Constants

A selection of mathematical, physical, and chemical constants.  Values and uncertainties were calculated with Cybernet Waterloo Maple 2023: The Essential Tool for Mathematics.  Sources for constants are listed in the Maple worksheet.

mathematical constants

symbol value derivation name
e 2.71828182845904523536028747135266E0 limx→∞([1 + x−1]x) Napier constant
nW 4.96511423174427630369875913132289E0 5 + W0(−5e−5) Wien number
π 3.14159265358979323846264338327950E0 ∫−1→1([1 − x2]−1/2)dx Archimedean constant
π2 6.28318530717958647692528676655901E0 2π circle constant

physical constants

symbol value units relative uncertainty derivation name
α 7.2973525643E-3 1.50739599095349139043105065779451E-10 Sommerfeld constant
α1 1.37035999177590126402822787072229E2 1.50739599095349139043105065779451E-10 α−1 inverse Sommerfeld constant
b 2.89777195518517266147860544809288E-3 K·m ch/(knW) Wien constant
c 2.997924580E8 m/s 0 celerity constant
c2 8.98755178736817640E16 J/kg 0 c2 energy to mass ratio
ε0 8.85418781884005976096014934214177E-12 F/m 1.50739599095349139043105065779451E-10 1/(μ0c2) electric constant
EP 1.95608132867888696349576E9 J 1.1E-5 c2mP Planck energy
G 6.67430210197253686085347591094350E-11 J·m/kg2 2.2E-5 cħ/mP2 gravitational constant
h 6.626070150E-34 J/Hz 0 Planck constant
ħ 1.05457181764615639126242800330228E-34 J·s h/π2 Dirac constant
k 1.3806490E-23 J/K 0 Boltzmann constant
lP 1.61625527893154928645272465099284E-35 m 1.1E-5 ħ/pP Planck length
mP 2.176434E-8 kg 1.1E-5 Planck mass
μ0 1.25663706126281475413387203816772E-6 H/m 1.50739599095349139043105065779451E-10 2αh/(cq02) magnetic constant
pP 6.52478498534772E0 kg·m/s 1.1E-5 cmP Planck momentum
q0 1.6021766340E-19 C 0 elementary charge
tP 5.39124729726039100841130783547878E-44 s 1.1E-5 lP/c Planck time
TP 1.41678393905973709718817744408608E32 K 1.1E-5 EP/k Planck temperature
Z0 3.76730313409875819140459159379771E2 Ω 1.50739599095349139043105065779451E-10 cμ0 impedance constant

chemical constants

symbol value units relative uncertainty derivation name
a0 5.29177210541025525934973936880563E-11 m 1.50765433690413549074234507744312E-10 α/(4πR∞) Bohr radius
Are 5.48579909051083516641361852636724E-4 4.31168768458334883015334268594404E-10 me/mDa electron relative atomic mass
Arn 1.00866491606E0 3.96563807892180292237376859914257E-10 neutron relative atomic mass
Arp 1.00727646658528754077117427537036E0 4.35567443677026511598298707493193E-10 mp/mDa proton relative atomic mass
ArR 1.46063115898819828970779788169955E-8 3.08226561161271430270057386645827E-10 mR/mDa Rydberg relative atomic mass
C0 3.32491847416565017617678917534282E-10 m 1.50765433690413549074234507744312E-10 d0π Bohr circumference
d0 1.05835442108205105186994787376113E-10 m 1.50765433690413549074234507744312E-10 2a0 Bohr diameter
EDa 1.49241808768E-10 J 3.08224621369391952074897007455706E-10 Dalton energy
Ee 8.18710578805686385337870712503001E-14 J 3.01503050856159941276600056958210E-10 c2me electron energy
EHa 4.35974472220597787042871668118E-18 J 1.09352046069916381315936989951839E-12 2ER Hartree energy
En 1.5053497651361729201408E-10 J 5.02260162613212940681058828922716E-10 c2mn neutron energy
Ep 1.50327761802628225122064594451625E-10 J 3.07760590025809887588172624252890E-10 c2mp proton energy
ER 2.17987236110298893521435834059E-18 J 1.09352046069916381315936989951839E-12 fRh Rydberg energy
fR 3.289841960249981559906E15 Hz 1.09352046069916381315936989951839E-12 cR∞ Rydberg frequency
mDa 1.66053906891258602808965513018275E-27 kg 3.08224621369391952074897007455706E-10 EDa/c2 Dalton mass
me 9.10938371399837347404522059737764E-31 kg 3.01503050856159941276600056958210E-10 2hR∞/(cα2) electron mass
mn 1.67492750055906414150058079404013E-27 kg 5.02260162613212940681058828922716E-10 ArnmDa neutron mass
mp 1.67262192596109294529342751530105E-27 kg 3.07760590025809887588172624252890E-10 Mp/NA proton mass
mR 2.42543510477097419887561013959864E-35 kg 1.09352046069916381315936989951839E-12 ER/c2 Rydberg mass
Me 5.48579909625497874717505250426594E-7 kg/mol 3.01503050856159941276600056958210E-10 meNA electron molar mass
Mp 1.00727646764E-3 kg/mol 3.07760590025809887588172624252890E-10 proton molar mass
NA 6.022140760E23 mol−1 0 Avogadro constant
R 8.314462618153240E0 J/(mol·K) 0 kNA ideal gas constant
R∞ 1.0973731568157E7 m−1 1.09352046069916381315936989951839E-12 Rydberg constant