Chronology of computation of π

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

Date	Who	Description/Computation method used	Value	Decimal places (world records in bold)
2000? BC	Ancient Egyptians^[1]	4 × (8⁄9)²	3.1605...	1
2000? BC	Ancient Babylonians^[1]	3 + 1⁄8	3.125	1
2000? BC	Ancient Sumerians^[2]	3 + 23/216	3.1065...	1
1200? BC	Ancient Chinese^[1]	3	3	0
800–600 BC	Shatapatha Brahmana – 7.1.1.18 ^[3]	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."^[4]	25⁄8 = 3.125	1
800? BC	Shulba Sutras^[5] ^[6]^[7]	(6⁄(2 + √2))²	3.088311 ...	0
550? BC	Bible (1 Kings 7:23)^[1]	"...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"	3	0
450 BC	Anaxagoras attempted to square the circle^[8]	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^[9]	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. ..."	3	0
c. 250 BC	Archimedes^[1]	223⁄71 < $π$ < 22⁄7	3.140845... < $π$ < 3.142857...	2
15 BC	Vitruvius^[6]	25⁄8	3.125	1
Between 1 BC and AD 5	Liu Xin^[6]^[10]^[11]	Unknown method giving a figure for a jialiang which implies a value for $π$ ≈ 162⁄(√50+0.095)².	3.1547...	1
AD 130	Zhang Heng (Book of the Later Han)^[1]	√10 = 3.162277... 736⁄232	3.1622...	1
150	Ptolemy^[1]	377⁄120	3.141666...	3
250	Wang Fan^[1]	142⁄45	3.155555...	1
263	Liu Hui^[1]	3.141024 < $π$ < 3.142074 3927⁄1250	3.1416	3
400	He Chengtian^[6]	111035⁄35329	3.142885...	2
480	Zu Chongzhi^[1]	3.1415926 < $π$ < 3.1415927 355⁄113	3.1415926	7
499	Aryabhata^[1]	62832⁄20000	3.1416	3
640	Brahmagupta^[1]	√10	3.162277...	1
800	Al Khwarizmi^[1]		3.1416	3
1150	Bhāskara II^[6]	3927⁄1250 and 754⁄240	3.1416	3
1220	Fibonacci^[1]		3.141818	3
1320	Zhao Youqin^[6]	Zhao Youqin's $π$ algorithm	3.141592	6

Date	Who	Note	Decimal places (world records in bold)
All records from 1400 onwards are given as the number of correct decimal places.
1400	Madhava of Sangamagrama	Discovered the infinite power series expansion of $π$ now known as the Leibniz formula for pi^[12]	10
1424	Jamshīd al-Kāshī^[13]		16
1573	Valentinus Otho	355⁄113	6
1579	François Viète^[14]		9
1593	Adriaan van Roomen^[15]		15
1596	Ludolph van Ceulen		20
1615	Ludolph van Ceulen		32
1621	Willebrord Snell (Snellius)	Pupil of Van Ceulen	35
1630	Christoph Grienberger^[16]^[17]		38
1654	Christiaan Huygens	Used a geometrical method equivalent to Richardson extrapolation	10
1665	Isaac Newton^[1]		16
1681	Takakazu Seki^[18]		11 16
1699	Abraham Sharp^[1]	Calculated pi to 72 digits, but not all were correct	71
1706	John Machin^[1]		100
1706	William Jones	Introduced the Greek letter ' $π$ '
1719	Thomas Fantet de Lagny^[1]	Calculated 127 decimal places, but not all were correct	112
1721	Anonymous	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.^[19]	152
1722	Toshikiyo Kamata		24
1722	Katahiro Takebe		41
1739	Yoshisuke Matsunaga		51
1748	Leonhard Euler	Used the Greek letter ' $π$ ' in his book Introductio in Analysin Infinitorum and assured its popularity.
1761	Johann Heinrich Lambert	Proved that $π$ is irrational
1775	Euler	Pointed out the possibility that $π$ might be transcendental
1789	Jurij Vega^[20]	Calculated 140 decimal places, but not all were correct	126
1794	Adrien-Marie Legendre	Showed that $π$ ² (and hence $π$ ) is irrational, and mentioned the possibility that $π$ might be transcendental.
1824	William Rutherford^[1]	Calculated 208 decimal places, but not all were correct	152
1844	Zacharias Dase and Strassnitzky^[1]	Calculated 205 decimal places, but not all were correct	200
1847	Thomas Clausen^[1]	Calculated 250 decimal places, but not all were correct	248
1853	Lehmann^[1]		261
1853	Rutherford^[1]		440
1853	William Shanks^[21]	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).	527
1882	Ferdinand von Lindemann	Proved that $π$ is transcendental (the Lindemann–Weierstrass theorem)
1897	The U.S. state of Indiana	Came close to legislating the value 3.2 (among others) for $π$ . 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.^[22]	0
1910	Srinivasa Ramanujan	Found several rapidly converging infinite series of $π$ , which can compute 8 decimal places of $π$ 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 $π$ .
1946	D. F. Ferguson	Made use of a desk calculator^[23]	620
1947	Ivan Niven	Gave a very elementary proof that $π$ is irrational
January 1947	D. F. Ferguson	Made use of a desk calculator^[23]	710
September 1947	D. F. Ferguson	Made use of a desk calculator^[23]	808
1949	Levi B. Smith and John Wrench	Made use of a desk calculator	1,120

Date	Who	Implementation	Time	Decimal places (world records in bold)
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 $π$ ^[24]	70 hours	2,037
1953	Kurt Mahler	Showed that $π$ is not a Liouville number
1954	S. C. Nicholson & J. Jeenel	Using the NORC^[25]	13 minutes	3,093
1957	George E. Felton	Ferranti Pegasus computer (London), calculated 10,021 digits, but not all were correct^[26]^[27]	33 hours	7,480
January 1958	Francois Genuys	IBM 704^[28]	1.7 hours	10,000
May 1958	George E. Felton	Pegasus computer (London)	33 hours	10,021
1959	Francois Genuys	IBM 704 (Paris)^[29]	4.3 hours	16,167
1961	Daniel Shanks and John Wrench	IBM 7090 (New York)^[30]	8.7 hours	100,265
1961	J.M. Gerard	IBM 7090 (London)	39 minutes	20,000
February 1966	Jean Guilloud and J. Filliatre	IBM 7030 (Paris)^[27]	41.92 hours	250,000
1967	Jean Guilloud and M. Dichampt	CDC 6600 (Paris)	28 hours	500,000
1973	Jean Guilloud and Martine Bouyer	CDC 7600	23.3 hours	1,001,250
1981	Kazunori Miyoshi and Yasumasa Kanada	FACOM M-200^[27]	137.3 hours	2,000,036
1981	Jean Guilloud	Not known		2,000,050
1982	Yoshiaki Tamura	MELCOM 900II^[27]	7.23 hours	2,097,144
1982	Yoshiaki Tamura and Yasumasa Kanada	HITAC M-280H^[27]	2.9 hours	4,194,288
1982	Yoshiaki Tamura and Yasumasa Kanada	HITAC M-280H^[27]	6.86 hours	8,388,576
1983	Yasumasa Kanada, Sayaka Yoshino and Yoshiaki Tamura	HITAC M-280H^[27]	<30 hours	16,777,206
October 1983	Yasunori Ushiro and Yasumasa Kanada	HITAC S-810/20		10,013,395
October 1985	Bill Gosper	Symbolics 3670		17,526,200
January 1986	David H. Bailey	CRAY-2^[27]	28 hours	29,360,111
September 1986	Yasumasa Kanada, Yoshiaki Tamura	HITAC S-810/20^[27]	6.6 hours	33,554,414
October 1986	Yasumasa Kanada, Yoshiaki Tamura	HITAC S-810/20^[27]	23 hours	67,108,839
January 1987	Yasumasa Kanada, Yoshiaki Tamura, Yoshinobu Kubo and others	NEC SX-2^[27]	35.25 hours	134,214,700
January 1988	Yasumasa Kanada and Yoshiaki Tamura	HITAC S-820/80^[31]	5.95 hours	201,326,551
May 1989	Gregory V. Chudnovsky & David V. Chudnovsky	CRAY-2 & IBM 3090/VF		480,000,000
June 1989	Gregory V. Chudnovsky & David V. Chudnovsky	IBM 3090		535,339,270
July 1989	Yasumasa Kanada and Yoshiaki Tamura	HITAC S-820/80		536,870,898
August 1989	Gregory V. Chudnovsky & David V. Chudnovsky	IBM 3090		1,011,196,691
19 November 1989	Yasumasa Kanada and Yoshiaki Tamura	HITAC S-820/80^[32]		1,073,740,799
August 1991	Gregory V. Chudnovsky & David V. Chudnovsky	Homemade parallel computer (details unknown, not verified)^[33]^[32]		2,260,000,000
18 May 1994	Gregory V. Chudnovsky & David V. Chudnovsky	New homemade parallel computer (details unknown, not verified)		4,044,000,000
26 June 1995	Yasumasa Kanada and Daisuke Takahashi	HITAC S-3800/480 (dual CPU)^[34]		3,221,220,000
1995	Simon Plouffe	Finds a formula that allows the `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)^[35]^[36]	56.74 hours?	4,294,960,000
11 October 1995	Yasumasa Kanada and Daisuke Takahashi	HITAC S-3800/480 (dual CPU)^[37]^[36]	116.63 hours	6,442,450,000
6 July 1997	Yasumasa Kanada and Daisuke Takahashi	HITACHI SR2201 (1024 CPU)^[38]^[39]	29.05 hours	51,539,600,000
5 April 1999	Yasumasa Kanada and Daisuke Takahashi	HITACHI SR8000 (64 of 128 nodes)^[40]^[41]	32.9 hours	68,719,470,000
20 September 1999	Yasumasa Kanada and Daisuke Takahashi	HITACHI SR8000/MPP (128 nodes)^[42]^[43]	37.35 hours	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^[44]	600 hours	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^[45]	29.09 hours	2,576,980,377,524

Date	Who	Implementation	Time	Decimal places (world records in bold)
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^[46]^[47]	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	2,699,999,990,000 = 2.7×10¹² − 10⁴
2 August 2010	Shigeru Kondo^[48]	using y-cruncher^[49] 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.^[50]	90 days	5,000,000,000,000 = 5×10¹²
17 October 2011	Shigeru Kondo^[51]	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	10,000,000,000,050 = 10¹³ + 50
28 December 2013	Shigeru Kondo^[52]	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	12,100,000,000,050 = 1.21×10¹³ + 50
8 October 2014	Sandon Nash Van Ness "houkouonchi"^[53]	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	13,300,000,000,000 = 1.33×10¹³
11 November 2016	Peter Trueb^[54]^[53]	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^[55]	105 days	22,459,157,718,361 $= ⌊ π e \times 1012 ⌋$
14 March 2019	Emma Haruka Iwao^[56]	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	31,415,926,535,897 $= ⌊ π \times 1013 ⌋$
29 January 2020	Timothy Mullican^[57]^[58]	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	50,000,000,000,000 = 5×10¹³
14 August 2021	Team DAViS of the University of Applied Sciences of the Grisons^[59]^[60]	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	62,831,853,071,796 $= ⌈ 2 π \times 1013 ⌉$
21 March 2022	Emma Haruka Iwao^[61]^[62]	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	100,000,000,000,000 = 10¹⁴
18 April 2023	Jordan Ranous^[63]^[64]	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	100,000,000,000,000 = 10¹⁴
14 March 2024	Jordan Ranous, Kevin O’Brien and Brian Beeler^[65]^[66]	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	105,000,000,000,000 = 1.05×10¹⁴
28 June 2024	Jordan Ranous, Kevin O’Brien and Brian Beeler^[67]^[68]	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	202,112,290,000,000 = 2.0211229×10¹⁴
2 April 2025	Linus Media Group, Kioxia^[69]^[70]	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	300,000,000,000,000 = 3×10¹⁴

Chronology of computation of π

Before 1400

1400–1949

1949–2009

2009–present

See also

References

External links

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