Institute of Physics Physical Constants guide

Values of Physical Constants

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SI base units Name Symbol metre m Base quantity kilogram kg length second s mass ampere A time kelvin K electric current mole mol thermodynamic temperature candela cd amount of substance luminous intensity

Fundamental constants Symbol Principal constants c h Speed of light in vacuum –h Planck constant e Reduced Planck constant (h/2π) me Elementary charge Na Mass of electron mu Avogadro constant F(=NAe) Atomic mass constant G Faraday constant Newtonian constant of gravitation

2010 CODATA value SI unit Relative standard uncertainty (parts in 106)299 792 458 m s–16.626 069 57 × 10–34 Js exact1.054 571 726 × 10–34 Js 0.0441.602 176 565 × 10–19 C 0.0449.109 382 91 × 10–31 kg 0.0226.022 141 29 × 1023 mol–1 0.0441.660 538 921 × 10–27 kg 0.04496 485.3365 C mol–1 0.0446.673 84 × 10–11 m3 kg–1 s–2 0.022 120

Spectroscopy and atoms SymbolPlanck constant hReduced Planck constant (h/2π) –hCharge/mass ratio of electron −e/meFine structure constant αFine structure constant, reciprocal α–1Rydberg constant (fixed nucleus) R∞Bohr radius (4π/μ0c2)h– 2/mee2 a0Reduced Compton wavelength of electron h– /(mec) λ–cClassical radius of electron (μ0c2/4π)e2/mec2 reThomson cross-section (8π/3)r2e σeBohr magneton eh–/2me mBNuclear magneton eh–/2mp mNRatio of masses proton/electron mp/meGyromagnetic ratio of proton γPShielded gyromagnetic ratio of proton γ ʹP

2010 CODATA value SI unit Relative standard uncertainty (parts in 106)4.135 667 516 × 10−15 eV s6.582 119 28 × 10−16 eV s 0.022−1.758 820 088 × 1011 C kg–1 0.0227.297 352 5698 × 10−3 0.022137.035 999 074 m–1 0.0003210 973 731.568 539 m 0.000325.291 772 1092 × 10–11 m 0.000005386.159 268 00 × 10–15 m 0.000322.817 940 3267 × 10–15 m2 0.000650.665 245 8734 × 10–28 J T–1 0.00097927.400 968 × 10–26 J T–1 0.00195.050 783 53 × 10–27 0.0221836.152 672 45 s–1 T–1 0.0222.675 222 005 × 108 s–1 T–1 0.000412.675 153 268 × 108 0.024 0.025

Thermal constants SymbolMolar gas constant RLoschmidt constant n0(number of molecules in 1 m3 of ideal gas at stp) kBoltzmann constant R/NA kBoltzmann constantEnergy kT for T = 273.15 K σStefan–Boltzmann constant π5k4/60c2h3 SymbolElectrical constants KJJosephson constant 2e/h KJ–90Josephson constant conventional value RKVon Klitzing constant h/e2 RK–90Von Klitzing constant conventional value

2010 CODATA value SI unit Relative standard uncertainty J mol–1 K–1 (parts in 106)8.314 46212.686 7805 × 1025 0.911.380 6488 × 10-238.617 3324 × 10-5 m-3 0.910.023 538 2435.670 373 × 10-8 J K–1 0.91 eV K–1 0.912010 CODATA value eV 0.91 W m–2 K–4 3.6483 597.870483 597.9 SI unit Relative standard uncertainty25 812.807 4434 (parts in 106)25 812.807 GHz V–1 GHz V–1 0.022 Ω exact Ω 0.00032 exact

Conversion factors for mass, energy, wavelength and frequencyElectron voltAtomic mass unit1 MeVRest mass of electron1 eV per moleculeQuantum energy ÷ wave numberEnergy × wavelengthWave number ÷ energyQuantum energy ÷ frequency Frequency ÷ energy

2010 CODATA value SI unit Relative standard uncertainty (parts in 106)1.602 176 565 × 10–19 J931.494 06 MeV 0.0221.073 544 150 × 10–3 u 0.0220.510 998 928 MeV 0.0229.648 533 65 × 107 J kmol–1 0.0221.986 445 68 × 10–25 Jm 0.0221.239 841 93 × 10–6 eV m 0.0448.065 544 29 × 105 eV–1 m–1 0.0224.135 667 513 × 10–15 eV Hz–1 0.0222.417 989 350 × 1014 Hz eV –1 0.022 0.022

SI derived units Derived quantity area volume speed, velocity acceleration wave number mass density current density magnetic field strength luminance dynamic viscosity moment of force surface tension angular velocity

Name Symbolsquare metre m2cubic metre m3metre per second m s–1metre per second squared m s–2reciprocal metre m–1kilogram per cubic metre kg m–3ampere per square metre A m–2ampere per metre A m–1candela per square metre cd m–2pascal second Pa snewton metre Nmnewton per metre N m–1radian per second rad s–1

SI derived units (continued) Derived quantity angular acceleration heat flux density, irradiance heat capacity, entropy specific heat capacity, specific entropy specific energy thermal conductivity energy density electric field strength electric charge density electric flux density permittivity permeability molar energy

Name Symbolradian per second squared rad s–2watt per square metre W m–2joule per kelvin JKjoule per kilogram kelvin J kg–1 K–1joule per kilogram J kg–1watt per metre kelvin W m–1 K–1joule per cubic metre J m–3volt per metre V m–1coulomb per cubic metre C m–3coulomb per square metre C m–2farad per metre F m–1henry per metre H m–1joule per mole J mol–1

SI derived units (continued) Derived quantity molar entropy, molar heat exposure (x and γ rays) absorbed dose rate radiant intensity radiance catalytic (activity) concentration

Name Symboljoule per mole kelvin J mol–1 K–1coulomb per kilogram C kg–1gray per second Gy s–1watt per steradian W sr–1watt per square metre steradian W m–2 sr–1katal per cubic metre kat m–3

SI derived quantity radian Symbol steradian rad Name hertz sr plane angle newton Hz solid angle pascal N frequency joule Pa force watt J pressure, stress coulomb W energy, work, quantity of heat volt C power, radiant flux farad V electric charge, quantity of electricity ohm F electric potential difference, electromotive force siemens Ω capacitance weber S electric resistance tesla Wb electric conductance T magnetic flux magnetic flux density

Expression in terms of other SI units Expression in terms of SI base units- m m–1 = 1 (b)m2 m–2 m m–2 = 1 (b)- s–1- m kg s–2N m–2 m–1 kg s–2Nm m2 kg s–2J s–1 m2 kg s–3- sAW A–1 m2 kg s–3 A–1C V–1 m–2 kg–1 s4 A2V A–1 m2 kg s–3 A-2A V–1 m–2 kg–1 s3 A2Vs m2 kg s–2 A–1Wb m–2 kg s–2 A–1

SI derived quantity (continued)Name Symbolinductancecelsius temperature henry Hluminous fluxilluminance degree celsius °Cactivity (of a radionuclide)absorbed dose, specfic energy (imparted), kerma lumen lmdose equivalentcatalytic activity lux lx becquerel Bq gray Gy sievert Sv katal kat

Expression in terms of other SI units Expression in terms of SI base unitsWb A–1 m2 kg s–2 A–2- Kcd sr m2 m–2 cd = cdlm m–2 m2 m–4 cd = m–2 cd- s–1J kg–1 m2 s–2J kg–1 m2 s–2 s–1mol

SI prefixesFactor Name Symbol Factor Name Symbol1024 yotta Y 10–1 deci d1021 zetta Z 10–2 centi c1018 exa E 10–3 milli m1015 peta P 10–6 micro μ1012 tera T 10–9 nano n109 giga G 10–12 pico p106 mega M 10–15 femto f103 kilo k 10–18 atto a102 hecto h 10–21 zepto z101 deka da 10–24 yocto y

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