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Chronology of computation of π

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{{DISPLAYTITLE:Chronology of computation of {{pi}}}}

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Pi (approximately 3.14159265358979323846264338327950288) is a mathematical sequence of numbers.

The table below is a brief chronology of computed numerical values of, or bounds on, the mathematical constant pi ({{pi}}). For more detailed explanations for some of these calculations, see Approximations of {{pi}}.

As of May 2025, {{pi}} has been calculated to 300,000,000,000,000 decimal digits.{{Cite AV media |url=https://www.youtube.com/watch?v=BD-AJwqzWsU&t=16m25s |title=This World Record took YEARS (and a Million dollars..) |date=2025-05-16 |last=Linus Tech Tips |access-date=2025-05-16 |via=YouTube}}

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File:PiComputationHistory.svg

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Before 1400

class="wikitable"
align="left"| Date

!align="left"| Who

!align="left"| Description/Computation method used

!align="right"| Value

!align="right"| Decimal places
(world records
in bold)

2000? BCAncient Egyptians{{cite journal|author1=David H. Bailey |author2=Jonathan M. Borwein |author3=Peter B. Borwein |author4=Simon Plouffe |year=1997|title=The quest for pi|url=http://crd-legacy.lbl.gov/~dhbailey/dhbpapers/pi-quest.pdf|journal=Mathematical Intelligencer|volume=19|issue=1|pages=50–57|doi=10.1007/BF03024340|s2cid=14318695}}

|4 × ({{frac|8|9}})2

|align="right"|3.1605...

1
2000? BCAncient Babylonians

|3 + {{frac|1|8

}

|align="right"|3.125||1

|-

|2000? BC

|Ancient Sumerians{{cite web |date=2022-03-14 |title=Origins: 3.14159265... |url=https://www.biblicalarchaeology.org/daily/ancient-cultures/origins-pi/ |access-date=2022-06-08 |website=Biblical Archaeology Society |language=en}}

|3 + 23/216

|align="right"|3.1065...

|1

|-

|1200? BC||Ancient Chinese

|3

|align="right"|3||0

|-

|800–600 BC || Shatapatha Brahmana – 7.1.1.18 {{Cite book|last=Eggeling|first=Julius|url=https://archive.org/details/satapathabrahman03egge|title=The Satapatha-brahmana, according to the text of the Madhyandina school|date=1882–1900|publisher=Oxford, The Clarendon Press|others=Princeton Theological Seminary Library|pages=302–303}}

||Instructions on how to construct a circular altar from oblong bricks:

"He puts on (the circular site) four (bricks) running eastwards 1; two behind running crosswise (from south to north), and two (such) in front. Now the four which he puts on running eastwards are the body; and as to there being four of these, it is because this body (of ours) consists, of four parts 2. The two at the back then are the thighs; and the two in front the arms; and where the body is that (includes) the head."{{cite book|title=The Sacred Books of the East: The Satapatha-Brahmana, pt. 3|year=1894|publisher=Clarendon Press|page=303}} {{PD-notice}}

|align="right"|{{frac|25|8}} = 3.125||1

|-

|800? BC||Shulba Sutras{{cite web|url=http://www-history.mcs.st-and.ac.uk/Projects/Pearce/Chapters/Ch4_2.html|title=4 II. Sulba Sutras|website=www-history.mcs.st-and.ac.uk}}

{{cite journal |author1=Ravi P. Agarwal |author2=Hans Agarwal |author3=Syamal K. Sen |year=2013 |title=Birth, growth and computation of pi to ten trillion digits |journal=Advances in Difference Equations |volume=2013 |page=100 |doi=10.1186/1687-1847-2013-100 |doi-access=free }}{{cite book|page=[https://books.google.com/books?id=DHvThPNp9yMC&pg=PA18 18]|title=Mathematics in India|title-link=Mathematics in India (book)|first=Kim|last=Plofker|date= 2009|publisher=Princeton University Press|isbn=978-0691120676}}

|({{frac|6|(2 + {{radic|2}})}})2

|align="right"|3.088311 ...||0

|-

|550? BC||Bible (1 Kings 7:23)

||"...a molten sea, ten cubits from the one brim to the other: it was round all about,... a line of thirty cubits did compass it round about"||align="right"|3||0

|-

|450 BC||Anaxagoras attempted to square the circle{{cite web |last1=Wilson |first1=David |title=The History of Pi |url=https://sites.math.rutgers.edu/~cherlin/History/Papers2000/wilson.html |website=sites.math.rutgers.edu |publisher=University Of Rutgers |archive-url=https://web.archive.org/web/20230507165826/https://sites.math.rutgers.edu/~cherlin/History/Papers2000/wilson.html |archive-date=7 May 2023 |language=en |date=2000 |url-status=live}}

|compass and straightedge||Anaxagoras did not offer a solution||0

|-

|420 BC||Bryson of Heraclea ||inscribed and circumscribed polygons|| 2 < \pi < 4 ||1

|-

| 400 BC to AD 400 || Vyasa{{Cite journal|last=Jadhav|first=Dipak|date=2018-01-01|title=On The Value Implied In The Data Referred To In The Mahābhārata for π|url=https://www.academia.edu/37922665|journal=Vidyottama Sanatana: International Journal of Hindu Science and Religious Studies|volume=2|issue=1|page=18|doi=10.25078/ijhsrs.v2i1.511|s2cid=146074061|issn=2550-0651|doi-access=free}} ||

verses: 6.12.40-45 of the Bhishma Parva of the Mahabharata offer:
"...

The Moon is handed down by memory to be eleven thousand yojanas in diameter. Its peripheral circle happens to be thirty three thousand yojanas when calculated.

...

The Sun is eight thousand yojanas and another two thousand yojanas in diameter. From that its peripheral circle comes to be equal to thirty thousand yojanas.

..."

|align="right"|3||0

|-

|c. 250 BC||Archimedes

|{{frac|223|71}} < {{pi}} < {{frac|22|7}}

|align="right"|3.140845... < {{pi}} < 3.142857...||2

|-

|15 BC||Vitruvius

|{{frac|25|8}}

|align="right"|3.125||1

|-

|Between 1 BC and AD 5||Liu Xin{{cite book|url=https://books.google.com/books?id=_1AsFyM0d84C|title=中西數學史的比較|last=趙良五|date=1991|publisher=臺灣商務印書館|isbn=978-9570502688|via=Google Books}}Needham, Joseph (1986). Science and Civilization in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth. Taipei: Caves Books, Ltd. Volume 3, 100.

|Unknown method giving a figure for a jialiang which implies a value for {{pi}} ≈ {{frac|162|({{radic|50}}+0.095)2}}.

|align="right"|3.1547...||1

|-

|AD 130||Zhang Heng (Book of the Later Han)

|{{radic|10}} = 3.162277...
{{frac|736|232}}

|align="right"|3.1622...||1

|-

|150||Ptolemy

|{{frac|377|120}}

|align="right"|3.141666...||3

|-

|250||Wang Fan

|{{frac|142|45}}

|align="right"|3.155555...||1

|-

|263||Liu Hui

|3.141024 < {{pi}} < 3.142074
{{frac|3927|1250}}

|align="right"|3.1416||3

|-

|400||He Chengtian

|{{frac|111035|35329}}

|align="right"|3.142885...||2

|-

|480||Zu Chongzhi

|3.1415926 < {{pi}} < 3.1415927
Milü

|align="right"|3.1415926||7

|-

|499||Aryabhata

|{{frac|62832|20000}}

|align="right"|3.1416||3

|-

|640||Brahmagupta

|{{radic|10}}

|align="right"|3.162277...||1

|-

|800||Al Khwarizmi

|

|align="right"|3.1416||3

|-

|1150||Bhāskara II

| {{frac|3927|1250}} and {{frac|754|240}}

|align="right"|3.1416||3

|-

|1220||Fibonacci

|

|align="right"|3.141818||3

|-

|1320|| Zhao Youqin

|Zhao Youqin's {{pi}} algorithm

|align="right"|3.141592||6

|}

1400–1949

class="wikitable"
align="left"| Date

!align="left"| Who

!align="left"| Note

!align="right"| Decimal places
{{nowrap| (world records in bold) }}

colspan="4" style="text-align:center;background:lightblue;"|All records from 1400 onwards are given as the number of correct decimal places.
1400Madhava of Sangamagrama

|Discovered the infinite power series expansion of {{pi}} now known as the Leibniz formula for pi{{cite journal| first=A. K.| last=Bag| year=1980| title=Indian Literature on Mathematics During 1400–1800 A.D.| journal=Indian Journal of History of Science| volume=15| issue=1| page=86| url=http://www.insa.nic.in/writereaddata/UpLoadedFiles/IJHS/Vol15_1_10_AKBag.pdf|quote={{pi}} ≈ 2,827,433,388,233/9×10−11 = 3.14159 26535 92222..., good to 10 decimal places.}}

|align="right"|10

1424Jamshīd al-Kāshīapproximated 2π to 9 sexagesimal digits. Al-Kashi, author: Adolf P. Youschkevitch, chief editor: Boris A. Rosenfeld, p. 256 {{MacTutor|id=Al-Kashi|title=Ghiyath al-Din Jamshid Mas'ud al-Kashi}} {{cite journal |last1=Azarian |first1=Mohammad K. |title=Al-Risāla Al-Muhītīyya: A Summary |journal=Missouri Journal of Mathematical Sciences |date=2010 |volume=22 |issue=2 |pages=64–85 |doi=10.35834/mjms/1312233136|doi-access=free}}

|

|align="right"|16

1573Valentinus Otho

|{{frac|355|113}}

|align="right"|6

1579François Viète{{cite book | first=François | last=Viète | author-link=François Viète | title=Canon mathematicus seu ad triangula : cum adpendicibus | year=1579 | language=la | url=http://gallica.bnf.fr/ark:/12148/bpt6k52673b/f171.image}}

|

|align="right"|9

1593Adriaan van Roomen{{cite book | first={{lang|la|Adrianus}} | last={{lang|la|Romanus}} | title=Ideae mathematicae pars prima, sive methodus polygonorum | year=1593 | publisher=apud Ioannem Keerbergium | hdl=2027/ucm.5320258006 | language=la }}

|

|align="right"|15

1596rowspan="2"|Ludolph van Ceulen

|rowspan="2"|

|align="right"|20

1615

|align="right"|32

1621Willebrord Snell (Snellius)

|Pupil of Van Ceulen

|align="right"|35

1630Christoph Grienberger{{cite book | first=Christophorus | last=Grienbergerus | author-link=Christoph Grienberger | language=la | year=1630 | title=Elementa Trigonometrica | url=http://librarsi.comune.palermo.it/gesuiti2/06.04.01.pdf | url-status=dead | archive-url=https://web.archive.org/web/20140201234124/http://librarsi.comune.palermo.it/gesuiti2/06.04.01.pdf | archive-date=2014-02-01 }}{{cite book | first1=Ernest William | last1=Hobson | author-link=E. W. Hobson | year=1913 | title='Squaring the Circle': a History of the Problem | page=27 | publisher=Cambridge University Press | url=https://archive.org/stream/squaringcirclehi00hobsuoft#page/27/mode/1up | format=PDF}}

|

|align="right"|38

1654

|Christiaan Huygens

|Used a geometrical method equivalent to Richardson extrapolation

|align="right"|10

1665Isaac Newton

|

|align="right"|16

1681Takakazu Seki{{Cite book|last1=Yoshio|author-link=Yoshio Mikami|first1=Mikami|last2=Eugene Smith|first2=David |orig-year=1914|date=2004|title=A History of Japanese Mathematics|edition=paperback|publisher=Dover Publications|isbn=0-486-43482-6|url=https://archive.org/details/historyofjapanes00smitiala}}

|

|align="right"|11
16

1699Abraham Sharp

|Calculated pi to 72 digits, but not all were correct

|align="right"|71

1706John Machin

|

|align="right"|100

1706William Jones

|Introduced the Greek letter '{{pi}}'

|

1719Thomas Fantet de Lagny

|Calculated 127 decimal places, but not all were correct

|align="right"|112

1721Anonymous

|Calculation made in Philadelphia, Pennsylvania, giving the value of pi to 154 digits, 152 of which were correct. First discovered by F. X. von Zach in a library in Oxford, England in the 1780s, and reported to Jean-Étienne Montucla, who published an account of it.Benjamin Wardhaugh, "Filling a Gap in the History of {{pi}}: An Exciting Discovery", Mathematical Intelligencer 38(1) (2016), 6-7

|align="right"|152

1722Toshikiyo Kamata

|

|align="right"|24

1722Katahiro Takebe

|

|align="right"|41

1739Yoshisuke Matsunaga

|

|align="right"|51

1748Leonhard Euler

|Used the Greek letter '{{pi}}' in his book Introductio in Analysin Infinitorum and assured its popularity.

|

1761Johann Heinrich Lambert

|Proved that {{pi}} is irrational

|

1775Euler

|Pointed out the possibility that {{pi}} might be transcendental

|

1789Jurij Vega{{cite journal |last=Vega |first=Géorge |year=1795 |orig-year=1789 |title=Detérmination de la demi-circonférence d'un cercle dont le diameter est {{math|{{=}} 1}}, exprimée en {{math|140}} figures decimals |journal=Nova Acta Academiae Scientiarum Petropolitanae |volume=11 |department=Supplement |pages=41–44 |url=https://archive.org/details/novaactaacademia09impe/page/n52/mode/2up}}

{{cite web |last=Sandifer |first=Ed |year=2006 |title=Why 140 Digits of Pi Matter |website=Southern Connecticut State University |url=http://www.southernct.edu/~sandifer/Ed/History/Preprints/Talks/Jurij%20Vega/Vega%20math%20script.pdf |url-status=dead |archive-date=2012-02-04 |archive-url=https://web.archive.org/web/20120204040635/http://www.southernct.edu/~sandifer/Ed/History/Preprints/Talks/Jurij%20Vega/Vega%20math%20script.pdf }}

|Calculated 140 decimal places, but not all were correct

|align="right"|126

1794Adrien-Marie Legendre

|Showed that {{pi}}2 (and hence {{pi}}) is irrational, and mentioned the possibility that {{pi}} might be transcendental.

|

1824William Rutherford

|Calculated 208 decimal places, but not all were correct

|align="right"|152

1844Zacharias Dase and Strassnitzky

|Calculated 205 decimal places, but not all were correct

|align="right"|200

1847Thomas Clausen

|Calculated 250 decimal places, but not all were correct

|align="right"|248

1853Lehmann

|

|align="right"|261

1853Rutherford

|

|align="right"|440

1853William Shanks{{cite magazine |last=Hayes |first=Brian |url=https://www.americanscientist.org/article/pencil-paper-and-pi |title=Pencil, Paper, and Pi |volume=102 |issue=5 |page=342 |magazine=American Scientist |date=September 2014 |access-date=13 February 2022 |doi=10.1511/2014.110.342}}

|Expanded his calculation to 707 decimal places in 1873, but an error introduced at the beginning of his new calculation rendered all of the subsequent digits invalid (the error was found by D. F. Ferguson in 1946).

|align="right"|527

1882Ferdinand von Lindemann

|Proved that {{pi}} is transcendental (the Lindemann–Weierstrass theorem)

|

1897The U.S. state of Indiana

|Came close to legislating the value 3.2 (among others) for {{pi}}. House Bill No. 246 passed unanimously. The bill stalled in the state Senate due to a suggestion of possible commercial motives involving publication of a textbook.{{cite web|url=http://www.cs.uu.nl/wais/html/na-dir/sci-math-faq/indianabill.html|title=Indiana Bill sets value of Pi to 3|last=Lopez-Ortiz|first=Alex|date=February 20, 1998|work=the news.answers WWW archive|publisher=Department of Information and Computing Sciences, Utrecht University|access-date=2009-02-01|archive-date=2005-01-09|archive-url=https://web.archive.org/web/20050109144036/http://www.cs.uu.nl/wais/html/na-dir/sci-math-faq/indianabill.html|url-status=dead}}

|align="right"|{{color|red|0}}

1910Srinivasa Ramanujan

|Found several rapidly converging infinite series of {{pi}}, which can compute 8 decimal places of {{pi}} with each term in the series. Since the 1980s, his series have become the basis for the fastest algorithms currently used by Yasumasa Kanada and the Chudnovsky brothers to compute {{pi}}.

|

1946

|D. F. Ferguson

|Made use of a desk calculator{{Cite book |last=Wells |first=D. G. |title=The Penguin Dictionary of Curious and Interesting Numbers |date=May 1, 1998 |publisher=Penguin Books |isbn=978-0140261493 |edition=Revised |pages=33}}

|align="right"|620

1947

|Ivan Niven

|Gave a very elementary proof that {{pi}} is irrational

|

January 1947

|D. F. Ferguson

|Made use of a desk calculator

|align="right"|710

September 1947

|D. F. Ferguson

|Made use of a desk calculator

|align="right"|808

1949

|Levi B. Smith and John Wrench

|Made use of a desk calculator

|align="right"|1,120

1949–2009

class="wikitable"
align="left"| Date

!align="left"| Who

!align="left"| Implementation

!align="left"| Time

!align="right"| Decimal places
{{nowrap| (world records in bold) }}

colspan="5" style="text-align:center;background:lightblue;"|All records from 1949 onwards were calculated with electronic computers.
September 1949

|G. W. Reitwiesner et al.

|The first to use an electronic computer (the ENIAC) to calculate {{pi}}{{cite journal |first=G. |last=Reitwiesner |title= An ENIAC determination of 𝜋 and 𝑒 to more than 2000 decimal places|journal= Mathematics of Computation|volume=4 |year=1950 |issue=29 |pages=11–15 |doi=10.1090/S0025-5718-1950-0037597-6 |doi-access=free }}

|70 hours

|align="right"|2,037

1953Kurt Mahler

|Showed that {{pi}} is not a Liouville number

|

|align="right"|

1954

|S. C. Nicholson & J. Jeenel

|Using the NORC{{cite journal |first1=S. C. |last1=Nicholson |first2=J. |last2=Jeenel |title= Some comments on a NORC computation of 𝜋|journal= Mathematics of Computation|volume=9 |year=1955 |issue=52 |pages=162–164 |doi=10.1090/S0025-5718-1955-0075672-5 |doi-access=free }}

|13 minutes

|align="right"|3,093

1957

|George E. Felton

|Ferranti Pegasus computer (London), calculated 10,021 digits, but not all were correctG. E. Felton, "Electronic computers and mathematicians," Abbreviated Proceedings of the Oxford Mathematical Conference for Schoolteachers and Industrialists at Trinity College, Oxford, April 8–18, 1957, pp. 12–17, footnote pp. 12–53. This published result is correct to only 7480D, as was established by Felton in a second calculation, using formula (5), completed in 1958 but apparently unpublished. For a detailed account of calculations of π see {{cite journal |first=J. W. Jr. |last=Wrench |title=The evolution of extended decimal approximations to π |journal=The Mathematics Teacher |volume=53 |year=1960 |pages=644–650 |issue=8|doi=10.5951/MT.53.8.0644 |jstor=27956272 }}{{Cite book |last1=Arndt |first1=Jörg |last2=Haenel |first2=Christoph |title=Pi - Unleashed |year=2001 |publisher=Springer |isbn=978-3-642-56735-3 |language=en}}

|33 hours

|align="right"|7,480

January 1958

|Francois Genuys

|IBM 704{{cite journal |first=F. |last=Genuys |title=Dix milles decimales de π |journal=Chiffres |volume=1 |year=1958 |pages=17–22 }}

|1.7 hours

|align="right"|10,000

May 1958

|George E. Felton

|Pegasus computer (London)

|33 hours

|align="right"|10,021

1959

|Francois Genuys

|IBM 704 (Paris)This unpublished value of x to 16167D was computed on an IBM 704 system at the French Alternative Energies and Atomic Energy Commission in Paris, by means of the program of Genuys

|4.3 hours

|align="right"|16,167

1961

|Daniel Shanks and John Wrench

|IBM 7090 (New York){{cite journal |first1=Daniel |last1=Shanks |first2=John W. J.r |last2=Wrench |title=Calculation of π to 100,000 decimals |journal=Mathematics of Computation |volume=16 |year=1962 |issue=77 |pages=76–99 |doi=10.1090/S0025-5718-1962-0136051-9 |doi-access=free }}

|8.7 hours

|align="right"|100,265

1961

|J.M. Gerard

|IBM 7090 (London)

|39 minutes

|align="right"|20,000

February 1966

|Jean Guilloud and J. Filliatre

|IBM 7030 (Paris)

|41.92 hours

|align="right"|250,000

1967

|Jean Guilloud and M. Dichampt

|CDC 6600 (Paris)

|28 hours

|align="right"|500,000

1973

|Jean Guilloud and Martine Bouyer

|CDC 7600

|23.3 hours

|align="right"|1,001,250

1981

|Kazunori Miyoshi and Yasumasa Kanada

|FACOM M-200

|137.3 hours

|align="right"|2,000,036

1981

|Jean Guilloud

|Not known

|

|align="right"|2,000,050

1982

|Yoshiaki Tamura

|MELCOM 900II

|7.23 hours

|align="right"|2,097,144

1982

|Yoshiaki Tamura and Yasumasa Kanada

|HITAC M-280H

|2.9 hours

|align="right"|4,194,288

1982

|Yoshiaki Tamura and Yasumasa Kanada

|HITAC M-280H

|6.86 hours

|align="right"|8,388,576

1983

|Yasumasa Kanada, Sayaka Yoshino and Yoshiaki Tamura

|HITAC M-280H

|<30 hours

|align="right"|16,777,206

October 1983

|Yasunori Ushiro and Yasumasa Kanada

|HITAC S-810/20

|

|align="right"|10,013,395

October 1985

|Bill Gosper

|Symbolics 3670

|

|align="right"|17,526,200

January 1986

|David H. Bailey

|CRAY-2

|28 hours

|align="right"|29,360,111

September 1986

|Yasumasa Kanada, Yoshiaki Tamura

|HITAC S-810/20

|6.6 hours

|align="right"|33,554,414

October 1986

|Yasumasa Kanada, Yoshiaki Tamura

|HITAC S-810/20

|23 hours

|align="right"|67,108,839

January 1987

|Yasumasa Kanada, Yoshiaki Tamura, Yoshinobu Kubo and others

|NEC SX-2

|35.25 hours

|align="right"|134,214,700

January 1988

|Yasumasa Kanada and Yoshiaki Tamura

|HITAC S-820/80{{Cite book |last=Kanada |first=Y. |title=Proceedings Supercomputing Vol.II: Science and Applications |chapter=Vectorization of multiple-precision arithmetic program and 201,326,000 decimal digits of pi calculation |date=November 1988 |chapter-url=https://ieeexplore.ieee.org/document/74139 |pages=117–128 vol.2 |doi=10.1109/SUPERC.1988.74139|isbn=0-8186-8923-4 |s2cid=122820709 }}

|5.95 hours

|align="right"|201,326,551

May 1989

|Gregory V. Chudnovsky & David V. Chudnovsky

|CRAY-2 & IBM 3090/VF

|

|align="right"|480,000,000

June 1989

|Gregory V. Chudnovsky & David V. Chudnovsky

|IBM 3090

|

|align="right"|535,339,270

July 1989

|Yasumasa Kanada and Yoshiaki Tamura

|HITAC S-820/80

|

|align="right"|536,870,898

August 1989

|Gregory V. Chudnovsky & David V. Chudnovsky

|IBM 3090

|

|align="right"|1,011,196,691

19 November 1989

|Yasumasa Kanada and Yoshiaki Tamura

|HITAC S-820/80{{cite web |title=Computers |url=https://www.sciencenews.org/archive/computers-25 |access-date=2022-08-04 |website=Science News |date=24 August 1991 |language=en-US}}

|

|align="right"|1,073,740,799

August 1991

|Gregory V. Chudnovsky & David V. Chudnovsky

|Homemade parallel computer (details unknown, not verified)Bigger slices of Pi (determination of the numerical value of pi reaches 2.16 billion decimal digits) Science News 24 August 1991 http://www.encyclopedia.com/doc/1G1-11235156.html

|

|align="right"|2,260,000,000

18 May 1994

|Gregory V. Chudnovsky & David V. Chudnovsky

|New homemade parallel computer (details unknown, not verified)

|

|align="right"|4,044,000,000

26 June 1995

|Yasumasa Kanada and Daisuke Takahashi

|HITAC S-3800/480 (dual CPU){{Cite FTP |url=ftp://pi.super-computing.org/README.our_last_record_3b |server=pi.super-computing.org |url-status=dead |title=FTP link }}

|

|align="right"|3,221,220,000

1995

|Simon Plouffe

|Finds a formula that allows the {{var|n}}th hexadecimal digit of pi to be calculated without calculating the preceding digits.

|

|

28 August 1995

|Yasumasa Kanada and Daisuke Takahashi

|HITAC S-3800/480 (dual CPU){{Cite FTP |url=ftp://pi.super-computing.org/README.our_last_record_4b |server=pi.super-computing.org |url-status=dead |title=FTP link }}{{cite web |title=GENERAL COMPUTATIONAL UPDATE |url=http://www.cecm.sfu.ca/organics/papers/borwein/paper/html/local/general/html/node1.html |access-date=2022-08-04 |website=www.cecm.sfu.ca}}

|56.74 hours?

|align="right"|4,294,960,000

11 October 1995

|Yasumasa Kanada and Daisuke Takahashi

|HITAC S-3800/480 (dual CPU){{Cite FTP |url=ftp://pi.super-computing.org/README.our_last_record_6b |server=pi.super-computing.org |url-status=dead |title=FTP link }}

|116.63 hours

|align="right"|6,442,450,000

6 July 1997

|Yasumasa Kanada and Daisuke Takahashi

|HITACHI SR2201 (1024 CPU){{Cite FTP |url=ftp://pi.super-computing.org/README.our_last_record_51b |server=pi.super-computing.org |url-status=dead |title=FTP link }}{{cite web |date=2005-12-24 |title=Record for pi : 51.5 billion decimal digits |url=http://oldweb.cecm.sfu.ca/personal/jborwein/Kanada_50b.html |access-date=2022-08-04 |archive-url=https://web.archive.org/web/20051224015531/http://oldweb.cecm.sfu.ca/personal/jborwein/Kanada_50b.html |archive-date=2005-12-24 }}

|29.05 hours

|align="right"|51,539,600,000

5 April 1999

|Yasumasa Kanada and Daisuke Takahashi

|HITACHI SR8000 (64 of 128 nodes){{Cite FTP |url=ftp://pi.super-computing.org/README.our_last_record_68b |server=pi.super-computing.org |url-status=dead |title=FTP link }}{{cite web |last1=Kanada |first1=Yasumasa |title=plouffe.fr/simon/constants/Pi68billion.txt |url=https://www.plouffe.fr/simon/constants/Pi68billion.txt |website=www.plouffe.fr |archive-url=https://web.archive.org/web/20220805103137/https://www.plouffe.fr/simon/constants/Pi68billion.txt |archive-date=5 August 2022 |language=en |url-status=live}}

|32.9 hours

|align="right"|68,719,470,000

20 September 1999

|Yasumasa Kanada and Daisuke Takahashi

|HITACHI SR8000/MPP (128 nodes){{Cite FTP |url=ftp://pi.super-computing.org/README.our_latest_record_206b |server=pi.super-computing.org |url-status=dead |title=FTP link }}{{cite web |title=Record for pi : 206 billion decimal digits |url=http://www.cecm.sfu.ca/~jborwein/Kanada_200b.html |access-date=2022-08-04 |website=www.cecm.sfu.ca}}

|37.35 hours

|align="right"|206,158,430,000

24 November 2002

|Yasumasa Kanada & 9 man team

|HITACHI SR8000/MPP (64 nodes), Department of Information Science at the University of Tokyo in Tokyo, Japan{{cite web |url=http://www.super-computing.org/pi_current.html |title=Current publisized world record of pi calculation is as in the followings. |access-date=2010-07-08 |archive-url=https://web.archive.org/web/20110312035524/http://www.super-computing.org/pi_current.html |archive-date=2011-03-12 |url-status=dead }}

|600 hours

|align="right"|1,241,100,000,000

29 April 2009

|Daisuke Takahashi et al.

|T2K Open Supercomputer (640 nodes), single node speed is 147.2 gigaflops, computer memory is 13.5 terabytes, Gauss–Legendre algorithm, Center for Computational Sciences at the University of Tsukuba in Tsukuba, Japan{{cite web |url=http://www.hpcs.is.tsukuba.ac.jp/~daisuke/pi.html |title=17th August 2009: Our latest record was established as the followings |access-date=2009-08-18 |archive-url=https://web.archive.org/web/20090823020534/http://www.hpcs.is.tsukuba.ac.jp/~daisuke/pi.html |archive-date=2009-08-23 |url-status=dead }}

|29.09 hours

|align="right"|2,576,980,377,524

2009–present

class="wikitable"
align="left"| Date

!align="left"| Who

!align="left"| Implementation

!align="left"| Time

!align="right"| Decimal places
{{nowrap| (world records in bold) }}

colspan="5" style="text-align:center;background:lightblue;"|All records from Dec 2009 onwards are calculated and verified on commodity x86 computers with commercially available parts. All use the Chudnovsky algorithm for the main computation, and Bellard's formula, the Bailey–Borwein–Plouffe formula, or both for verification.
31 December 2009

|Fabrice Bellard{{cite web |last=Bellard |first=Fabrice |authorlink=Fabrice Bellard |title=Computation of 2700 billion decimal digits of Pi using a Desktop Computer |date=11 Feb 2010 |version=4th revision |url=https://bellard.org/pi/pi2700e9/pipcrecord.pdf |language=en |s2cid=12242318}}{{Cite web |title=TachusPI |url=https://bellard.org/pi/pi2700e9/tpi.html |access-date=2024-10-10 |website=bellard.org}}

|

  • Computation: Intel Core i7 @ 2.93 GHz (4 cores, 6 GiB DDR3-1066 RAM)
  • Storage: 7.5 TB (5x 1.5 TB)
  • Red Hat Fedora 10 (x64)
  • Computation of the binary digits (Chudnovsky algorithm): 103 days
  • Verification of the binary digits (Bellard's formula): 13 days
  • Conversion to base 10: 12 days
  • Verification of the conversion: 3 days
  • Verification of the binary digits used a network of 9 Desktop PCs during 34 hours.

|131 days

|align="right"|2,699,999,990,000
= {{val|2.7|e=12}} − {{val|e=4}}

2 August 2010

|Shigeru Kondo{{cite web|url=http://piworld.calico.jp/estart.html|title=PI-world|work=calico.jp|access-date=28 August 2015|archive-url=https://web.archive.org/web/20150831180053/http://piworld.calico.jp/estart.html|archive-date=31 August 2015|url-status=dead}}

|

  • using y-cruncher{{cite web|url=http://www.numberworld.org/y-cruncher/|title=y-cruncher – A Multi-Threaded Pi Program|work=numberworld.org|access-date=28 August 2015}} 0.5.4 by Alexander Yee
  • with 2× Intel Xeon X5680 @ 3.33 GHz – (12 physical cores, 24 hyperthreaded)
  • 96 GiB DDR3 @ 1066 MHz – (12× 8 GiB – 6 channels) – Samsung (M393B1K70BH1)
  • 1 TB SATA II (Boot drive) – Hitachi (HDS721010CLA332), 3× 2 TB SATA II (Store Pi Output) – Seagate (ST32000542AS) 16× 2 TB SATA II (Computation) – Seagate (ST32000641AS)
  • Windows Server 2008 R2 Enterprise (x64)
  • Computation of binary digits: 80 days
  • Conversion to base 10: 8.2 days
  • Verification of the conversion: 45.6 hours
  • Verification of the binary digits: 64 hours (Bellard formula), 66 hours (BBP formula)
  • Verification of the binary digits were done simultaneously on two separate computers during the main computation. Both computed 32 hexadecimal digits ending with the 4,152,410,118,610th.{{cite web|url=http://www.numberworld.org/misc_runs/pi-5t/announce_en.html|title=Pi – 5 Trillion Digits|work=numberworld.org|access-date=28 August 2015}}

|90 days

|align="right"|5,000,000,000,000
= {{val|5|e=12}}

17 October 2011

|Shigeru Kondo{{cite web|url=http://www.numberworld.org/misc_runs/pi-10t/details.html|title=Pi – 10 Trillion Digits|work=numberworld.org|access-date=28 August 2015}}

|

  • using y-cruncher 0.5.5
  • with 2× Intel Xeon X5680 @ 3.33 GHz – (12 physical cores, 24 hyperthreaded)
  • 96 GiB DDR3 @ 1066 MHz – (12× 8 GiB – 6 channels) – Samsung (M393B1K70BH1)
  • 1 TB SATA II (Boot drive) – Hitachi (HDS721010CLA332), 5× 2 TB SATA II (Store Pi Output), 24× 2 TB SATA II (Computation)
  • Windows Server 2008 R2 Enterprise (x64)
  • Verification: 1.86 days (Bellard formula) and 4.94 days (BBP formula)

|371 days

|align="right"|10,000,000,000,050
= {{val|e=13}} + 50

28 December 2013

|Shigeru Kondo{{cite web|url=http://www.numberworld.org/misc_runs/pi-12t/|title=Pi – 12.1 Trillion Digits|work=numberworld.org|access-date=28 August 2015}}

|

  • using y-cruncher 0.6.3
  • Computation: 2× Intel Xeon E5-2690 @ 2.9 GHz – (32 cores, 128 GiB DDR3-1600 RAM)
  • Storage: 97 TB (32x 3 TB, 1x 1 TB)
  • Windows Server 2012 (x64)
  • Verification using Bellard's formula: 46 hours

|94 days

|align="right"|12,100,000,000,050
= {{val|1.21|e=13}} + 50

8 October 2014

|Sandon Nash Van Ness "houkouonchi"{{cite web |url=http://www.numberworld.org/digits/Pi/ |title=Pi: Notable large computations |work=numberworld.org |access-date=16 March 2024}}

|

  • using y-cruncher 0.6.3
  • Computation: 2× Xeon E5-4650L @ 2.6 GHz (16 cores, 192 GiB DDR3-1333 RAM)
  • Storage: 186 TB (24× 4 TB + 30× 3 TB)
  • Verification using Bellard's formula: 182 hours

|208 days

|align="right"|13,300,000,000,000
= {{val|1.33|e=13}}

11 November 2016

|Peter Trueb{{cite web|url=http://pi2e.ch/|title=pi2e|work=pi2e.ch|access-date=15 November 2016}}

|

  • using y-cruncher 0.7.1
  • Computation: 4× Xeon E7-8890 v3 @ 2.50 GHz (72 cores, 1.25 TiB DDR4 RAM)
  • Storage: 120 TB (20× 6 TB)
  • Linux (x64)
  • Verification using Bellard's formula: 28 hours{{cite web|url=http://pi2e.ch/blog/2016/10/31/hexadecimal-digits-are-correct/|title=Hexadecimal Digits are Correct! – pi2e trillion digits of pi|work=pi2e.ch|date=31 October 2016|access-date=15 November 2016}}

|105 days

|align="right"|22,459,157,718,361
{{math|1== {{floor|{{pi}}e{{x10^|12}}}}}}

14 March 2019

|Emma Haruka Iwao{{cite web|url=http://www.numberworld.org/blogs/2019_3_14_pi_record/|title=Google Cloud Topples the Pi Record|access-date=14 March 2019}}

|

  • using y-cruncher v0.7.6
  • Computation: 1× n1-megamem-96 (96 vCPU, 1.4 TB) with 30 TB of SSD
  • Storage: 24× n1-standard-16 (16 vCPU, 60 GB) with 10 TB of SSD
  • Windows Server 2016 (x64)
  • Verification: 20 hours using Bellard's 7-term formula, and 28 hours using Plouffe's 4-term formula

|121 days

|align="right"|31,415,926,535,897
{{math|1== {{floor|{{pi}}{{x10^|13}}}}}}

29 January 2020

|Timothy Mullican{{cite web|url=http://numberworld.org/y-cruncher/news/2020.html#2020_1_29|title=The Pi Record Returns to the Personal Computer|access-date=30 January 2020}}{{cite web|url=https://blog.timothymullican.com/calculating-pi-my-attempt-breaking-pi-record|title=Calculating Pi: My attempt at breaking the Pi World Record|date=26 June 2019|access-date=30 January 2020}}

|

  • using y-cruncher v0.7.7
  • Computation: 4× Intel Xeon CPU E7-4880 v2 @ 2.5 GHz (60 cores, 320 GB DDR3-1066 RAM)
  • Storage: 406.5 TB – 48× 6 TB HDDs (Computation) + 47× LTO Ultrium 5 1.5 TB Tapes (Checkpoint Backups) + 12× 4 TB HDDs (Digit Storage)
  • Ubuntu 18.10 (x64)
  • Verification: 17 hours using Bellard's 7-term formula, 24 hours using Plouffe's 4-term formula

|303 days

|align="right"|50,000,000,000,000
= {{val|5|e=13}}

14 August 2021

|Team DAViS of the University of Applied Sciences of the Grisons{{cite web|date=2021-08-14|title=Pi-Challenge - world record attempt by UAS Grisons - University of Applied Sciences of the Grisons|url=https://www.fhgr.ch/en/specialist-areas/applied-future-technologies/davis-centre/pi-challenge/|url-status=dead|access-date=2021-08-17|website=www.fhgr.ch|archive-url=https://web.archive.org/web/20210817040515/https://www.fhgr.ch/en/specialist-areas/applied-future-technologies/davis-centre/pi-challenge/ |archive-date=2021-08-17 }}{{cite web|date=2021-08-16|title=Die FH Graubünden kennt Pi am genauesten – Weltrekord! - News - FH Graubünden|url=https://www.fhgr.ch/news/newsdetail/die-fh-graubuenden-kennt-pi-am-genauesten-weltrekord/|url-status=live|access-date=2021-08-17|website=www.fhgr.ch|language=de|archive-url=https://web.archive.org/web/20210817060326/https://www.fhgr.ch/news/newsdetail/die-fh-graubuenden-kennt-pi-am-genauesten-weltrekord/ |archive-date=2021-08-17 }}

|

  • using y-cruncher v0.7.8
  • Computation: AMD Epyc 7542 @ 2.9 GHz (32 cores, 1 TiB RAM)
  • Storage: 608 TB (38× 16 TB HDDs, 34 are used for swapping and 4 used for storage)
  • Ubuntu 20.04 (x64)
  • Verification using the 4-term BBP formula: 34 hours

|108 days

|align="right"|62,831,853,071,796
{{math|1== {{ceil|2{{pi}}{{x10^|13}}}}}}

21 March 2022

|Emma Haruka Iwao{{cite web |title=Calculating 100 trillion digits of pi on Google Cloud |url=https://cloud.google.com/blog/products/compute/calculating-100-trillion-digits-of-pi-on-google-cloud/ |access-date=2022-06-10 |website=Google Cloud Blog |language=en}}{{cite web |title=100 Trillion Digits of Pi |url=http://numberworld.org/y-cruncher/news/2022.html#2022_6_8 |access-date=2022-06-10 |website=numberworld.org}}

|

  • using y-cruncher v0.7.8
  • Computation: n2-highmem-128 (128 vCPU and 864 GB RAM)
  • Storage: 663 TB
  • Debian Linux 11 (x64)
  • Verification: 12.6 hours using BBP formula

|158 days

|align="right"|100,000,000,000,000
= {{val|e=14}}

18 April 2023

|Jordan Ranous{{cite web |title=StorageReview Calculated 100 Trillion Digits of Pi in 54 days, Besting Google Cloud |url=https://www.storagereview.com/review/storagereview-calculated-100-trillion-digits-of-pi-in-54-days-besting-google-cloud |access-date=2023-12-02 |website=storagereview.com |date=18 April 2023 |language=en}}{{cite web |title=The Need for Speed! |date=19 April 2023 |url=http://www.numberworld.org/y-cruncher/news/2023.html#2023_4_19 |access-date=2023-12-25 |website=numberworld.org}}

|

  • using y-cruncher v0.7.10
  • Computation: 2 x AMD EPYC 9654 @ 2.4 GHz (96 cores, 1.5 TiB RAM)
  • Storage: 583 TB (19× 30.72 TB)
  • Windows Server 2022 (x64)

|59 days

|align="right"|100,000,000,000,000
= {{val|e=14}}

14 March 2024

|Jordan Ranous, Kevin O’Brien and Brian Beeler{{Cite web |last=Ranous |first=Jordan |date=2024-03-13 |title=105 Trillion Pi Digits: The Journey to a New Pi Calculation Record |url=https://www.storagereview.com/review/breaking-records-storagereviews-105-trillion-digit-pi-calculation |access-date=2024-03-14 |website=StorageReview.com |language=en-US}}{{Cite web |first=Alexander J. |last=Yee |date=2024-03-14 |title=Limping to a new Pi Record of 105 Trillion Digits |url=http://www.numberworld.org/y-cruncher/news/2024.html#2024_3_13 |website=NumberWorld.org |access-date=2024-03-16}}

|

  • using y-cruncher v0.8.3
  • Computation: 2 x AMD EPYC 9754 @ 2.25 GHz (128 cores, 1.5 TiB RAM)
  • Storage: 1,105 TB (36× 30.72 TB)
  • Windows Server 2022 (x64)

|75 days

|align="right"|105,000,000,000,000
= {{val|1.05|e=14}}

28 June 2024

|Jordan Ranous, Kevin O’Brien and Brian Beeler{{Cite web |last=Ranous |first=Jordan |date=2024-06-28 |title=StorageReview Lab Breaks Pi Calculation World Record with Over 202 Trillion Digits |url=https://www.storagereview.com/news/storagereview-lab-breaks-pi-calculation-world-record-with-over-202-trillion-digits |access-date=2024-07-02 |website=StorageReview.com |language=en-US}}{{Cite web |first=Alexander J. |last=Yee |date=2024-06-28 |title=Pi Record Smashed at 202 Trillion Digits |url=http://www.numberworld.org/y-cruncher/news/2024.html#2024_6_28 |website=NumberWorld.org |access-date=2024-06-30}}

|

  • using y-cruncher v0.8.3
  • Computation: 2 x Intel Xeon Platinum 8592+ @ 1.9 GHz (128 cores, 1.0 TiB DDR5 RAM)
  • Storage: 1.5 PB (28× 61.44 TB)
  • Windows 10 (x64)

|104 days

|align="right"|202,112,290,000,000
= {{val|2.0211229|e=14}}

2 April 2025

|Linus Media Group, Kioxia{{Cite web |title=Most accurate value of pi |url=https://www.guinnessworldrecords.com/world-records/66179-most-accurate-value-of-pi |access-date=2025-05-16 |website=Guinness World Records}}{{Cite AV media |url=https://www.youtube.com/watch?v=BD-AJwqzWsU&t |title=This World Record took YEARS (and a Million dollars..) |date=2025-05-16 |last=Linus Tech Tips |access-date=2025-05-16 |via=YouTube}}

|

  • using y-cruncher v0.8.5
  • Computation: 2x AMD EPYC 9684X 3D V-Cache @ 2.55GHz (192 cores, 3.0 TiB DDR5 RAM)
  • Storage: 2.2 PB (80x 15.36TB + 32x 30.72TB)
  • Ubuntu 24.04 (x64)

|226 days

|align="right" | 300,000,000,000,000
= {{val|3|e=14}}

See also

References

{{Reflist|2}}

External links

  • Borwein, Jonathan, "[http://www.cecm.sfu.ca/~jborwein/pi-slides.pdf The Life of Pi] {{Webarchive|url=https://web.archive.org/web/20061207191617/http://www.cecm.sfu.ca/~jborwein/pi-slides.pdf |date=2006-12-07 }}"
  • [https://web.archive.org/web/20110824110203/http://pi2.cc.u-tokyo.ac.jp/index.html Kanada Laboratory home page]
  • [https://web.archive.org/web/20160303221814/http://members.shaw.ca/francislyster/pi/supercomputer.html Stu's Pi page]
  • [https://web.archive.org/web/20090823020534/http://www.hpcs.is.tsukuba.ac.jp/~daisuke/pi.html Takahashi's page]
  • [https://pi.delivery/ Google's web service making all 100 trillion digits available]

{{DEFAULTSORT:Chronology Of Computation Of Pi}}

Category:Pi

Category:History of mathematics

Pi

Category:Pi algorithms