Taken from "The Fundamental Physical Constants"

by E. Richard Cohen and Barry N. Taylor,

Physics Today, August 1997

Recommended values for the physical constants based on the 1986 adjustment 
Quantity Symbol Value Error units Relative uncertainty (ppm)
Universal constants          
Speed of light in vacuum c 299792458   m s-1  exact
Permeability of vacuum m0  1.26E-06   N A-2  exact
Permittivity of vacuum e0  8.85E-12   F m-1  exact
Newtonian constant of gravitation G 6.67259E-11 8.5E-15 m3 kg-1 s-2  128
Planck constant h 6.6260755E-34 400.0E-42 J s 0.60
Planck constant in eV h 4.1356692E-15 1.2E-21 eV s 0.30
Planck constant over 2p  hbar 1.05457266E-34 63.0E-42 J s 0.60
Planck constant over 2p in eV  hbar 6.5821220E-16 200.0E-24 eV s 0.30
Planck mass ((hbar c)/G)0.5 mP  2.17671E-08 1.4E-12 kg 64
Planck length (hbar / (mP c)) lP  1.61605E-35 1.0E-39 m 64
Planck time (lP / c) tP  5.39056E-44 3.4E-48 s 64
Electromagnetic constants          
Elementary charge 1.60217733E-19 49.0E-27 C 0.30
Elementary charge e/h 2.41798836E+14 72.0E+6 A J-1  0.30
Magnetic flux quantum F0  2.06783461E-15 610.0E-24 Wb 0.30
Josephson frequency-voltage quotient 2e/h 4.8359767E+14 140.0E+6 Hz V-1  0.30
Quantized Hall conductance e2/h 3.87404614E-05 1.7E-12 S 0.045
Quantized Hall resistance RH  25812.8056 0.0012 W 0.045
Bohr magneton (e hbar) / (2 me) mB  9.2740154E-24 3.1E-30 J T-1  0.34
Bohr magneton in eV   5.78838263E-05 5.2E-12 eV T-1  0.089
Bohr magneton in hertz   1.39962418E+10 4.2E+3 Hz T-1  0.30
Bohr magneton in wavenumbers   46.686437 0.000014 m-1 T-1  0.30
Bohr magneton in kelvins   6.7170990E-01 5.7E-6 K T-1  8.5
Nuclear magneton (e hbar) / (2 mp) mN  5.0507866E-27 1.7E-33 J T-1  0.34
Nuclear magneton in eV   3.15245166E-08 2.8E-15 eV T-1  0.089
Nuclear magneton in hertz   7.6225914E+00 2.3E-6 MHz T-1  0.30
Nuclear magneton in wavenumbers   2.54262281E-02 7.7E-9 m-1 T-1  0.30
Nuclear magneton in kelvins   3.658246E-04 3.1E-9 K T-1  8.5
Atomic constants          
Fine-structure constant, m0ce2/2h a 7.29735308E-03 330.0E-12   0.045
inverse fine-structure constant a-1  137.0359895 0.0000061   0.045
Rydberg constant (meca2/2h)  Rinf  10973731.534 0.013 m-1  0.0012
Rydberg constant in hertz   3.2898419499E+15 3.9E+6 Hz 0.0012
Rydberg constant in joules   2.1798741E-18 1.3E-24 J 0.60
Rydberg constant in eV   13.6056981 0.0000040 eV 0.30
Bohr radius (a/4pRinf)  a0  5.29177249E-11 2.4E-18 m 0.045
Hartree energy (e2/4pe0a0)  Eh  4.3597482E-18 2.6E-24 J 0.60
Hartree energy in eV   27.2113961 0.0000081 eV 0.30
Quantum of circulation h/2me  3.63694807E-04 33.0E-12 m2 s-1  0.089
  h/me  7.27389614E-04 65.0E-12 m2 s-1  0.089
Mass me  9.1093897E-31 540.0E-39 kg 0.59
Mass in atomic mass units   5.48579903E-04 13.0E-12 u 0.023
Mass in eV   5.10999060E-01 150.0E-9 eV 0.30
Electron-muon mass ratio me/mm  4.83633218E-03 710.0E-12   0.15
Electron-proton mass ratio me/mp  5.44617013E-04 11.0E-12   0.020
Electron-deuteron mass ratio me/md  2.72443707E-04 6.0E-12   0.020
Electron-a-particle mass ratio me/ma  1.37093354E-04 3.0E-12   0.021
Specific charge e/me  1.75881962E+11 53.0E+3 C kg-1  0.30
Molar mass M(e) 5.48579903E-07 13.0E-15 kg mol-1  0.023
Compton wavelength (h/mec) lC  -2.42631058E-12 220.0E-21 m 0.089
Compton wavelength /2p  lC/2p  3.86159323E-13 35.0E-21 m 0.089
Classical radius, a2a0  re  2.81794092E-15 380.0E-24 m 0.13
Thomson cross section (8p/3)re2  se  6.65246160E-29 18.0E-36 m 0.27
Magnetic moment me  9.2847701E-24 3.1E-30 J T-1  0.34
Magnetic moment in Bohr magnetons me/mB  1.001159652193 0.000000000010   1E-05
Magnetic moment in Nuclear magnetons me/mN  1838.282000 0.000037   0.020
Magnetic moment anomaly (me/mB - 1)  ae  1.159652193E-03 10.0E-12   0.0086
g-factor (2 (1 + ae)) ge 2.002319304386 0.000000000020   1E-05
Electron-muon magnetic moment ratio me/mm  206.766967 0.000030   0.15
Electron-proton magnetic moment ratio me/mp  658.210688 0.000007   0.010
Mass mm  1.8835327E-28 110.0E-36 kg 0.61
Mass in atomic mass units   0.113428913 0.000000017 u 0.15
Mass in eV   105.658389 0.000034 MeV 0.32
Muon-electron mass ratio mm/me  206.768262 0.000030   0.15
Molar mass M(m)  1.13428913E-04 17.0E-12 kg mol-1 0.015
Magnetic moment mm  4.4904514E-26 15.0E-33 J T-1 0.33
Magnetic moment in Bohr magnetons mm/mB  4.84197097E+00 710.0E-9   0.15
Magnetic moment in Nuclear magnetons mm/mN  8.8905981 0.0000013   0.15
Magnetic moment anomaly (mm/((e hbar)/2mm) - 1)  am  1.1659230E-03 8.4E-9    
g-factor (2 (1 + am))  gm  2.002331846 0.000000017   0.0084
Muon-proton magnetic moment ratio mm/mp  3.18334547 0.00000047   0.15
Mass mp  1.67E-27 1.0E-33 kg 0.59
Mass in atomic mass units   1.007276470 0.000000012 u 0.012
Mass in eV   938.27231 0.00028 MeV 0.30
Proton-electron mass ratio mp/me  1836.152701 0.000037   0.02
Proton-muon mass ratio mp/mm  8.8802444 0.0000013   0.15
Specific charge e/mp  9.5788309E+07 29.0E+0 C kg-1  0.30
Molar mass M(p) 1.007267470E-03 12.0E-12 kg mol-1  0.012
Compton wavelength lC,p  1.32141002E-15 120.0E-24 m 0.089
Compton wavelength over 2p  lbarC,p  2.10308937E-16 19.0E-24 m 0.089
Magnetic moment mp  1.41060761E-26 4.7E-33 J T-1  0.34
Magnetic moment in Bohr magnetons mp/mB  1.521032202E-03 15.0E-12   0.010
Magnetic moment in Nuclear magnetons mp/mN  2.792847386 0.000000063   0.023
Diamagnetic shielding correction for protons (H2O, spherical sample, 25C) 1-mp'/mp  sH2O  2.5689E-05 15.0E-9    
Shielded proton moment (H2O,spherical sample, 25C) mp'  1.41057138E-26 4.7E-33 J T-1  0.34
Shielded proton moment in Bohr magnetons mp'/mB  1.520993129E-03 17.0E-12   0.011
Shielded proton moment in Nuclear magnetons mp'/mN  2.792775642 64.0E-9   0.023
Gyromagnetic ratio gp  267522128 81 s-1 T-1  0.30
Gyromagnetic ratio over 2p  gp/2p  42.577469 0.000013 MHz T-1  0.30
Gyromagnetic ratio (uncorrected, H2O,spherical sample,25C) gp'  267515255 81 s-1 T-1  0.30
Gyromagnetic ratio over 2p(uncorrected, H2O,spherical sample,25C)  gp'/2p  42.576375 0.000013 MHz T-1  0.30
Mass mn  1.6749286E-27 1.0E-33 kg 0.59
Mass in atomic mass units   1.008664904 0.000000014 u 0.014
Mass in eV   939.56563 0.00028 MeV 0.30
Neutron-electron mass ratio mn/me  1838.683662 0.000040   0.022
Neutron-proton mass ratio mn/mp  1.001378404 0.000000009   0.009
Molar mass M(n) 1.008664904E-03 14.0E-12 kg mol-1  0.014
Compton wavelength lC,n  1.31959110E-15 120.0E-24 m 0.089
Compton wavelength over 2p  lbarC,n  2.10019445E-16 19.0E-24 m 0.089
Magnetic moment (scalar magnitude) mn  9.66237070E-27 4.0E-33 J T-1  0.41
Magnetic moment in Bohr magnetons mn/mB  1.04187563E-03 250.0E-12   0.24
Magnetic moment in Nuclear magnetons mn/mN  1.91304275 0.00000045   0.24
Neutron-electron magnetic moment ratio mn/me  1.04066882E-03 250.0E-12   0.24
Neutron-proton magnetic moment ratio mn/mp  0.68497934 0.00000016   0.24
Mass md  3.3483586E-27 2.0E-33 kg 0.59
Mass in atomic mass units   2.013553214 0.000000024 u 0.012
Mass in eV   1875.61339 0.00057 MeV 0.30
Deuteron-electron mass ratio md/me  3670.483014 75.0E-6   0.020
Deuteron-proton mass ratio md/mp  1.999007496 6.0E-9   0.003
Molar mass M(d) 2.013553214E-03 24.0E-12 kg mol-1  0.012
Magnetic moment md  4.3307375E-27 1.5E-33 J T-1  0.34
Magnetic moment in Bohr magnetons md/mB  4.669754479E-04 9.1E-12   0.019
Magnetic moment in Nuclear magnetons md/mN  0.857438230 0.000000024   0.028
Deuteron-electron magnetic moment ratio md/me  4.66434546E-04 9.1E-12   0.019
Deuteron-proton magnetic moment ratio md/mp  0.307012204 5.1E-9   0.017
Physicochemical constants          
Avogadro constant NA,L 6.0221367E+23 360.0E+15 mol-1  0.59
Atomic mass constant, m(12C)/12 mu  1.6605402E-27 1.0E-33 kg 0.59
Atomic mass constant in eV   931.49432 0.00028 MeV 0.30
Faraday constant F 96485.309 29.0E-3 C mol-1  0.30
Molar Planck constant NAh 3.99031323E-10 36.0E-18 J s mol-1  0.089
  NAhc 0.11962658 11.0E-9 J m mol-1  0.089
Molar gas constant R 8.314510 0.000070 J mol-1 K-1  8.4
Boltzmann constant k 1.380658E-23 120.0E-30 J K-1  8.4
Boltzmann constant in eV   8.617385E-05 730.0E-12 eV K-1  8.4
Boltzmann constant in hertz   2.083674E+10 180.0E+3 Hz K-1  8.4
Boltzmann constant in wavenumbers   69.50387 0.00059 m-1 K-1  8.4
Molar volume (ideal gas),RT/p (at 273.15K, 101325 Pa) Vm  22414.10 0.19 cm3 mol-1  8.4
Loschmidt constant NA/Vm  n0  2.686763E+25 230.0E+18 m-3  8.5
Stefan-Boltzmann constant (p2/60)k4/hbar3c2  5.67051E-08 1.9E-12 W m-2 K-4  34
First radiation constant 2phc2  c1  3.7417749E-16 220.0E-24 W m2  0.60
Second radiation constant hc/k c2  0.01438769 120.0E-9 m K 8.4
Wien displacement law constant b 2.897756E-03 24.0E-9 m K 8.4
Conversion factors and units          
Electron volt eV 1.60217733E-19 49.0E-27 J 0.30
Atomic mass unit (unified) u 1.6605402E-27 1.0E-33 kg 0.59
Standard atmosphere atm 101325   Pa exact
Standard acceleration of gravity gn  9.80665   m s-2  exact
As-maintained electrical units          
BIPM-maintained ohm,W69-BI as of 1 Jan 1985  WBI85  0.999998437 0.000000050 W 0.050
drift rate of W69-BI  dW69-BI/dt  -0.0566 0.0015 mW / yr   
BIPM-maintained volt, 483594 GHz(h/2e) V76-BI  0.99999241 0.00000030 V 0.30
BIPM-maintained ampere, ABIPM=V76-BI/W69-BI  ABI85  0.99999397 0.00000030 A 0.30
X-ray standards          
Cu x-unit:l(CuKa1)=1537.400 xu  xu(CuKa1)  1.00207789E-13 70.0E-21 m 0.70
Mo x-unit:l(MoKa1)=707.831 xu  xu(MoKa1)  1.00209938E-13 45.0E-21 m 0.45
A *:=l(WKa1)=0.2090100A* A* 1.00001481E-10 92.0E-18 m 0.92
Lattice spacing of Si(in vacuum, 22.5C) a 0.54310196 0.00000011 nm 0.21
d220=a/(8)0.5  d220  0.192015540 0.000000040 nm 0.21
Molar volume of Si, M(Si)/r(Si)=NAa3/8 Vm(Si) 12.0588179 0.0000089 cm3 mol-1  0.74

Last Updated on 9/9/97
By Emil Hallin
Email: hallin@pnc.aps.anl.gov