The table below is a brief chronology of computed numerical values of, or bounds on, the mathematical constant . For more detailed explanations for some of these calculations, see Approximations of .
Before 1400 Date Who Description/Computation method used Value Decimal places(world records in bold) Percent error(rounded to nearest thousandth)2000? BCAncient Egyptians4 × ()23.1605...1 +0.602%2000? BCAncient Babylonians3 + 3.1251 −0.528%2000? BCAncient Sumerians3 + 3.1065...1 −1.118%1200? BCAncient Chinese330 −4.507%800–600 BC Shatapatha Brahmana – 7.1.1.18 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." = 3.1251 −0.528%800? BCShulba Sutras()23.088311 ...0 −1.696%550? BCBible (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"30 −4.507%450 BCAnaxagoras attempted to square the circlecompass and straightedgeAnaxagoras did not offer a solution0 N/A420 BCBryson of Heraclea inscribed and circumscribed polygons 0 400 BC to AD 400 Vyasa 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. ..."30 −4.507%c. 250 BCArchimedes < < 3.140845... < < 3.142857...215 BCVitruvius3.1251 −0.528%Between 1 BC and AD 5Liu XinNeedham, 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 ≈ .3.1547...1 +0.416%AD 130Zhang Heng (Book of the Later Han) = 3.162277...3.1622...1 +0.658%+0.981%150Ptolemy3.141666...3 +0.002%250Wang Fan3.155555...1 +0.444%263Liu Hui3.141024 < < 3.1420743.14163%400He Chengtian3.142885...2 +0.041%480Zu Chongzhi3.1415926 < < 3.1415927 3.14159267 +%499Aryabhata3.14163%640Brahmagupta3.162277...1 +0.658%800Al Khwarizmi3.14163%1150Bhāskara II and 3.14163%1220Fibonacci3.1418183 +0.007%1320 Zhao YouqinZhao Youqin's algorithm3.1415926%
1400–1949 Date Who Note Decimal placesAll records from 1400 onwards are given as the number of correct decimal places.1400Madhava of SangamagramaDiscovered the infinite power series expansion of now known as the Leibniz formula for pi101424Jamshīd al-Kāshīapproximated 2π to 9 sexagesimal digits. Al-Kashi, author: Adolf P. Youschkevitch, chief editor: Boris A. Rosenfeld, p. 256 16Around 1500Kerala School Recorded using Katapayadi number system 3.1415926535897932384626433832792311573Valentinus Otho61579François Viète91593Adriaan van Roomen151596Ludolph van Ceulen201615321621Willebrord Snell (Snellius)Pupil of Van Ceulen351630Christoph Grienberger38 1654Christiaan HuygensUsed a geometrical method equivalent to Richardson extrapolation101665Isaac Newton161681Takakazu Seki11 161699Abraham SharpCalculated pi to 72 digits, but not all were correct711706John Machin1001706William JonesIntroduced the Greek letter ''1719Thomas Fantet de LagnyCalculated 127 decimal places, but not all were correct1121721AnonymousCalculation 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 : An Exciting Discovery", Mathematical Intelligencer 38(1) (2016), 6-71521722Toshikiyo Kamata241722Katahiro Takebe411739Yoshisuke Matsunaga511748Leonhard EulerUsed the Greek letter '' in his book Introductio in Analysin Infinitorum and assured its popularity.1761Johann Heinrich LambertProved that is irrational1775EulerPointed out the possibility that might be transcendental1789Jurij VegaCalculated 140 decimal places, but not all were correct1261794Adrien-Marie LegendreShowed that 2 (and hence ) is irrational, and mentioned the possibility that might be transcendental.1824William RutherfordCalculated 208 decimal places, but not all were correct1521844Zacharias Dase and StrassnitzkyCalculated 205 decimal places, but not all were correct2001847Thomas ClausenCalculated 250 decimal places, but not all were correct2481853Lehmann2611853Rutherford4401853William ShanksExpanded 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).5271882Ferdinand von LindemannProved that is transcendental (the Lindemann–Weierstrass theorem)1897The U.S. state of IndianaCame close to legislating the value 3.2 (among others) for . 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.1910Srinivasa RamanujanFound several rapidly converging infinite series of , which can compute 8 decimal places of 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 .1946D. F. FergusonMade use of a desk calculator6201947Ivan NivenGave a very elementary proof that is irrationalJanuary 1947D. F. FergusonMade use of a desk calculator710September 1947D. F. FergusonMade use of a desk calculator8081949Levi B. Smith and John WrenchMade use of a desk calculator1,120
1949–2009 Date Who Implementation Time Decimal placesAll records from 1949 onwards were calculated with electronic computers.September 1949G. W. Reitwiesner et al. The first to use an electronic computer (the ENIAC) to calculate 70 hours2,0371953Kurt MahlerShowed that is not a Liouville number1954S. C. Nicholson & J. JeenelUsing the NORC13 minutes3,0931957George E. FeltonFerranti 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 33 hours7,480January 1958Francois GenuysIBM 7041.7 hours10,000May 1958George E. FeltonPegasus computer (London)33 hours10,0211959Francois GenuysIBM 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 Genuys4.3 hours16,1671961Daniel Shanks and John WrenchIBM 7090 (New York)8.7 hours100,2651961J.M. GerardIBM 7090 (London)39 minutes20,000February 1966Jean Guilloud and J. FilliatreIBM 7030 (Paris)41.92 hours250,0001967Jean Guilloud and M. DichamptCDC 6600 (Paris)28 hours500,0001973Jean Guilloud and Martine BouyerCDC 760023.3 hours1,001,2501981Kazunori Miyoshi and Yasumasa KanadaFACOM M-200137.3 hours2,000,0361981Jean GuilloudNot known2,000,0501982Yoshiaki TamuraMELCOM 900II7.23 hours2,097,1441982Yoshiaki Tamura and Yasumasa KanadaHITAC M-280H2.9 hours4,194,2881982Yoshiaki Tamura and Yasumasa KanadaHITAC M-280H6.86 hours8,388,5761983Yasumasa Kanada, Sayaka Yoshino and Yoshiaki TamuraHITAC M-280H<30 hours16,777,206October 1983Yasunori Ushiro and Yasumasa KanadaHITAC S-810/2010,013,395October 1985Bill GosperSymbolics 367017,526,200January 1986David H. BaileyCRAY-228 hours29,360,111September 1986Yasumasa Kanada, Yoshiaki TamuraHITAC S-810/206.6 hours33,554,414October 1986Yasumasa Kanada, Yoshiaki TamuraHITAC S-810/2023 hours67,108,839January 1987Yasumasa Kanada, Yoshiaki Tamura, Yoshinobu Kubo and othersNEC SX-235.25 hours134,214,700January 1988Yasumasa Kanada and Yoshiaki TamuraHITAC S-820/805.95 hours201,326,551May 1989Gregory V. Chudnovsky & David V. ChudnovskyCRAY-2 & IBM 3090/VF480,000,000June 1989Gregory V. Chudnovsky & David V. ChudnovskyIBM 3090535,339,27013 July 1989Yasumasa Kanada and Yoshiaki TamuraHITAC S-820/80536,870,898August 1989Gregory V. Chudnovsky & David V. ChudnovskyIBM 30901,011,196,69119 November 1989Yasumasa Kanada and Yoshiaki TamuraHITAC S-820/801,073,740,799August 1991Gregory V. Chudnovsky & David V. ChudnovskyHomemade 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.html2,260,000,00018 May 1994Gregory V. Chudnovsky & David V. ChudnovskyNew homemade parallel computer (details unknown, not verified)4,044,000,00026 June 1995Yasumasa Kanada and Daisuke TakahashiHITAC S-3800/480 (dual CPU)3,221,220,0001995Simon PlouffeFinds a formula that allows the th hexadecimal digit of pi to be calculated without calculating the preceding digits.28 August 1995Yasumasa Kanada and Daisuke TakahashiHITAC S-3800/480 (dual CPU)56.74 hours?4,294,960,00011 October 1995Yasumasa Kanada and Daisuke TakahashiHITAC S-3800/480 (dual CPU)116.63 hours6,442,450,0006 July 1997Yasumasa Kanada and Daisuke TakahashiHITACHI SR2201 (1024 CPU)29.05 hours51,539,600,0005 April 1999Yasumasa Kanada and Daisuke TakahashiHITACHI SR8000 (64 of 128 nodes)32.9 hours68,719,470,00020 September 1999Yasumasa Kanada and Daisuke TakahashiHITACHI SR8000/MPP (128 nodes)37.35 hours206,158,430,00024 November 2002Yasumasa Kanada & 9 man teamHITACHI SR8000/MPP (64 nodes), Department of Information Science at the University of Tokyo in Tokyo, Japan600 hours1,241,100,000,00029 April 2009Daisuke 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, Japan29.09 hours2,576,980,377,524
2009–present Date Who Implementation Time Decimal placesAll 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 2009Fabrice Bellard 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 days2,699,999,990,000= − 2 August 2010Shigeru Kondo using y-cruncher 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