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Fundamental Physical Constants

July 2007

Table II |  Table IV |  Table VII |  Table VIII
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CODATA Recommended Values of the Fundamental Physical Constants—2006
Quantity Symbol Value Unit Relative standard uncertainty ur
UNIVERSAL
speed of light in vacuum c, c0 299 792 458 m s–1 (exact)
magnetic constant µ0 4π10−7 N A−2  
    =12.566 370 614 . . . ×10−7 N A−2 (exact)
electric constant 1/µ0c2 ϵ0 8.854 187 817 . . . ×10−12 F m−1 (exact)
characteristic impedance of vacuum √[µ0 /ϵ0]=µ0c Z0 376.730 313 461 . . . Ω (exact)
Newtonian constant of gravitation G 6.674 28(67)×10−11 m3 kg−1 s−2 1.0×10−4
  G/ℏc 6.708 81(67)×10−39 c 1.0×10−4
Planck constant ℎ 6.626 068 96(33)×10−34 J s 5.0×10−8
in eV s   4.135 667 33(10)×10−15 eV s 2.5×10−8
ℎ/2π ℏ 1.054 571 628(53)×10−34 J s 5.0×10−8
in eV s   6.582 118 99(16)×10−16 eV s 2.5×10−8
ℏc in MeV fm   197.326 9631(49) MeV fm 2.5×10−8
Planck mass (ℏc/G)1/2 mP 2.176 44(11)×10−8 kg 5.0×10−5
energy equivalent in GeV mPc2 1.220 892(61)×1019 GeV 5.0×10−5
k TP 1.416 785(71)×1032 K 5.0×10−5
Planck length ℏ/mPc=(ℏG/c3)1/2 lP 1.616 252(81)×10−35 m 5.0×10−5
Planck time lP/c=(ℏG/c5)1/2 tP 5.391 24(27)×10−44 s 5.0×10−5
ELECTROMAGNETIC
elementary charge e 1.602 176 487(40)×10−19 C 2.5×10−8
  e/ℎ 2.417 989 454(60)×1014 A J−1 2.5×10−8
magnetic flux quantum ℎ/2e Φ0 2.067 833 667(52)×10−15 Wb 2.5×10−8
conductance quantum 2e2/ℎ G0 7.748 091 7004(53)×10−5 S 6.8×10−10
inverse of conductance quantum G0−1 12 906.403 7787(88) Ω 6.8×10−10
Josephson constanta 2e/ℎ KJ 483 597.891(12)×109 Hz V−1 2.5×10−8
von Klitzing constantb ℎ/e2 = µ0c/2α RK 25 812.807 557(18) Ω 6.8×10−10
Bohr magneton eℏ/2me µB 927.400 915(23)×10−26 J T−1 2.5×10−8
in eV T−1   5.788 381 7555(79)×10−5 eV T−1 1.4×10−9
  µB/ℎ 13.996 246 04(35)×109 Hz T−1 2.5×10−8
  µB/hc 46.686 4515(12) m−1 T−1 2.5×10−8
  µB/k 0.671 7131(12) K T−1 1.7×10−6
nuclear magneton eℏ/2mp µN 5.050 783 24(13)×10−27 J T−1 2.5×10−8
in eV T−1   3.152 451 2326(45)×10−8 eV T−1 1.4×10−9
  µN/ℎ 7.622 593 84(19) MHz T−1 2.5×10−8
  µN/hc 2.542 623 616(64)×10−2 m−1 T−1 2.5×10−8
  µN/k 3.658 2637(64)×10−4 K T−1 1.7×10−6
ATOMIC AND NUCLEAR
General
fine-structure constant e2/4πϵ0ℏc α 7.297 352 5376(50)×10−3   6.8×10−10
inverse fine-structure constant α−1 137.035 999 679(94)   6.8×10−10
Rydberg constant α2mec/2ℎ R∞ 10 973 731.568 527(73) m−1 6.6×10−12
  R∞c 3.289 841 960 361(22)×1015 Hz 6.6×10−12
  R∞hc 2.179 871 97(11)×10−18 J 5.0×10−8
R∞hc in eV   13.605 691 93(34) eV 2.5×10−8
Bohr radius α/4πR∞ = 4πϵ0ℏ2/mee2 a0 0.529 177 208 59(36)×10−10 m 6.8×10−10
Hartree energy e2/4πϵ0a0 = 2R∞ℎc = α2mec2 Eh 4.359 743 94(22)×10−18 J 5.0×10−8
in eV   27.211 383 86(68) eV 2.5×10−8
quantum of circulation ℎ/2me 3.636 947 5199(50)×10−4 m2 s−1 1.4×10−9
  ℎ/me 7.273 895 040(10)×10−4 m2 s−1 1.4×10−9
Electroweak
Fermi coupling constantc GF /(ℏc)3 1.166 37(1)×10−5 GeV−2 8.6×10−6
weak mixing angled θW (on-shell scheme)        
sin2 θW = s2W × 1−(mW /mZ)2 sin2 θW 0.222 55(56)   2.5×10−3
Electron, e–
electron mass me 9.109 382 15(45)×10−31 kg 5.0×10−8
in u, me = Ar(e) u (electron rel. atomic mass times u)   5.485 799 0943(23)×10−4 u 4.2×10−10
energy equivalent me c2 8.187 104 38(41)×10-14 J 5.0×10−8
in MeV   0.510 998 910(13) MeV 2.5×10−8
electron–muon mass ratio me /mµ 4.836 331 71(12)×10−3   2.5×10−8
electron–tau mass ratio me /mτ 2.875 64(47)×10−4   1.6×10−4
electron–proton mass ratio me /mp 5.446 170 2177(24)×10−4   4.3×10−10
electron–neutron mass ratio me /mn 5.438 673 4459(33)×10−4   6.0×10−10
electron–deuteron mass ratio me /md 2.724 437 1093(12)×10−4   4.3×10−10
electron to alpha particle mass ratio me /mα 1.370 933 555 70(58)×10−4   4.2×10−10
electron charge to mass quotient −e/me −1.758 820 150(44)×1011 C kg−1 2.5×10−8
electron molar mass NA me M(e), Me 5.485 799 0943(23)×10−7 kg mol−1 4.2×10−10
Compton wavelength ℎ/mec λC 2.426 310 2175(33)×10−12 m 1.4×10−9
λC/2π=αa0=α2/4πR∞ ƛC 386.159 264 59(53)×10−15 m 1.4×10−9
classical electron radius α2a0 re 2.817 940 2894(58)×10−15 m 2.1×10−9
Thomson cross section (8π/3) re2 σe 0.665 245 8558(27)×10−28 m2 4.1×10−9
electron magnetic moment µe −928.476 377(23)×10−26 J T−1 2.5×10−8
to Bohr magneton ratio µe /µB −1.001 159 652 181 11(74)   7.4×10−13
to nuclear magneton ratio µe /µN −1838.281 970 92(80)   4.3×10−10
electron magnetic moment anomaly |µe|/µB−1 ae 1.159 652 181 11(74)×10−3   6.4×10−10
electron g-factor −2(1+ae) ge −2.002 319 304 3622(15)   7.4×10−13
electron–muon magnetic moment ratio µe /µµ 206.766 9877(52)   2.5×10−8
electron–proton magnetic moment ratio µe /µp −658.210 6848(54)   8.1×10−9
electron to shielded proton magnetic moment ratio        
(H2O, sphere, 25 °C) µe /µ´p −658.227 5971(72)   1.1×10−8
electron–neutron magnetic moment ratio µe /µn 960.920 50(23)   2.4×10−7
electron–deuteron magnetic moment ratio µe /µd −2143.923 498(18)   8.4×10−9
electron to shielded helion magnetic moment ratio        
(gas, sphere, 25 °C) µe /µ´h 864.058 257(10)   1.2×10−8
electron gyromagnetic ratio 2|µe|/ℏ γe 1.760 859 770(44)×1011 s−1 T−1 2.5×10−8
  γe /2π 28 024.953 64(70) MHz T−1 2.5×10−8
Muon, µ−
muon mass mµ 1.883 531 30(11)×10−28 kg 5.6×10−8
in u, mµ= Ar(µ) u (muon rel. atomic mass times u)   0.113 428 9256(29) u 2.5×10−8
energy equivalent mµc2 1.692 833 510(95)×10−11 J 5.6×10−8
in MeV   105.658 3668(38) MeV 3.6×10−8
muon–electron mass ratio mµ /me 206.768 2823(52)   2.5×10−8
muon–tau mass ratio mµ /mτ 5.945 92(97)×10−2   1.6×10−4
muon–proton mass ratio mµ /mp 0.112 609 5261(29)   2.5×10−8
muon–neutron mass ratio mµ /mn 0.112 454 5167(29)   2.5×10−8
muon molar mass NAmµ M(µ), Mµ 0.113 428 9256(29)×10−3 kg mol−1 2.5×10−8
muon Compton wavelength ℎ/mµc λC,µ 11.734 441 04(30)×10−15 m 2.5×10−8
λC,µ/2π ƛC,µ 1.867 594 295(47)×10−15 m 2.5×10−8
muon magnetic moment µµ −4.490 447 86(16)×10−26 J T−1 3.6×10−8
to Bohr magneton ratio µµ/µB −4.841 970 49(12)×10−3   2.5×10−8
to nuclear magneton ratio µµ /µN −8.890 597 05(23)   2.5×10−8
muon magnetic moment anomaly |µµ|/(eℏ/2mµ)−1 aµ 1.165 920 69(60)×10−3   5.2×10−7
muon g-factor −2(1+aµ) gµ −2.002 331 8414(12)   6.0×10−10
muon–proton magnetic moment ratio µµ p −3.183 345 137(85)   2.7×10−8
Tau, τ−        
tau masse mτ 3.167 77(52)×10−27 kg 1.6×10−4
in u, mτ= Ar (τ) u (tau rel. atomic mass times u)   1.907 68(31) u 1.6×10−4
energy equivalent mτ c2 2.847 05(46)×10−10 J 1.6×10−4
in MeV   1776.99(29) MeV 1.6×10−4
tau–electron mass ratio mτ /me 3477.48(57)   1.6×10−4
tau–muon mass ratio mτ /mµ 16.8183(27)   1.6×10−4
tau–proton mass ratio mτ /mp 1.893 90(31)   1.6×10−4
tau–neutron mass ratio mτ /mn 1.891 29(31)   1.6×10−4
tau molar mass NAmτ M(τ), Mτ 1.907 68(31)×10−3 kg mol−1 1.6×10−4
tau Compton wavelength ℎ/mτc λC,τ 0.697 72(11)×10−15 m 1.6×10−4
λC,τ/2π ƛC,τ 0.111 046(18)×10−15 m 1.6×10−4
Proton, p
proton mass mp 1.672 621 637(83)×10−27 kg 5.0×10−8
in u, mp= Ar(p) u (proton rel. atomic mass times u)   1.007 276 466 77(10) u 1.0×10−10
energy equivalent mpc2 1.503 277 359(75)×10−10 J 5.0×10−8
in MeV   938.272 013(23) MeV 2.5×10−8
proton–electron mass ratio mp /me 1836.152 672 47(80)   4.3×10−10
proton–muon mass ratio mp /mµ 8.880 243 39(23)   2.5×10−8
proton–tau mass ratio mp /mτ 0.528 012(86)   1.6×10−4
proton–neutron mass ratio mp /mn 0.998 623 478 24(46)   4.6×10−10
proton charge to mass quotient e/mp 9.578 833 92(24)×107 C kg−1 2.5×10−8
proton molar mass NAmp M(p), Mp 1.007 276 466 77(10)×10−3 kg mol−1 1.0×10−10
proton Compton wavelength ℎ/mp c λC,p 1.321 409 8446(19)×10−15 m 1.4×10−9
λC,p/2π ƛC,p 0.210 308 908 61(30)×10−15 m 1.4×10−9
proton rms charge radius Rp 0.8768(69)×10−15 m 7.8×10−3
proton magnetic moment µp 1.410 606 662(37)×10−26 J T−1 2.6×10−8
to Bohr magneton ratio µp /µB 1.521 032 209(12)×10−3   8.1×10−9
to nuclear magneton ratio µp /µN 2.792 847 356(23)   8.2×10−9
proton g-factor 2µp /µN gp 5.585 694 713(46)   8.2×10−9
proton–neutron magnetic moment ratio µp /µn −1.459 898 06(34)   2.4×10−7
shielded proton magnetic moment (H2O, sphere, 25 °C) µ´p 1.410 570 419(38)×10−26 J T−1 2.7×10−8
to Bohr magneton ratio µ´p /µB 1.520 993 128(17)×10−3   1.1×10−8
to nuclear magneton ratio µ´p /µN 2.792 775 598(30)   1.1×10−8
proton magnetic shielding correction 1 − µ´p /µp        
(H2O, sphere, 25 °C) σ´p 25.694(14)×10−6   5.3×10−4
proton gyromagnetic ratio 2µp/ℏ γp 2.675 222 099(70)×108 s−1 T−1 2.6×10−8
  γp /2π 42.577 4821(11) MHz T−1 2.6×10−8
shielded proton gyromagnetic ratio 2µ´p/ℏ        
(H2O, sphere, 25 °C) γ´p 2.675 153 362(73)×108 s−1 T−1 2.7×10−8
  γ´p/2π 42.576 3881(12) MHz T−1 2.7×10−8
Neutron, n
neutron mass mn 1.674 927 211(84)×10−27 kg 5.0×10−8
in u, mn = Ar(n) u (neutron rel. atomic mass times u)   1.008 664 915 97(43) u 4.3×10−10
energy equivalent mnc2 1.505 349 505(75)×10−10 J 5.0×10−8
in MeV   939.565 346(23) MeV 2.5×10−8
neutron–electron mass ratio mn/me 1838.683 6605(11)   6.0×10−10
neutron–muon mass ratio mn/mµ 8.892 484 09(23)   2.5×10−8
neutron–tau mass ratio mn/mτ 0.528 740(86)   1.6×10−4
neutron–proton mass ratio mn/mp 1.001 378 419 18(46)   4.6×10−10
neutron molar mass NAmn M(n), Mn 1.008 664 915 97(43)×10−3 kg mol−1 4.3×10−10
neutron Compton wavelength ℎ/mnc λC,n 1.319 590 8951(20)×10−15 m 1.5×10−9
λC,n/2π ƛC,n 0.210 019 413 82(31)×10−15 m 1.5×10−9
neutron magnetic moment µn −0.966 236 41(23)×10−26 J T−1 2.4×10−7
to Bohr magneton ratio µn/µB −1.041 875 63(25)×10−3   2.4×10−7
to nuclear magneton ratio µn/µN −1.913 042 73(45)   2.4×10−7
neutron g-factor 2µn/µN gn −3.826 085 45(90)   2.4×10−7
neutron–electron magnetic moment ratio µn/µe 1.040 668 82(25)×10−3   2.4×10−7
neutron–proton magnetic moment ratio µn/µp −0.684 979 34(16)   2.4×10−7
neutron to shielded proton magnetic moment ratio        
(H2O, sphere, 25 °C) µn/µ´p −0.684 996 94(16)   2.4×10−7
neutron gyromagnetic ratio 2|µn|/ℏ γn 1.832 471 85(43)×108 s−1 T−1 2.4×10−7
  γn/2π 29.164 6954(69) MHz T−1 2.4×10−7
Deuteron, d
deuteron mass md 3.343 583 20(17)×10−27 kg 5.0×10−8
in u, md = Ar(d) u (deuteron rel. atomic mass times u)   2.013 553 212 724(78) u 3.9×10−11
energy equivalent mdc2 3.005 062 72(15)×10−10 J 5.0×10−8
in MeV   1875.612 793(47) MeV 2.5×10−8
deuteron–electron mass ratio md/me 3670.482 9654(16)   4.3×10−10
deuteron–proton mass ratio md/mp 1.999 007 501 08(22)   1.1×10−10
deuteron molar mass NAmd M(d), Md 2.013 553 212 724(78)×10−3 kg mol−1 3.9×10−11
deuteron rms charge radius Rd 2.1402(28)×10−15 m 1.3×10−3
deuteron magnetic moment µd 0.433 073 465(11)×10−26 J T−1 2.6×10−8
to Bohr magneton ratio µd/µB 0.466 975 4556(39)×10−3   8.4×10−9
to nuclear magneton ratio µd/µN 0.857 438 2308(72)   8.4×10−9
deuteron g-factor µd/µN gd 0.857 438 2308(72)   8.4×10−9
deuteron–electron magnetic moment ratio µd/µe −4.664 345 537(39)×10−4   8.4×10−9
deuteron–proton magnetic moment ratio µd/µp 0.307 012 2070(24)   7.7×10−9
deuteron–neutron magnetic moment ratio µd/µn −0.448 206 52(11)   2.4×10−7
Triton, t
triton mass mt 5.007 355 88(25)×10–27 kg 5.0×10−8
in u, mt = Ar(t) u (triton rel. atomic mass times u)   3.015 500 7134(25) u 8.3×10−10
energy equivalent mtc2 4.500 387 03(22)×10–10 J 5.0×10−8
in MeV   2808.920 906(70) MeV 2.5×10−8
triton–electron mass ratio mt/me 5496.921 5269(51)   9.3×10−10
triton–proton mass ratio mt/mp 2.993 717 0309(25)   8.4×10−10
triton molar mass NAmt M(t), Mt 3.015 500 7134(25)×10–3 kg mol−1 8.3×10−10
triton magnetic moment µt 1.504 609 361(42)×10−26 J T−1 2.8×10−8
to Bohr magneton ratio µt/µB 1.622 393 657(21)×10−3   1.3×10−8
to nuclear magneton ratio µt/µN 2.978 962 448(38)   1.3×10−8
triton g-factor 2µt/µN gt 5.957 924 896(76)   1.3×10−8
triton–electron magnetic moment ratio µt/µe −1.620 514 423(21)×10−3   1.3×10−8
triton–proton magnetic moment ratio µt/µp 1.066 639 908(10)   9.8×10−9
triton–neutron magnetic moment ratio µt/µn −1.557 185 53(37)   2.4×10−7
Helion, h
helion massf mh 5.006 411 92(25)×10−27 kg 5.0×10−8
in u, mh = Ar(h) u (helion rel. atomic mass times u)   3.014 932 2473(26) u 8.6×10−10
energy equivalent mhc2 4.499 538 64(22)×10−10 J 5.0×10−8
in MeV   2808.391 383(70) MeV 2.5×10−8
helion–electron mass ratio mh/me 5495.885 2765(52)   9.5×10−10
helion–proton mass ratio mh/mp 2.993 152 6713(26)   8.7×10−10
helion molar mass NAmh M(h), Mh 3.014 932 2473(26)×10−3 kg mol−1 8.6×10−10
shielded helion magnetic moment (gas, sphere, 25 °C) µ´h −1.074 552 982(30)×10−26 J T−1 2.8×10−8
to Bohr magneton ratio µ´h/µB −1.158 671 471(14)×10−3   1.2×10−8
to nuclear magneton ratio µ´h /µN −2.127 497 718(25)   1.2×10−8
shielded helion to proton magnetic moment ratio        
(gas, sphere, 25 °C) µ´h /µp −0.761 766 558(11)   1.4×10−8
shielded helion to shielded proton        
magnetic moment ratio (gas/H2O, spheres, 25 °C) µ´h /µ´p −0.761 786 1313(33)   4.3×10−9
shielded helion gyromagnetic ratio 2|µ´h|/ℏ (gas, sphere, 25 °C) γ´h 2.037 894 730(56)×108 s−1 T−1 2.8×10−8
  γ´h/2π 32.434 101 98(90) MHz T−1 2.8×10−8
Alpha particle, α
alpha particle mass mα 6.644 656 20(33)×10−27 kg 5.0×10−8
in u, mα = Ar(α) u (alpha particle        
rel. atomic mass times u)   4.001 506 179 127(62) u 1.5×10−11
energy equivalent mαc2 5.971 919 17(30)×10−10 J 5.0×10−8
in MeV   3727.379 109(93) MeV 2.5×10−8
alpha particle to electron mass ratio mα/me 7294.299 5365(31)   4.2×10−10
alpha particle to proton mass ratio mα/mp 3.972 599 689 51(41)   1.0×10−10
alpha particle molar mass NAmα M(α), Mα 4.001 506 179 127(62)×10−3 kg mol−1 1.5×10−11
PHYSICOCHEMICAL
Avogadro constant NA, L 6.022 141 79(30)×1023 mol−1 5.0×10−8
atomic mass constant        
mu=1⁄12m(12C)=1 u=10−3 kg mol−1/NA mu 1.660 538 782(83)×10−27 kg 5.0×10−8
energy equivalent muc2 1.492 417 830(74)×10−10 J 5.0×10−8
in MeV   931.494 028(23) MeV 2.5×10−8
Faraday constantg NAe F 96 485.3399(24) C mol−1 2.5×10−8
molar Planck constant NAℎ 3.990 312 6821(57)×10−10 J s mol−1 1.4×10−9
  NAhc 0.119 626 564 72(17) J m mol−1 1.4×10−9
molar gas constant R 8.314 472(15) J mol−1 K−1 1.7×10−6
Boltzmann constant R/NA k 1.380 6504(24)×10−23 J K−1 1.7×10−6
in eV K−1   8.617 343(15)×10−5 eV K−1 1.7×10−6
  k/ℎ 2.083 6644(36)×1010 Hz K−1 1.7×10−6
  k/hc 69.503 56(12) m−1 K−1 1.7×10−6
molar volume of ideal gas RT/p        
T=273.15 K, p=101.325 kPa Vm 22.413 996(39)×10−3 m3 mol−1 1.7×10−6
Loschmidt constant NA/Vm n0 2.686 7774(47)×1025 m−3 1.7×10−6
T=273.15 K, p=100 kPa Vm 22.710 981(40)×10−3 m3 mol−1 1.7×10−6
Sackur–Tetrode constant (absolute entropy constant)h        
52+ln[(2πmukT1/ℎ2)3/2kT1/p0]        
T1=1 K, p0=100 kPa S0/R −1.151 7047(44)   3.8×10−6
T1=1 K, p0=101.325 kPa   −1.164 8677(44)   3.8×10−6
Stefan–Boltzmann constant (π2/60)k4/ℏ3c2 σ 5.670 400(40)×10−8 W m−2 K−4 7.0×10−6
first radiation constant 2πhc2 c1 3.741 771 18(19)×10−16 W m2 5.0×10−8
first radiation constant for spectral radiance 2hc2 c1L 1.191 042 759(59)×10−16 W m2 sr−1 5.0×10−8
second radiation constant hc/k c2 1.438 7752(25)×10−2 m K 1.7×10−6
Wien displacement law constants        
b=λmaxT=c2/4.965 114 231 . . . b 2.897 7685(51)×10−3 m K 1.7×10−6
b´=νmax/T=2.821 439 372 . . . c/c2 b´ 5.878 933(10)×1010 Hz K−1 1.7×10−6

a See the "Adopted values" table for the conventional value adopted internationally for realizing representations of the volt using the Josephson effect.
b See the "Adopted values" table for the conventional value adopted internationally for realizing representations of the ohm using the quantum Hall effect.
c Value recommended by the Particle Data Group (Yao et al., J. Phys. G 33, 1, 2006).
d Based on the ratio of the masses of the W and Z bosons mW/mZ recommended by the Particle Data Group (Yao et al., J. Phys. G 33, 1, 2006). The value for sin2θW they recommend, which is based on a particular variant of the modified minimal subtraction (MS) scheme, is sin2θ^W(MZ)=0.231 22(15).
e This and all other values involving mτ are based on the value of mτc2 in MeV recommended by the Particle Data Group (Yao et al., J. Phys. G 33, 1, 2006), but with a standard uncertainty of 0.29 MeV rather than the quoted uncertainty of –0.26 MeV, &43;0.29 MeV.
f The helion, symbol h, is the nucleus of the 3He atom.
g The numerical value of F to be used in coulometric chemical measurements is 96 485.3401(48) [5.0×10–8] when the relevant current is measured in terms of representations of the volt and ohm based on the Josephson and quantum Hall effects and the internationally adopted conventional values of the Josephson and von Klitzing constants KJ–90 and RK–90 given in the "Adopted values" table.
h The entropy of an ideal monoatomic gas of relative atomic mass Ar is given by S=S0+32 R ln Ar–R ln(p/p0)&43;52 R ln(T/K).

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Internationally Adopted Values of Various Quantities
Quantity Symbol Value Unit Relative standarduncertainty ur
relative atomic massa of 12C Ar(12C) 12 (exact)
molar mass constant Mu 1 × 10−3 kg mol−1 (exact)
molar mass of 12C M(12C) 12 × 10−3 kg mol−1 (exact)
conventional value of Josephson constantb KJ−90 483 597.9 GHz V−1 (exact)
conventional value of von Klitzing constantc RK−90 25 812.807 Ω (exact)
standard atmosphere 101 325 Pa (exact)

a The relative atomic mass Ar(X) of particle X with mass m(X) is defined by Ar(X) = m(X)/mu, where mu = m(12C)/12 = Mu/NA = 1 u is the atomic mass constant, Mu is the molar mass constant, NA is the Avogadro constant, and u is the unified atomic mass unit. Thus the mass of particle X is m(X) = Ar(X) u and the molar mass of X is M(X) = Ar(X)Mu.
b This is the value adopted internationally for realizing representations of the volt using the Josephson effect.
c This is the value adopted internationally for realizing representations of the ohm using the quantum Hall effect.

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CODATA Recommended Values of Energy Equivalents—2006
Relevant unit
J kg m-1 Hz
1 J (1 J) = 1 J (1 J)/c2 = 1.112 650 056 . . . × 10−17 kg (1 J)/hc = 5.034 117 47(25) × 1024 m−1 (1 J)/ℎ = 1.509 190 450(75) × 1033 Hz
1 kg (1 kg)c2 = 8.987 551 787 . . . × 1016 J (1 kg) = 1 kg (1 kg)c/ℎ = 4.524 439 15(23) × 1041 m−1 (1 kg)c2/ℎ = 1.356 392 733(68) × 1050 Hz
1 m−1 (1 m−1)hc = 1.986 445 501(99) × 10−25 J (1 m−1)ℎ/c = 2.210 218 70(11) × 10−42 kg (1 m−1) = 1 m−1 (1 m−1)c = 299 792 458 Hz
1 Hz (1 Hz)ℎ = 6.626 068 96(33) × 10−34 J (1 Hz)ℎ/c2 = 7.372 496 00(37) × 10−51 kg (1 Hz)/c = 3.335 640 951 . . . × 10−9 m−1 (1 Hz) = 1 Hz
1 K (1 K)k = 1.380 6504(24) × 10−23 J (1 K)k/c2 = 1.536 1807(27) × 10−40 kg (1 K)k/hc = 69.503 56(12) m−1 (1 K)k/ℎ = 2.083 6644(36) × 1010 Hz
1 eV (1 eV) = 1.602 176 487(40) × 10−19 J (1 eV)/c2 = 1.782 661 758(44) × 10−36 kg (1 eV)/hc = 8.065 544 65(20) × 105 m−1 (1 eV)/ℎ = 2.417 989 454(60) × 1014 Hz
1 u (1 u)c2 = 1.492 417 830(74) × 10−10 J (1 u) = 1.660 538 782(83) × 10−27 kg (1 u)c/ℎ = 7.513 006 671(11) × 1014 m−1 (1 u)c2/ℎ = 2.252 342 7369(32) × 1023 Hz
1 Eh (1 Eh) = 4.359 743 94(22) × 10−18 J (1 Eh)/c2 = 4.850 869 34(24) × 10−35 kg (1 Eh)/hc = 2.194 746 313 705(15) × 107 m−1 (1 Eh)/ℎ = 6.579 683 920 722(44) × 1015 Hz

The values of some energy equivalents derived from the relations E = mc2 = hc/λ = hν = kT, and based on the 2006 CODATA adjustment of the values of the constants; 1 eV = (e/C) J, 1 u = mu = 112 m(12C) = 10−3 kg mol−1/NA, and Eh = 2R∞hc = α2mec2 is the Hartree energy (hartree).

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CODATA Recommended Values of Energy Equivalents—2006
Relevant unit
K eV u Eh
1 J (1 J)/k = 7.242 963(13) × 1022 K (1 J) = 6.241 509 65(16) × 1018 eV (1 J)/c2 = 6.700 536 41(33) × 109 u (1 J) = 2.293 712 69(11) × 1017 Eh
1 kg (1 kg)c2/k = 6.509 651(11) × 1039 K (1 kg)c2 = 5.609 589 12(14) × 1035 eV (1 kg) = 6.022 141 79(30) × 1026 u (1 kg)c2 = 2.061 486 16(10) × 1034 Eh
1 m−1 (1 m−1)hc/k = 1.438 7752(25) × 10−2 K (1 m−1)hc = 1.239 841 875(31) × 10−6 eV (1 m−1)ℎ/c = 1.331 025 0394(19) × 10−15 u (1 m−1)hc = 4.556 335 252 760(30) × 10−8 Eh
1 Hz (1 Hz)ℎ/k = 4.799 2374(84) × 10−11 K (1 Hz)ℎ = 4.135 667 33(10) × 10−15 eV (1 Hz)ℎ/c2 = 4.439 821 6294(64) × 10−24 u (1 Hz)ℎ = 1.519 829 846 006(10) × 10−16 Eh
1 K (1 K) = 1 K (1 K)k = 8.617 343(15) × 10−5 eV (1 K)k/c2 = 9.251 098(16) × 10−14 u (1 K)k = 3.166 8153(55) × 10−6 Eh
1 eV (1 eV)/k = 1.160 4505(20) × 104 K (1 eV) = 1 eV (1 eV)/c2 = 1.073 544 188(27) × 10−9 u (1 eV) = 3.674 932 540(92) × 10−2 Eh
1 u (1 u)c2/k = 1.080 9527(19) × 1013 K (1 u)c2 = 931.494 028(23) × 106 eV (1 u) = 1 u (1 u)c2 = 3.423 177 7149(49) × 107 Eh
1 Eh (1 Eh)/k = 3.157 7465(55) × 105 K (1 Eh) = 27.211 383 86(68) eV (1 Eh)/c2 = 2.921 262 2986(42) × 10−8 u (1 Eh) = 1 Eh

The values of some energy equivalents derived from the relations E = mc2 = hc/λ = hν = kT, and based on the 2006 CODATA adjustment of the values of the constants; 1 eV = (e/C) J, 1 u = mu = 112 m(12C) = 10−3 kg mol−1/NA, and Eh = 2R∞hc = α2mec2 is the Hartree energy (hartree).

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