Method & limits

Takeaway

The 1969, 1973 and 1986 values were transcribed by hand from page images of the published tables, later editions from NIST's tables; every value used was checked against a separately typeset version.
The checks found three rows of NIST's archived 2002 ASCII table that differ from the published report; the published values are used.
Editions are not independent and the 2022 values are not the true values; every number should be read with both in mind.

Uncertainty — the width, expressed as a standard deviation, within which a measured value may differ from the true value; the length of the ±1σ error bars in the plots. Unlike the error, the actual difference from the true value, the uncertainty is an estimate of how large that difference may be. It is the standard term in metrology (ISO/IEC Guide 98-3, the Guide to the Expression of Uncertainty in Measurement). What this site measures is whether that estimated width covered the actual moves between editions.

Edition — one set of recommended values published by the CODATA Task Group on Fundamental Constants after a least-squares adjustment of all the measurements and theoretical calculations available at the time. An edition is named after the closing year of its data (the 2022 edition uses data to the end of 2022 and was published in 2024). After the 1973 and 1986 editions, a new edition has appeared every four years since 1998. The 1969 edition is the pre-CODATA adjustment by Taylor, Parker and Langenberg, included for comparison. With each new edition the values and uncertainties of the same constants change; this site counts those changes.

Data

CODATA recommended values of the fundamental physical constants, editions 1973, 1986, 1998, 2002, 2006, 2010, 2014, 2018 and 2022, taken from the tables NIST publishes for each edition: NIST's ASCII tables from 1998 on, and the published tables for 1973 (Cohen & Taylor, J. Phys. Chem. Ref. Data 2, 663) and 1986 (Cohen & Taylor, J. Res. Natl. Bur. Stand. 92(2), 1987). One pre-CODATA adjustment is included: B. N. Taylor, W. H. Parker and D. N. Langenberg (1969), Rev. Mod. Phys. 41, 375, table XXXII, which NIST provides alongside the CODATA archive for historical reference.

1998–2022: NIST ASCII tables, parsed. 1998–2006 use concise notation, value(uncertainty), the digits in parentheses referring to the last digits; from 2010 value and uncertainty are in separate columns. Values ending in “...” and “(exact)” are exact.
1969, 1973, 1986: the quantities used here were transcribed by hand from page images of the published tables. All 66 values (63 measured, 3 exact) were compared automatically with the PDF text layer: 64 are identical, and the other two are OCR errors in the text layer, the image reading being correct. These editions state their uncertainties as standard deviations (1969: heading of table XXXII; 1973: table 33.1, note a; 1986: endnote 3).
All 213 rows used from 1998–2022 were checked against NIST's separately typeset “all values” PDF tables; a random sample of 10 rows per edition was also compared with the same PDFs.

Corrections to the sources

The archived 2002 ASCII table gives the Boltzmann constant as 1.380 6504(24)×10⁻²³; the 2002 PDF table and the published report (Rev. Mod. Phys. 77, 1) give 1.380 6505(24)×10⁻²³. The published value is used. Two other rows of the same file (electron magnetic moment, proton charge-to-mass quotient) differ from the publication in the last digit and were corrected too; neither enters the statistics.
The 1998–2006 ASCII tables have no elementary-charge row; the row for the electron volt in joules carries the same number and is used instead.
The 1998 ASCII row for the vacuum magnetic permeability lacks its exponent; the exact value 4π×10⁻⁷ was restored.

Choice of constants

The 17 core constants that form every denominator were chosen so that none is an exact function of the others. Before 2019, e = √(2αh/(μ₀c)) and mₑ = 2R∞h/(cα²); with α, h and R∞ in, e and mₑ are out. The Avogadro constant is tied to h through the molar Planck constant and is out. The relative atomic masses of the electron, proton, neutron, deuteron and alpha particle are in, and their ratio mₚ/mₑ is out. Quantities CODATA adopts from the PDG (tau mass, Fermi coupling constant, weak mixing angle) are not used. The speed of light was measured in the 1969 and 1973 editions, so in those two editions the relations above involve c as a further measured quantity; with only two measured editions it is not a core constant. μ₀ and M_u were exact up to 2014.

The 17 were chosen at the design stage. Other quantities meet the same rule (no exact relation, measured in at least four editions, not adopted from the PDG) but were not included: the helion and triton relative atomic masses, the deuteron magnetic moment, the silicon lattice spacing and others. The M2 and M3 pages give, as a sensitivity check, the values with the first three added (20 constants; sens_candidates.csv). The absence of exact relations does not make the constants statistically independent.

Statistics

Intervals for the rates (M2, M3) and for M4: cluster bootstrap resampling whole constants, 10,000 resamples (2,000 for M4), seed 2026, 95% percentile intervals. M1 intervals are t(n−2) intervals of the regression slope.
M4 is fitted without the pairs whose printed value did not change (z = 0); with them, the likelihood of a zero-centered Student-t is unbounded as the scale goes to zero and no maximum-likelihood estimate exists.
Edition year is the year in the edition's name (data cut-off); the 1998 edition was published in 2000.
Editions in which a constant is exact are left out of its M1–M4 calculations.

Limits

Consecutive editions share experimental data and are not independent; sharing pulls the moves toward zero.
Recent adjustments expand the uncertainties of mutually inconsistent input data (expansion factors), so recommended uncertainties already contain such judgments.
The 2022 values are not the true values.
Korean names: the speed of light in vacuum, Planck constant, elementary charge, Boltzmann constant and Avogadro constant follow Table 1 of the Enforcement Decree of the Korean Framework Act on National Standards; the other Korean names follow common usage and have not been checked against the Korean Physical Society glossary.

Reproduction

Every table is made by src/ in the repository: fetch_raw.py (download and hash the source files) → parse_codata.py (parse, correct, map) → handcheck.py (checks) → metrics.py (metrics) → build_site.py (site).