 yr 100 yr 51.12 min
Manvantara-sandhyā [MS] Kṛta-yuga length 1,728,000 yr 57,600 yr 4,800 yr ~6.76 mo 2.88 min
Catur-yuga [CY] Kṛta, Tretā, Dvāpara & Kali yugas 4,320,000 yr 144,000 yr 12,000 yr ~1.41 yr 43.20 sec
 
Kṛta-yuga sum total 1,728,000 yr 57,600 yr 4,800 yr ~6.76 mo 2.88 min
kṛta-yuga-sandhyā ​1⁄10 kṛta-yuga length 144,000 yr 4,800 yr 400 yr ~16.90 day 1.44 sec
kṛta-yuga-sandhyāṃśa
kṛta-yuga 4 kali-yuga lengths 1,440,000 yr 48,000 yr 4,000 yr ~5.63 mo 14.40 sec
 
Tretā-yuga sum total 1,296,000 yr 43,200 yr 3,600 yr ~5.07 mo 12.96 sec
tretā-yuga-sandhyā ​1⁄10 tretā-yuga length 108,000 yr 3,600 yr 300 yr ~12.68 day 1.08 sec
tretā-yuga-sandhyāṃśa
tretā-yuga 3 kali-yuga lengths 1,080,000 yr 36,000 yr 3,000 yr ~4.23 mo 10.80 sec
 
Dvāpara-yuga sum total 864,000 yr 28,800 yr 2,400 yr ~3.38 mo 8.64 sec
dvāpara-yuga-sandhyā ​1⁄10 dvāpara-yuga length 72,000 yr 2,400 yr 200 yr ~8.45 day 0.72 sec
dvāpara-yuga-sandhyāṃśa
dvāpara-yuga 2 kali-yuga lengths 720,000 yr 24,000 yr 2,000 yr ~2.82 mo 7.20 sec
 
Kali-yuga sum total 432,000 yr 14,400 yr 1,200 yr ~1.69 mo 4.32 sec
kali-yuga-sandhyā ​1⁄10 kali-yuga length 36,000 yr 1,200 yr 100 yr ~4.23 day 0.36 sec
kali-yuga-sandhyāṃśa
kali-yuga 1,000 Deva years 360,000 yr 12,000 yr 1,000 yr ~1.41 mo 3.60 sec

Time dilation

Time dilation affects the lifespan differently for humans, Pitris (forefathers), Devas (gods), Manus (progenitors of mankind), and of Brahma (creator god). The division of a year for each is twelve 30-day months or 360 days, where a day is divided into a 12-hour dawn and 12-hour dusk. A 30-day month amounts to four 7-day weeks with an extra 8th day every two weeks (48-week year). A traditional human year is measured by the sun's northern and southern movements in the sky,[lower-alpha 2] where the new year commences only when the sun returns to the same starting point and a pause on the commencement otherwise. For this reason, a traditional 360-day year is equivalent to a modern ≈365.24-day solar or tropical year.

Unit[lower-alpha 1] Human Pitri Deva Manu Brahma
Brahma year 3,110,400,000,000 yr 103,680,000,000 yr 8,640,000,000 yr ~1,014,084.51 yr 1 yr
Manu year 3,067,200 yr 102,240 yr 8,520 yr 1 yr 30.67 sec
Deva year 360 yr 12 yr 1 yr ~1.01 hr 3.60 ms
Pitri year 30 yr 1 yr 1 mo ~5.07 min 300 μs
Human year 1 yr 12 day 1 day ~10.14 sec 10 μs

Cosmic date

According to Puranic sources,[lower-alpha 3] Krishna's departure marks the end of the human age of Dvapara Yuga and the start of Kali Yuga, which is dated to midnight on 17/18 February 3102 BCE of the proleptic Julian calendar. (See Kali Yuga). We are currently halfway through Brahma's life (Mahā-Kalpa), whose lifespan is equal to the duration of the manifested material elements, from which Brahma manifests his universe in Kalpa cycles:[12][13][14][15][16]

A Mahā-Kalpa is followed by a Mahā-Pralaya (full dissolution) of equal length. Each Kalpa (day of Brahma) is followed by a Pralaya (night of Brahma or partial dissolution) of equal length. Preceding the first and following each Manvantara is a Manvantara-Sandhyā (connection period), each with a length of Kṛta Yuga (a.k.a. Satya Yuga).[12][13]

Hindu texts specify that the start and end of each of the Yugas are marked by astronomical alignments. This cycle's Treta Yuga began with 5 planets residing in the "Aries" constellation. This cycle's Dwapara Yuga ended with the "Saptarshi" constellation (Ursa major) residing in the "Magha" constellation. The current Kali Yuga will end with the Sun, Moon and Jupiter residing in the "Pushya" sector.[17]

Human
Main article: Yuga Cycle

The history of humanity is divided up into four yugas (a.k.a. dharmic ages or world ages)—Krita Yuga (a.k.a. Satya Yuga), Treta Yuga, Dvapara Yuga and Kali Yuga—each with a 25% decline in dharmic practices and length, giving proportions (caraṇas) of 4:3:2:1 (e.g. Satya: 100% start; Kali: 25% start, 0% end), indicating a de-evolution in spiritual consciousness and an evolution in material consciousness. Kali Yuga is followed by Satya Yuga of the next cycle, where a cycle is called a Chatur Yuga (a.k.a. Maha Yuga or Yuga Cycle). Each yuga is divided into a main period (sometimes called the Yuga) and two Sandhis or Sandhyās (connecting periods)⁠—Sandhyā (dawn) and Sandhyāṃśa or Sandhyānśa (dusk)⁠—where each Sandhi lasts for 10% of the main period. Lengths are given in divine years (a.k.a. celestial or Deva years), where a divine year lasts for 360 solar (human) years. A Yuga Cycle lasts for 4.32 million solar or 12,000 divine years.[18][19][20][21][22][lower-alpha 4]

Elapsed yuga

A Kali Yuga lasts for 432,000 years and is the 4th of 4 Yugas as well as the current Yuga, with Sandhyās that last for 36,000 years:[lower-alpha 5]

  • Yuga started 3102 BCE in past:
= 2020 + 3102 - 1
= 5121 years
  • Sandhyā (dawn) ends 32,899 CE in:
= 36000 - 2020 - 3102 + 1
= 30879 years
  • Sandhyāṃśa (dusk) starts 392,899 CE in:
= 432000 - 36000 - 2020 - 3102 + 1
= 390879 years
  • Yuga ends 428,899 CE in:
= 432000 - 2020 - 3102 + 1
= 426879 years

Elapsed chatur yuga

A Chatur Yuga (a.k.a. Maha Yuga) lasts for 4.32 million years, where the current is the 28th of 71:[lower-alpha 5]

  • Started 3,891,102 BCE in past:
= 4320000 - 432000 + (2020 + 3102 - 1)
= 3893121 years
≈ 3.89 million years
  • Ends 428,899 CE in:
= 432000 - 2020 - 3102 + 1
= 426879 years
28th Chatur (Maha) Yuga
Yuga Start Length
Satya 3,891,102 BCE 1,728,000 (4,800)
Treta 2,163,102 BCE 1,296,000 (3,600)
Dvapara 867,102 BCE 864,000 (2,400)
Kali* 3102 BCE – 428,899 CE[lower-alpha 6] 432,000 (1,200)
Years: 4,320,000 solar (12,000 divine)
(*) Current.

Pitri

The lifespan of the Pitris (forefathers) lasts for 100 of their years.[8]

  • 1 day of Pitris = 1 solar month (masa)
  • 30 days (1 month) of Pitris = 30 solar months (2.5 solar years)
  • 12 months (1 year) of Pitris = 30 solar years (1 month of Devas)
  • 100 years (lifespan) of Pitris = 3,000 solar years (​1⁄4 Mahā-Yuga)

Deva

The lifespan of the Devas (gods) lasts for 100 of their years.[8]

  • 1 day of Devas = 1 solar year
  • 30 days (1 month) of Devas = 30 solar years (1 year of pitras)
  • 12 months (1 year) of Devas = 360 solar years
  • 100 years (lifespan) of Devas = 36,000 solar years (3 Mahā-Yugas)

Manu
Main article: Manvantara

The lifespan of the Manus (progenitors of mankind) lasts for 100 of their years. Each Manu reigns over a period called a Manvantara, each lasting for 71 Mahā-Yugas. A total of 14 Manus reign successively in one Kalpa (day of Brahma). Preceding the first and following each Manvantara is a Sandhyā (connection period), each lasting the duration of a Satya Yuga. During each Manvantara-Sandhyā, the earth (bhu-loka) is submerged in water.[12][18][23][24]

  • 1 day of Manu = 8,520 solar years
  • 30 days (1 month) of Manu = 255,600 solar years
  • 12 months (1 year) of Manu = 3,067,200 solar years
  • 100 years (lifespan) of Manu = 306,720,000 solar years (71 Mahā-Yugas)

Elapsed manvantara

A Manvantara lasts for 306.72 million years, where the current (ruled by Vaivasvatha Manu) is the 7th of 14:[lower-alpha 5]

  • Started in past:
= (4320000 - 432000 + (2020 + 3102 - 1)) + 4320000 * 27
= 120533121 years
≈ 120.53 million years
  • Ends in:
= (432000 - 2020 - 3102 + 1) + 4320000 * 43
= 186186879 years
≈ 186.19 million years

Brahma
Main article: Kalpa (aeon)

The lifespan of Brahma (creator god) lasts for 100 of his years. His 12-hour day or Kalpa (a.k.a. day of Brahma) is followed by a 12-hour night or Pralaya (a.k.a. night of Brahma) of equal length. At the start of his days, he is re-born and creates the planets and the first living entities. At the end of his days, he and his creations are unmanifest (partial dissolution). His 100-year life is called a Mahā-Kalpa, which is followed by a Mahā-Pralaya (full dissolution) of equal duration, where the bases of the universe, Prakriti, is manifest at the start and unmanifest at the end of a Mahā-Kalpa.[13][24][25]

  • 1 day (12 hrs: Kalpa) of Brahma = 4.32 billion solar years (1,000 Mahā-Yugas) (14 Manvantaras + 15 Sandhyās)
  • 1 Day (24 hrs: Kalpa + Pralaya) of Brahma = 8.64 billion solar years
  • 30 Days (1 month) of Brahma = 259.2 billion solar years
  • 12 months (1 year) of Brahma = 3.1104 trillion solar years
  • 50 years (Parārdha) of Brahma = 155.52 trillion solar years
  • 100 years (lifespan: 2 Parārdha) of Brahma = 311.04 trillion solar years

Elapsed kalpa

A day of Brahma (Kalpa) lasts for 4.32 billion years, where the current (Shveta-Varaha) is the 1st of 30 in his 1st month of his 51st year:[lower-alpha 5]

  • Started in past:
= ((4320000 - 432000 + (2020 + 3102 - 1)) + 4320000 * 27) + 1728000 * 7 + 306720000 * 6
= 1972949121 years
≈ 1.97 billion years
  • Ends in:
= ((432000 - 2020 - 3102 + 1) + 4320000 * 43) + 1728000 * 8 + 306720000 * 7
= 2347050879 years
≈ 2.35 billion years

Elapsed maha kalpa

A life of Brahma (Maha Kalpa) lasts for 311.04 trillion years:[lower-alpha 5]

  • Started in past:
= (((4320000 - 432000 + (2020 + 3102 - 1)) + 4320000 * 27) + 1728000 * 7 + 306720000 * 6) + 4320000000 * 36000
= 155521972949121 years
≈ 155.52 trillion years
  • Ends in:
= (((432000 - 2020 - 3102 + 1) + 4320000 * 43) + 1728000 * 8 + 306720000 * 7) + 4320000000 * 35999
= 155518027050879 years
≈ 155.52 trillion years

Avatar
Main article: Dashavatara § Lists

The Puranas describe Vishnu avatars that come during specific yugas, but may not occur in every Yuga Cycle.

Rama appears at the end of Treta Yuga.[26] According to Vayu Purana and Matsya Purana, Rama appeared in the 24th Yuga Cycle.[27] According to the Padma Purana, Rama also appeared in the 27th Yuga Cycle of the 6th Manvantara. [28]

Krishna's departure marked the end of Dvapara Yuga and the start of Kali Yuga according to Puranic sources.[lower-alpha 3] In the 28th Yuga Cycle, Krishna appeared as His original self, which only happens once in a Kalpa (day of Brahma).

Yuga avatars
Krita (Satya) Treta Dvapara Kali
Matsya
Kurma
Varaha
Narasimha
Vamana
Parashurama
Rama
Krishna
Buddha
Kalki

See also

Notes
  1. Calculations use a traditional 360-day year (twelve 30-day months) and a standard 24-hour day for all entities:
    * Brahma: creator god.
    * Manu: progenitor of mankind.
    * Devas: gods, celestials or divine.
    * Pitris: forefathers or ancestors.
    * Humans: year equals Sun's northern and southern movements in Earth's sky (a.k.a. solar or tropical year).
  2. A human year is divided into twelve equal months, measured by the sun's six month movements in the north BG 8.24 and south BG 8.25, as indicated in Bhagavad-gita.
  3. The Bhagavata Purana (1.18.6),[9] Vishnu Purana (5.38.8),[10] and Brahma Purana (2.103.8)[11] state that the day Krishna left the earth was the day that the Dvapara Yuga ended and the Kali Yuga began
  4. Viṣṇu Purāṇa, Book I, Ch. III
  5. Calculations as of midnight on 17/18 February 2020 CE. Note, the number of years from 1 BCE to 1 CE is 1 year and not 2 years since there is no year zero.
  6. Each Kali-yuga-sandhi lasts for 36,000 solar (100 divine) years:
    * Sandhyā: 3102 BCE – 32,899 CE
    * Sandhyāṃśa: 392,899 CE – 428,899 CE

References
  1. Gupta, Dr. S. V. (2010). "Ch. 1.2.4 Time Measurements". In Hull, Prof. Robert; Osgood, Jr., Prof. Richard M.; Parisi, Prof. Jurgen; Warlimont, Prof. Hans (eds.). Units of Measurement: Past, Present and Future. International System of Units. Google Books. Springer Series in Materials Science: 122. Springer. p. 3. ISBN 9783642007378.
  2. Dick Teresi. Lost Discoveries: The Ancient Roots of Modern Science—from the Babylonians to the Maya. SimonandSchuster. p. 174.
  3. Gupta 2010, p. 8.
  4. "Vedic Time System - वेद Veda". veda.wikidot.com. Retrieved 4 December 2019.
  5. Gupta 2010, p. 5.
  6. Gupta 2010, p. 5-6.
  7. Kumar, Ashwini (2005). Vaastu: The Art And Science Of Living. Sterling Publishers Pvt. Ltd. p. 50. ISBN 81-207-2569-7.
  8. Gupta 2010, p. 6.
  9. "Skanda I, Ch. 18: Curse of the Brahmana, Sloka 6". Bhagavata Purana. Part I. Motilal Banarsidass Publishers Private Limited. 1950. p. 137. On the very day, and at the very moment the Lord [Krishna] left the earth, on that very day this Kali, the source of irreligiousness, (in this world), entered here.
  10. Wilson, H. H. (1895). "Book V, Ch. 38: Arjuna burns the dead, etc., Sloka 8". The Vishnu Purana. S.P.C.K. Press. p. 61. The Parijata tree proceeded to heaven, and on the same day that Hari [Krishna] departed from the earth the dark-bodied Kali age descended.
  11. "Ch. 103, Episode of Krsna concluded, Sloka 8". Brahma Purana. Part II. Motilal Banarsidass. 1955. p. 515. It was on the day on which Krishna left the Earth and went to heaven that the Kali age, with time for its body set in.
  12. Krishnamurthy, Prof. V. (2019). "Ch. 20: The Cosmic Flow of Time as per Scriptures". Meet the Ancient Scriptures of Hinduism. Google Books. Notion Press. ISBN 9781684669387. Each manvantara is preceded and followed by a period of 1,728,000 (= 4K) years when the entire earthly universe (bhu-loka) will submerge under water. The period of this deluge is known as manvantara-sandhya (sandhya meaning, twilight). ... According to the traditional time-keeping ... Thus in Brahma's calendar the present time may be coded as his 51st year - first month - first day - 7th manvantara - 28th maha-yuga - 4th yuga or kaliyuga.
  13. Gupta 2010, pp. 7-8.
  14. Godwin 2011, p. 301: Vishnu Purana, translated by the great Sanskritist Horace Hayman Wilson: One Pararddha, or half [Brahma's] existence, has expired, terminating with the Maha Kalpa called Padma. The Kalpa (or day of Brahma) termed Varaha is the first of the second period of Brahma's existence. ... The Hindu astronomers agree that the Kali Yuga began at midnight between February 17 and 18, 3102 BCE. Consequently it is due to end about 427,000 CE, whereupon a new Golden Age will dawn.
  15. Burgess, Ebenezer (1860). "Ch. I, Of the Mean Motions of the Planets". Translation of the Sûrya-Siddhânta: A text-book of Hindu astronomy, with notes and an appendix. Google Books. Journal of the American Oriental Society. pp. 10-12 (1.21-24), 17.
  16. Matchett, Freda; Yano, Michio (2003). "Part II, Ch. 6: The Puranas / Part III, Ch. 18: Calendar, Astrology, and Astronomy". In Flood, Gavin (ed.). The Blackwell Companion to Hinduism. Google Books. Blackwell Publishing. pp. 139–140, 390 (Kali yuga epoch). ISBN 0631215352.
  17. Bharatbarsha – A Living Legend.
  18. Gupta 2010, p. 7.
  19. Godwin, Joscelyn (2011). Atlantis and the Cycles of Time: Prophecies, Traditions, and Occult Revelations. Inner Traditions. p. 300-301. ISBN 9781594778575.
  20. Merriam-Webster (1999). "Merriam-Webster's Encyclopedia of World Religions". In Doniger, Wendy; Hawley, John Stratton (eds.). Merriam-Webster. Merriam-Webster, Incorporated. pp. 445 (Hinduism), 1159 (Yuga). ISBN 0877790442.
    * HINDUISM: Myths of time and eternity: ... Each yuga is preceded by an intermediate "dawn" and "dusk." The Krita yuga lasts 4,000 god-years, with a dawn and dusk of 400 god-years each, or a total of 4,800 god-years; Treta a total of 3,600 god-years; Dvapara 2,400 god-years; and Kali (the current yuga) 1,200 god-years. A mahayuga thus lasts 12,000 god-years ... Since each god-year lasts 360 human years, a mahayuga is 4,320,000 years long in human time. Two thousand mahayugas form one kalpa (eon) [and pralaya], which is itself but one day in the life of Brahma, whose full life lasts 100 years; the present is the midpoint of his life. Each kalpa is followed by an equally long period of abeyance (pralaya), in which the universe is asleep. Seemingly the universe will come to an end at the end of Brahma's life, but Brahmas too are innumerable, and a new universe is reborn with each new Brahma.
    * YUGA: Each yuga is progressively shorter than the preceding one, corresponding to a decline in the moral and physical state of humanity. Four such yugas ... make up a mahayuga ("great yuga") ... The first yuga (Krita) was an age of perfection, lasting 1,728,000 years. The fourth and most degenerate yuga (Kali) began in 3102 BCE and will last 432,000 years. At the close of the Kali yuga, the world will be destroyed by fire and flood, to be re-created as the cycle resumes. In a partially competing vision of time, Vishnu's 10th and final Avatar, Kalki, is described as bringing the present cosmic cycle to a close by destroying the evil forces that rule the Kali yuga and ushering in an immediate return to the idyllic Krita yuga.
  21. Hans Kng (31 October 2006). Tracing The Way: Spiritual Dimensions of the World Religions. A&C Black. p. 50. ISBN 9780826494238.
  22. "Śrīmad-Bhāgavatam (Bhāgavata Purāṇa) 3.11.19". Bhaktivedanta Vedabase. Retrieved 10 July 2020.
    catvāri trīṇi dve caikaṁ kṛtādiṣu yathā-kramam ।
    saṅkhyātāni sahasrāṇi dvi-guṇāni śatāni ca ॥ 19 ॥
    (19) The duration of the Satya millennium equals 4,800 years of the years of the demigods; the duration of the Tretā millennium equals 3,600 years of the demigods; the duration of the Dvāpara millennium equals 2,400 years; and that of the Kali millennium is 1,200 years of the demigods. PURPORT: As aforementioned, one year of the demigods is equal to 360 years of the human beings. The duration of the Satya-yuga is therefore 4,800 × 360, or 1,728,000 years. The duration of the Tretā-yuga is 3,600 × 360, or 1,296,000 years. The duration of the Dvāpara-yuga is 2,400 × 360, or 864,000 years. And the last, the Kali-yuga, is 1,200 × 360, or 432,000 years.
  23. Doniger, Wendy; Hawley, John Stratton, eds. (1999). "Merriam-Webster's Encyclopedia of World Religions". Merriam-Webster. Merriam-Webster, Incorporated. p. 691 (Manu). ISBN 0877790442. a day in the life of Brahma is divided into 14 periods called manvantaras ("Manu intervals"), each of which lasts for 306,720,000 years. In every second cycle [(new kalpa after pralaya)] the world is recreated, and a new Manu appears to become the father of the next human race. The present age is considered to be the seventh Manu cycle.
  24. Penprase, Bryan E. (2017). The Power of Stars (2nd ed.). Springer. p. 182. ISBN 9783319525976.
  25. Johnson, W.J. (2009). A Dictionary of Hinduism. Oxford University Press. p. 165. ISBN 978-0-19-861025-0.
  26. "Śrīmad-Bhāgavatam (Bhāgavata Purāṇa) 9.10.51". Bhaktivedanta Vedabase. Retrieved 18 May 2020. Lord Rāmacandra became King during Tretā-yuga, but because of His good government, the age was like Satya-yuga. Everyone was religious and completely happy.
  27. Knapp, Stephen. "Lord Rama: Fact or Fiction". Stephen Knapp and His Books on Vedic Culture, Eastern Philosophy and Spirituality. Retrieved 17 May 2020. In the Vayu Purana (70.47-48) [published by Motilal Banarsidass] there is a description of the length of Ravana’s life. It explains that when Ravana’s merit of penance began to decline, he met Lord Rama, the son of Dasarath, in a battle wherein Ravana and his followers were killed in the 24th Treta-yuga. ... The Matsya Purana (47/240,243-246) is another source that also gives more detail of various avataras and says Bhagawan Rama appeared at the end of the 24th Treta-yuga.
  28. Mani, Vettam (1975). "RAKTAJA". A Comprehensive Dictionary with Special Reference to the Epic and Puranic Literature. Puranic Encyclopedia. Motilal Banarsidass. p. 630(b). ISBN 0842608222. In Padma Purana (Chapter 14). Devendra raised a legal objection to the above injunction of Vishnu as follows: "You, who incarnated yourself as Rama in the twentyseventh yuga of the last Manvantara for the purpose of killing Ravana, killed my son Bali. Therefore I do not wish to procreate Nara as my son." To this objection of Indra, Vishnu assured him that as a penalty for the mistake of killing Bali, he would be a companion of Nara (Arjuna) who would be born as Indra's son.
  • Victor J. Katz. A History of Mathematics: An Introduction, 1998.
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