# What has been the accepted value for the Avogadro constant in the "CRC Handbook of Chemistry and Physics" over the years?

Some questions about the constant made me curious as to exactly how much the accepted value has changed over the years. I am pretty sure that I learned a rounded value of $$6.023\times10^{23}$$ about 1970 which would have been around the 50th edition. I know that sometime after that the accepted value rounded to 4 significant figures was $$6.022\times10^{23}$$. Of course since 2019 the accepted value has been fixed at exactly $$6.02214076\times10^{23}$$

It would seem that the CRC handbook is a reasonable source for the accepted value of the constant since it has been updated almost yearly.

Please update the table in the answer in the community wiki page with other values

• You can find the value in past CODATA publications. This is probably the most reliable and easily found historical record. Dec 31 '20 at 3:48
• See Table 1 in Becker, P. History and Progress in the Accurate Determination of the Avogadro Constant. Rep. Prog. Phys. 2001, 64 (12), 1945–2008. DOI: 10.1088/0034-4885/64/12/206. It covers year up to the year 2001 and is going to save a lot of time. Dec 31 '20 at 4:33

I dislike offsite image links since they disappear over time. So below is Table 1 from andselisk's comment on the question.

The paper itself is behind a firewall and I can't see it.

See Table 1 in Becker, P. History and Progress in the Accurate Determination of the Avogadro Constant. Rep. Prog. Phys. 2001, 64 (12), 1945–2008. DOI: 10.1088/0034-4885/64/12/206. It covers year up to the year 2001 and is going to save a lot of time. – andselisk

• Couple of things about the table. (1) It shows individual values determined by experimenters with improving exactness. The CRC data and CODATA show weighted values. (2) the basis for the AMU changed in 1961 from oxygen-16 to carbon-12. I don't think that the table corrects for that. (3) I'm assuming that $\mathrm{u_{rel}}$ is an absolute value not a % value. // The particular article is behind a firewall that I can see.
– MaxW
Dec 31 '20 at 8:48

Please edit the table to include missing data

Avogadro constant in the "CRC Handbook of Chemistry and Physics"

Edition Years(s) page value CODATA?
1 (Link) 1913 -- Not Given --
2 1914 No
3 (Link) 1914 123 6.42(31) × 1023 No
4 1915 6.42(31) × 1023 (note) No
5 1917 6.42(31) × 1023 (note) No
6 (Link) 1917 286 6.42(31) × 1023 No
7 (Link) 1918 369 6.42(31) × 1023 No
8 (Link) 1920 523 6.06 × 1023 No
9 (Link) 1922 605 6.06 × 1023 No
10 (Link) 1924 678 6.06 × 1023 No
11 (Link) 1926 784 6.06 × 1023 No
12 1927 884 6.06 × 1023 No
13 1928 986 6.06 × 1023 No
14 1929 1151 6.06 × 1023 No
15 1930 No
16 1931 1244 6.064(6) × 1023 No
17 1932 6.064(6) × 1023 (Note) No
18 1933 1488 6.064(6) × 1023 No
19 1934 1890 6.064(6) × 1023 No
20 1935 6.064(6) × 1023 (Note) No
21 1936 1980 6.064(6) × 1023 No
22 1937 2026 6.064(6) × 1023 No
23 1939 2177 6.064(6) × 1023 No
24 1940 2519 6.064(6) × 1023 No
25 1941 2454 6.064(6) × 1023 No
26 1942 2403 6.0228(11) × 1023 No
27 1943 2499 6.0228(11) × 1023 No
28 1944 2517 6.0228(11) × 1023 No
29 1945 2585 6.0228(11) × 1023 No
30 (Link) 1946 2631 6.0228(11) × 1023 No
30(Rev) 1947 2631 6.0228(11) × 1023 No
31 (Link) 1949 2683 6.0228(11) × 1023 No
32 1950 2811 6.0228(11) × 1023 No
33 1951 2833 6.0228(11) × 1023 No
34 1952 No
35 1953 3092 6.0228(11) × 1023 No
36 1954 3104 6.025 44(11) × 1023 No
37 1955 3080 6.0228(11) × 1023 No
38 1956 3136 6.0247(2) × 1023 No
39 (Link) 1957 3134 6.0228(11) × 1023 No
40 1958 3376 6.022 8(11) × 1023 No
41 1959 3301 6.022 8(11) × 1023 No
42 1960 3399 6.022 8(11) × 1023 No
43 1961 No
44 1962 No
45 1964 F-95 6.022 57(9) × 1023 No
46 1965 No
47 1966-1967 F-138 6.022 52(28) × 1023 No
48 1967-1968 No
49 1968–1969 F-167 6.022 52(28) × 1023 No
50 1969-1970 F-168 6.022 52(28) × 1023 No
51 1970-1971
52 (Link) 1971-1972 F-189 6.022 169(40) × 1023 No
53 1972-1973 F195 6.022 169(40) × 1023
54 1973-1974
55 (Link) 1974-1975 F-222 6.022 169(40) × 1023 No
56 1975–1976 6.022 045(31) × 1023
57 (Link) 1976–1977 F-242 6.022 045(31) × 1023 Yes, bulletin #11
58 1977-1978 F-242 6.022 045(31) × 1023 Yes, bulletin #11
59 1978-1979 F-250 6.022 045(31) × 1023 Yes, bulletin #11
60 1979-1980 F-244 6.022 045(31) × 1023 Yes, bulletin #11
61 1980-1981
62 1981-1982
63 1982-1983
64 (Link) 1983-1984 F-198 6.022 045(31) × 1023 Yes
65 (Link) 1984-1985 F-192 6.022 045(31) × 1023 Yes
66 1985-1986
67 1986-1987
68 1987-1988
69 1988-1989
70 1989-1990 F-215 & F-217 6.022 1367(36) × 1023 Yes, 1986
71 (Link) 1990-1991 1-1 6.022 1367(36) × 1023 Yes, 1986
72 (Link) 1991-1992 1-1 6.022 1367(36) × 1023 Yes, 1986
73 1992-1993
74 1993-1994
75 1994-1995
76 1995-1996
77 1996-1997
78 1997-1998
79 1998-1999
80 1999-2000
81 Link 2000-2001 1-7 6.022 141 99(47) × 1023 Yes, 1998
82 2001–2002 1-7 6.022 141 99(47) × 1023 Yes, 1998
83 2002-2003 6.022 141 99(47) × 1023 (Note) (Yes, 1998)
84 2003–2004 1-7 6.022 141 99(47) × 1023 Yes, 1998
85 2004-2005 1-2 6.022 141 5(10) × 1023 Yes, 2002
86 2005–2006 1-5 6.022 141 5(10) × 1023 Yes, 2002
87 2006–2007 1-5 6.022 141 5(10) × 1023 Yes, 2002
88 2007–2008 1-1 6.022 141 5(10) × 1023 Yes, 2002
89 (Link) 2008-2009 1-1 6.022 141 79(30) × 1023 Yes, 2006
90 2009-2010 1-1 6.022 141 79(30) × 1023 Yes, 2006
91 2010-2011 6.022 141 79(30) × 1023 (Note) (Yes, 2006)
92 2011–2012 1-1 6.022 141 79(30) × 1023 Yes, 2006
93 2012–2013 1-2 6.022 141 29(27) × 1023 Yes, 2010
94 2013–2014 1-2 6.022 141 29(27) × 1023 Yes, 2010
95 2014–2015 1-2 6.022 141 29(27) × 1023 Yes, 2010
96 2015–2016 1-2 6.022 141 29(27) × 1023 Yes, 2010
97 (Link) 2016–2017 1-1 6.022 140 857(74) × 1023 Yes, 2014
98 2017-2018 6.022 140 857(74) × 1023 (Note) (Yes, 2014)
99 2019-2020 6.022 140 857(74) × 1023 (Note) (Yes, 2014)
100 2020-2021 6.022 140 857(74) × 1023 (Note) (Yes, 2014)
>101? 2021-2022 ? 6.022 140 76 × 1023 (exact) Yes, 2018

NOTES FOR TABLE

• Early editions are actually titled "Handbook of Chemistry and Physics". Not sure when the title formally switched to the "CRC Handbook of Chemistry and Physics".

• Some early editions are available online at HathiTrust. The "Limited search" editions can only be searched for a hit. There is no page number or preview for the found text.

• The first edition that I found to hit on the phrase "Avogadro number" was the 16th edition. It would seem to that phrase until at least the 31st edition.

• By 84th edition the phrase was changed to "Avogadro constant"

• A CODATA newsletter had a list of publications which listed: No. 11 (Dec 1973) 8 pp, Recommended Consistent Values of the Fundamental Physical Constants, 1973 (Report of the CODATA Task Group on Fundamental Constants, August 1973).

1st Edition

The link is to the facsimile edition.

3rd edition (c)1914

This version is online at HathiTrust. An old edit of the Wikipedia article CRC Handbook of Chemistry and Physics indicates the third edition has 322 pages.

3rd thru 12th Editions

In at least the 3rd through 12th editions of the CRC Handbook in have a "Heat" category in the Table of Contents where there is an entry for "Number of molecules in a molecule-gram" which points to a table with three values. Note also that none of these three values are in Becker's paper. (Only seen 1st, 3rd, and 6th through 12th editions)

My calculation is that the mean = $$6.42(31)\times 10^{23}$$

Millikan 1910 would seem to be from rounding $$6.18^\times10^{23}$$ value in Phil.Mag. Feb,1910,209

4th and 5th edition See likely that these editions are same as 3rd and 6th.

8th through ? edition

In at least the 8th through 12th editions of the CRC Handbook the Table of Contents contains a category "Miscellaneous Tables" which has a link to "Atomic and Molecular Constants" which references the "Smithsonian Tables" and gives a value of $$6.06\times10^{23}$$ for the "Number of molecules in a gram molecule".

The reference to the Smithsonian Physical Tablesdoesn't give any more indication as to which tables those are. This seems to be the 2nd reprint of 6th rev. ed. Prepared by Frederick E. Fowle. in 1916

13th through and 30th(?) Editions

There is another version of the table Number of Molecules in a Gram-Molecule which has four values.

• In the 13th, 14th, 16th, 18th, 19th, 23rd, 25th, 26th and 27th editions the table is listed in the table of contents in the Heat section.

• In the 29th, 30th and 30th (rev) editions the table is listed in the table of contents in the Miscellaneous section.

• The table is gone in the 31st edition (and presumably in any subsequent editions).

16th, 18th, 19th, 21st, 23rd, 24th, 25th and 27th Editions

These editions have identical entries, listing it as "Avogadro's number" in a table named "Probable Values of the General Physical Constants" which is in the "Miscellaneous Tables" section of the Table of Contents. The tables cite Raymond T. Birge: The Physical Review Supplement, Vol. 1, No. 1, July, 1929, as the source for the entire "Probable Values of the General Physical Constants" table. Note however that the value given here doesn't match the one attributed to R T Birge in 1929 in Becker, P. "History and Progress in the Accurate Determination of the Avogadro Constants"

17th, 19th, 20th, and 22nd Editions

These editions are book ended by editions which have the same value. These editions are assumed to have this value too.

28th, 29th, 30th, 30th (rev), 31st, 32nd and 35th Editions

The 30th revised edition has "Revised" above "Thirtieth Edition" on the title page

Listed as "Avogadro number (chemical scale)" in "New Table of Values of the General Physical Constants." The table is listed in the "Miscellaneous" section of the Table of Contents.

Cites: Raymond T. Birge: The Physical Review Supplement, Vol. 13, 233, 1941 as the source for the entire table. (This is the value listed for R T Birge in 1941 in Becker, P. "History and Progress in the Accurate Determination of the Avogadro Constants". With the quoted error the extra 3 is unnecessary.)

The reference is better known as: "A New Table of Values of the General Physical Constants (as of August, 1941)", Raymond T. Birge Rev. Mod. Phys. 13, 233 (1941) DOI: 10.1103/RevModPhys.13.233

36th edition

Value found in table of "Atomic Constants" which references James W. M. DuMond and E. Richard Cohen, Physical Review 82:555, 1951

38th edition

Found in table of "Atomic Constants" which references "A survey of Atomic Constants (1955) by J. A. Bearden and John H. Thomsen, The John Hopkins University"

40th, 41st and 42nd Editions

This cites Raymond T. Birge: Reviews of Modern Physics 13, 233, 1941. This matches the value attributed to Birge in the same year by Becker. (Because of the error the extra 3 is superfluous so I left it off.)

45th Edition

"Avogadro's Number" in table "Values of the General Physical Constants" which simply states "Furnished by R. D. Huntoon."

50th Edition

Cites source for data in Table named "Physical Constants" as "National Bureau of Standards Technical News Bulletin, October 1963."

52th, 53rd and 55th editions

References Rev. Mod. Phys 41, 375 (1969)

56th edition

From user theorist's comment on this post.

57th, 58th, 59th, and 60th Editions

Avogadro Constant in table Recommended Consistent Values of the Fundamental Physical Constants.

Table cites: Data from CODATA Bulletin No. 11, ICSU CODATA Central Office, CODATA Secretariat: 19 Westendstrasse, 6 Frankfurt/Main, German Federal Republic (copies of this bulletin are available at no cost from this office).

64th and 65th editions

Avogadro Constant in table titled Recommended Consistent Values of the Fundamental Physical Constants.

Table cites: Data from CODATA Bulletin No. 11, ICSU CODATA Central Office, CODATA Secretariat: 51 Boulevard de Montmorency, 75016 Paris, France (copies of this bulletin are available at no cost from this office).

70th through 72nd Editions

Cites 1986 CODATA values as published in E. Richard Cohen and Barry N. Taylor, Journal of Research of the National Bureau of Standards, 92, 85, 1987.

83rd edition

Based on pattern of CODATA being used for 4 years.

84th edition

calculated page number from on-line pdf file

85th edition

Internet edition

85th edition

Got value via "Look Inside" at Amazon

90th edition

Based on the 2006 CODATA recommended values

91st edition

Surely same as 90th and 92nd data. Pattern of using CODATA for four Years.

92nd edition

From print copy (MaxW)

98th through 100th Editions

Based on pattern of CODATA being used for four years.

• The 56th edition (1975-1976) has it as 6.022045(31) x 10^23. Since the uncertainty gives the estimated value an upper bound of 6.022076 x 10^23, it seems they underestimated the uncertainty. The uncertainty they'd need to encompass the value at the redefiniton is 6.022045(97) x 10^23. Dec 31 '20 at 2:26
• I chose the CRC handbook because it has been published for about as long as scientists have been able to determine a reasonably accurate value, and it is updated yearly. Given the CODATA values it seems worth noting CRC's reliance on that data, so added a column to track that.
– MaxW
Jan 2 at 16:50
• @theorist - Typically the error number is the standard deviation. So (6.022140 - 6.022045)/0.000031 = 3.06 standard deviations which doesn't seem horrible.
– MaxW
Jan 4 at 21:30
• 3.06 stand deviations means that, according to their predicted uncertainty, there was only a 1:500 chance that the actual value would be that far from their predicted value. If you subsequently asked those who provided that value about this, I think they themselves would acknowledge they significantly underestimated the uncertainty. Feb 13 at 21:59

The Committee on Data of the International Science Council (CODATA) was established as ICSU Committee on Data for Science and Technology in 1966.

Year(s) page value
1969 477 6.022 169(40) × 1023
1973 718 6.022045(31) × 1023
1986 6 6.022 136 7(36) × 1023
1998 6 6.022 141 99(47) × 1023
2002 6 6.022 141 5(10) × 1023
2006 7 6.022 141 79(30) × 1023
2010 5 6.022 141 29(27) × 1023
2014 5 6.022 140 857(74) × 1023
2018 5 6.022 140 76 × 1023 (exact)

NOTES FOR TABLE

2018 - exact by new definition of constant

• I wonder if it would be helpful to note that the definition of mole was standardized to a new definition in 1971: en.wikipedia.org/wiki/Avogadro_constant#SI_definition_of_1971
– Zhe
Dec 31 '20 at 13:29
• @Zhe - The values do need to be corrected. In 1961 the amu was based on 1/12 of a $\ce{^{12}C}$ atom, so 1 amu was $1.0\bar0$ g/mol. With the 2018 suggested values now accepted, the molar mass constant is now 0.999 999 999 65(30) g/mol. So if I figured this correctly the values from 1969 to 2014 need to be multiplied by 0.999 999 999 65.
– MaxW
Dec 31 '20 at 16:43
• @Zhe - pragmatically the 0.999 999 999 65 correction only changes the value if there are at least 9 decimal places in the value.
– MaxW
Dec 31 '20 at 17:27
• Oh, yes, practically, there's no difference, but it just felt weird to juxtapose values with (slightly) different meanings.
– Zhe
Dec 31 '20 at 17:52

Here are plots of the historical CODATA and CRC values for $$N_{\text {A}}$$ listed in MaxW's posts. Plots were made in Mathematica.

I've provided plots with successively later lower bounds for the dates, and correspondingly smaller $$N_{\text {A}}$$ ranges, so that the shrinking uncertainties in later years can be visualized.

N.B.: When the CRC value had a two-year range, I averaged the years (e.g., 1975-76 became 1975.5). When the CRC values were repeated in successive editions, I plotted only the earlier value.

The last three of the four CRC values shown each correspond to the CODATA value from 3–5 years past. This suprised me—especially with its emphasis on yearly updates, I would have thought the CRC would be kept more up-to-date than that. I wonder if this is generally the case for data in the CRC—that data updates stop a few years before the publication date, to give time for proofreading, typesetting, etc.

1998 CODATA => 2003–04 CRC

2002 CODATA => 2005 CRC

2006 CODATA => 2010 CRC