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In science, a physical constant is a physical quantity whose numerical value is fixed. It can be constrasted to a mathematical constant which is a fixed number that does not directly involve a physical measurement.
There are many such constants used in science, some of the most famous of which being: Planck's constant, the gravitational constant and Avogadro's constant (better known as Avogadro's number). Constants can take many forms; some, such as the Planck length represents a fundamental physical distance, others such as the speed of light signifies the maximun speed limit of the universe, yet others are dimensionless quantities such as the finestructure constant which embodies the interaction between electrons and photons.
Below is a list of physical constants:
Quantity  Symbol  Value  Ref. 

speed of light in vacuum  c  299 792 458 m·s^{1} (defined)  a 
permeability of vacuum  μ_{0}  4π × 10^{7} N A^{2} (defined)  a 
12.566 370 614... × 10^{7} N A^{2}  a  
permittivity of vacuum  ε_{0} = 1/(μ_{0}c^{2})  8.854 187 817 ... × 10^{12} F·m^{1}  a 
characteristic impedance of vacuum  Z_{0} = μ_{0}c  376.730 313 461... Ω (defined)  a 
gravitational constant  G  6.672 59(85) × 10^{11} m^{3}·kg^{1}·s^{2}  ? 
Planck's constant  h  6.626 068 76(52) × 10^{34} J·s  a 
Dirac's constant  1.054 571 596(82) × 10^{34} J·s  a  
Planck mass  m_{p} = ( 
2.1767(16) × 10^{8} kg  a 
Planck length  l_{p}= ( 
1.6160(12) × 10^{35} m  a 
Planck time  t_{p} = ( 
5.3906(40) × 10^{44} s  a 
elementary charge  e  1.602 176 462(63) × 10^{19} C  a 
electron rest mass  m_{e}  9.109 381 88(72) × 10^{31} kg  a 
proton rest mass  m_{p}  1.672 621 58(13) × 10^{27} kg  a 
neutron rest mass  m_{n}  1.674 927 16(13) × 10^{27} kg  a 
atomic mass constant[?], (unified atomic mass unit)  m_{u} = 1 u  1.660 538 73(13) × 10^{27} kg  a 
Avogadro constant  L, N_{A}  6.022 141 99(47) × 10^{23} mol^{1}  a 
Boltzmann constant  k  1.380 6503(24) × 10^{23} J·K^{1}  a 
Faraday constant  F  9.648 534 15(39) × 10^{4} C·mol^{1}  a 
gas constant  R  8.314 472(15) J·K^{1}·mol^{1}  a 
zero of the Celsius scale  273.15 K (defined)  ?  
molar volume, ideal gas, p = 1 bar, θ = 0^{0}C  22.710 981(40) L·mol^{1}  a  
standard atmosphere  atm  101 325 Pa (defined)  a 
fine structure constant  α = μ_{0}e^{2}c / (2h)  7.297 352 533(27) × 10^{3}  a 
α^{1}  137.035 999 76(50)  a  
Bohr radius  a_{0}  5.291 772 083(19) × 10^{11} m  a 
Hartree energy  E_{h}  4.359 743 81(34) × 10^{18} J  a 
Rydberg constant  R_{∞}  1.097 373 156 8549(83) × 10^{7} m^{1}  a 
Bohr magneton  μ_{B}  9.274 008 99(37) × 10^{24} J·T^{1}  a 
electron magnetic moment[?]  μ_{e}  9.284 763 62(37) × 10^{24} J·T^{1}  a 
Lande gfactor for free electron  g_{e}  2.002 319 304 386(20)  ? 
nuclear magneton  μ_{N}  5.050 786 6(17) × 10^{27} J·T^{1}  ? 
proton magnetic moment[?]  μ_{p}  1.410 607 61(47) × 10^{26} J·T^{1}  ? 
proton magnetogyric ratio  γ_{p}  2.675 221 28(81) × 10^{8} s^{1}·T^{1}  ? 
magnetic moment of protons in H_{2}0, μ'_{p}  μ'_{p} / μ_{B}  1.520 993 129(17) × 10^{3}  ? 
proton resonance frequency per field in H_{2}0  γ'_{p} / (2π)  42.576 375 (13) M·Hz·T^{1}  ? 
StefanBoltzmann constant  σ  5.670 400(40) × 10^{8} W·m^{2}·K^{4}  a 
first radiation constant  c_{1}  3.741 774 9(22) × 10^{16} W·m^{2}  ? 
second radiation constant  c_{2}  1.438 769 (12) × 10^{2} m·K  ? 
standard acceleration of free fall  g_{n}  9.80665 m·s^{2} (defined)  ? 
^{a}Peter J. Mohr and Barry N. Taylor, "CODATA Recommended Values of the Fundamental Physical Constants: 1998," Journal of Physical and Chemical Reference Data, Vol. 28, No. 6, 1999 and Reviews of Modern Physics, Vol. 72, No. 2, 2000.[[1] (http://physics.nist.gov/cuu/Constants/)]
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