In physics, a physical constant is a physical quantity of a value that is generally believed to be both universal in nature and not believed to change in time. It can be contrasted with a mathematical constant, which is also a fixed value but does not directly involve any physical measurement. The first few hydrogen atom electron orbitals shown as cross-sections with color-coded probability density. ... A physical quantity is either a quantity within physics that can be measured (e. ... A mathematical constant is a quantity, usually a real number or a complex number, that arises naturally in mathematics and does not change. ...

There are many physical constants in science, some of the most widely recognized being the rationalized Planck's constant ħ, the gravitational constant G, the speed of light in the vacuum c, the electric constant ε₀, and the elementary charge e. Physical constants can take many dimensional forms: the speed of light signifies a maximum speed limit of the universe and is expressed dimensionally as length divided by time; while the fine-structure constant α, which characterizes the strength of the electromagnetic interaction, is dimensionless. A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ... The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness. In metric units, c is exactly 299,792,458 metres per second (1,079,252,848. ... The electric constant () is the permittivity of vacuum, a physical constant, defined by: where: - magnetic constant - speed of light In SI units, the value is exactly expressed by: = 2. ... The elementary charge (symbol e or sometimes q) is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron. ... :For other senses of this word, see dimension (disambiguation). ... Speed is the rate of motion, or equivalently the rate of change of position, many times expressed as distance d moved per unit of time t. ... The deepest visible-light image of the cosmos, the Hubble Ultra Deep Field. ... Length is the long dimension of any object. ... Two distinct views exist on the meaning of time. ... The fine-structure constant or Sommerfeld fine-structure constant, usually denoted , is the fundamental physical constant characterizing the strength of the electromagnetic interaction. ... In the physical sciences, a dimensionless number (or more precisely, a number with the dimensions of 1) is a quantity which describes a certain physical system and which is a pure number without any physical units; it does not change if one alters ones system of units of measurement...

Dimensionful and dimensionless physical constants

The numerical values of dimensionful physical constants depend on the unit system used, such as SI or cgs. As such, numbers such as the speed of light, c, expressed in units of meters per second (299792458) are not values that a theory of physics can be expected to predict. Cover of brochure The International System of Units. ... This article or section is in need of attention from an expert on the subject. ... The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness. In metric units, c is exactly 299,792,458 metres per second (1,079,252,848. ...

Ratios of like-dimensioned physical constants do not depend on unit systems in this way (the units cancel), so they are pure (dimensionless) numbers whose values a future theory of physics could conceivably hope to predict. Additionally, all equations describing laws of physics can be expressed without dimensionful physical constants via a process known as nondimensionalization, but the dimensionless constants will remain. Thus, theoretical physicists tend to regard these dimensionless quantities as fundamental physical constants. A physical law, scientific law, or a law of nature is a scientific generalization based on empirical observations of physical behavior. ... Nondimensionalization refers to the partial or full removal of units from a mathematical equation by a suitable substitution of variables. ... In physics, fundamental physical constants are, in the strictest sense, physical constants that are independent of systems of units and hence are dimensionless numbers. ...

However, the phrase fundamental physical constant is also used in other ways. For example, the National Institute of Standards and Technology [1] uses it to refer to any universal physical quantity believed to be constant, such as the speed of light, c, and the gravitational constant G. As a non-regulatory agency of the United States Department of Commerce’s Technology Administration, the National Institute of Standards (NIST) develops and promotes measurement, standards, and technology to enhance productivity, facilitate trade, and improve the quality of life. ... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ...

The fine-structure constant α is probably the best known dimensionless fundamental physical constant. Nobody knows why it takes on the value that it does (currently measured at about (137.035999)^-1). Many attempts have been made to derive this value from theory, but so far none have succeeded. The same holds for the dimensionless ratios of masses of fundamental particles (the most apparent is m_p/m_e, approximately 1836.152672). But, with the development of quantum chemistry in the 20^th century, a vast number of previously inexplicable dimensionless physical constants were successfully computed from theory. As such, some theoretical physicists still hope for continued progress in explaining the values of dimensionless physical constants. The fine-structure constant or Sommerfeld fine-structure constant, usually denoted , is the fundamental physical constant characterizing the strength of the electromagnetic interaction. ... In the physical sciences, a dimensionless number (or more precisely, a number with the dimensions of 1) is a quantity which describes a certain physical system and which is a pure number without any physical units; it does not change if one alters ones system of units of measurement... ...

It is known that the universe would be very different if these constants took values significantly different from those we observe. For example, a few percent change in the value of the fine structure constant would be enough to eliminate stars like our Sun. This has prompted attempts at anthropic explanations of the dimensionless physical constants. In cosmology, the anthropic principle in its most basic form states the truism that any valid theory of the universe must be consistent with our existence as carbon-based human beings at this particular time and place in the universe. ...

How constant are the physical constants?

Beginning with Paul Dirac in 1937, some scientists have speculated that physical constants may actually decrease in proportion to the age of the universe. Scientific experiments have not yet pinpointed any definite evidence that this is the case, although they have placed upper bounds on the maximum possible relative change per year at very small amounts (roughly 10^-5 per year for the fine structure constant α and 10^-11 for the gravitational constant G). Paul Adrien Maurice Dirac, OM, FRS (IPA: [dɪræk]) (August 8, 1902 – October 20, 1984) was a British theoretical physicist and a founder of the field of quantum physics. ... 1937 (MCMXXXVII) was a common year starting on Friday (link will take you to calendar). ...

It is currently disputed [2] [3] that any changes in dimensionful physical constants such as G, c, ħ, or ε₀ are operationally meaningful; however, a sufficient change in a dimensionless constant such as α is generally agreed to be something that would definitely be noticed. If a measurement indicated that a dimensionful physical constant had changed, this would be the result or interpretation of a more fundamental dimensionless constant changing, which is the salient metric. From John D. Barrow 2002: John David Barrow FRS (born November 29, 1952, London) is an English cosmologist, theoretical physicist, and mathematician. ...

"[An] important lesson we learn from the way that pure numbers like α define the world is what it really means for worlds to be different. The pure number we call the fine structure constant and denote by α is a combination of the electron charge, e, the speed of light, c, and Planck's constant, h. At first we might be tempted to think that a world in which the speed of light was slower would be a different world. But this would be a mistake. If c, h, and e were all changed so that the values they have in metric (or any other) units were different when we looked them up in our tables of physical constants, but the value of α remained the same, this new world would be observationally indistinguishable from our world. The only thing that counts in the definition of worlds are the values of the dimensionless constants of Nature. If all masses were doubled in value you cannot tell because all the pure numbers defined by the ratios of any pair of masses are unchanged."

Anthropic principle

Some physicists have explored the notion that if the (dimensionless) fundamental physical constants had sufficiently different values, our universe would be so radically different that intelligent life would probably not have emerged, and that our universe therefore seems to be fine-tuned for intelligent life. The weak anthropic principle simply states that it is only because these fundamental constants acquired their respective values that there was sufficient order and richness in elemental diversity for life to have formed, which subsequently evolved the necessary intelligence toward observing that these constants have taken on the values they have. In physics, fundamental physical constants are physical constants that are independent of systems of units and are in general dimensionless numbers. ... The deepest visible-light image of the cosmos. ... In cosmology, the anthropic principle in its most basic form states the truism that any valid theory of the universe must be consistent with our existence as carbon-based human beings at this particular time and place in the universe. ...

Table of universal constants

Quantity	Symbol	Value	Relative Standard Uncertainty
characteristic impedance of vacuum		376.730 313 461... Ω	defined
electric constant (permittivity of free space)		8.854 187 817... × 10-12F·m-1	defined
magnetic constant (permeability of free space)		4π × 10-7 N·A-2 = 1.2566 370 614... × 10-6 N·A-2	defined
Newtonian constant of gravitation		6.6742(10) × 10-11m3·kg-1·s-2	1.5 × 10-4
Planck's constant		6.626 0693(11) × 10-34 J·s	1.7 × 10-7
Dirac's constant		1.054 571 68(18) × 10-34 J·s	1.7 × 10-7
speed of light in vacuum		299 792 458 m·s-1	defined

To meet Wikipedias quality standards, this article or section may require cleanup. ... The electric constant () is the permittivity of vacuum, a physical constant, defined by: where: - magnetic constant - speed of light In SI units, the value is exactly expressed by: = 2. ... Permittivity is a physical quantity that describes how an electric field affects and is affected by a dielectric medium and is determined by the ability of a material to polarize in response to an applied electric field, and thereby to cancel, partially, the field inside the material. ... The magnetic constant () is the permeability of vacuum. ... Permeability has several meanings: In electromagnetism, permeability is the degree of magnetisation of a material in response to a magnetic field. ... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ... A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ... Plancks constant, denoted h, is a physical constant that is used to describe the sizes of quanta. ... The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness. In metric units, c is exactly 299,792,458 metres per second (1,079,252,848. ... Look up Vacuum in Wiktionary, the free dictionary. ...

Table of electromagnetic constants

Quantity	Symbol	Value1 (SI units)	Relative Standard Uncertainty
Bohr magneton		927.400 949(80) × 10-26 J·T-1	8.6 × 10-8
conductance quantum		7.748 091 733(26) × 10-5 S	3.3 × 10-9
Coulomb's constant		8.987 742 438 × 109 N·m2C-2	defined
elementary charge		1.602 176 53(14) × 10-19 C	8.5 × 10-8
Josephson constant		483 597.879(41) × 109 Hz· V-1	8.5 × 10-8
magnetic flux quantum		2.067 833 72(18) × 10-15 Wb	8.5 × 10-8
nuclear magneton		5.050 783 43(43) × 10-27 J·T-1	8.6 × 10-8
resistance quantum		12 906.403 725(43) Ω	3.3 × 10-9
von Klitzing constant		25 812.807 449(86) Ω	3.3 × 10-9

Cover of brochure The International System of Units. ... In atomic physics, the Bohr magneton (symbol ) is named after the physicist Niels Bohr. ... The conductance quantum is the quantized unit of conductance. ... It has been suggested that this article or section be merged into Electrostatic force. ... The elementary charge (symbol e or sometimes q) is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron. ... Josephson junctions, first postulated by B. D. Josephson and first made by John Rowell and Philip Anderson, are quantum-mechanical circuit elements of superconducting devices. ... The magnetic flux quantum Φ0 is the quantum of magnetic flux passing through a superconductor. ... The nuclear magneton (symbol ), is a physical constant of magnetic moment, defined by: where: is the elementary charge, is the reduced Plancks constant, is the proton rest mass In the SI system of units its value is approximately: = 5. ... The quantum Hall effect is a quantum mechanical version of the Hall effect, observed in two-dimensional systems of electrons subjected to low temperatures and strong magnetic fields, in which the Hall conductance σ takes on the quantized values where e is the elementary charge and h is Plancks...

Table of atomic and nuclear constants

Quantity		Symbol	Value1 (SI units)	Relative Standard Uncertainty
Bohr radius			0.529 177 2108(18) × 10-10 m	3.3 × 10-9
Fermi coupling constant			1.166 39(1) × 10-5 GeV-2	8.6 × 10-6
fine-structure constant			7.297 352 568(24) × 10-3	3.3 × 10-9
Hartree energy			4.359 744 17(75) × 10-18 J	1.7 × 10-7
quantum of circulation			3.636 947 550(24) × 10-4 m2 s-1	6.7 × 10-9
Rydberg constant			10 973 731.568 525(73) m-1	6.6 × 10-12
Thomson cross section			0.665 245 873(13) × 10-28 m2	2.0 × 10-8
weak mixing angle			0.222 15(76)	3.4 × 10-3

Cover of brochure The International System of Units. ... In the Bohr model of the structure of an atom, put forward by Niels Bohr in 1913, electrons orbit a central nucleus. ... The fine-structure constant or Sommerfeld fine-structure constant, usually denoted , is the fundamental physical constant characterizing the strength of the electromagnetic interaction. ... A Hartree (symbol Eh) is the atomic unit of energy and is named after physicist Douglas Hartree. ... The Rydberg constant, named after physicist Janne Rydberg, is a physical constant discovered when measuring the spectrum of hydrogen, and building upon results from Anders Jonas Ångström and Johann Balmer. ... Cross section may refer to the following In geometry, Cross section is the intersection of a 3-dimensional body with a plane. ... The Weinberg angle or weak mixing angle is a parameter in the Abdus-Salam theory of the electroweak force. ...

Table of physico-chemical constants

Quantity		Symbol	Value1 (SI units)	Relative Standard Uncertainty
atomic mass unit (unified atomic mass unit)			1.660 538 86(28) × 10-27 kg	1.7 × 10-7
Avogadro's number			6.022 1415(10) × 1023	1.7 × 10-7
Boltzmann constant			1.380 6505(24) × 10-23 J·K-1	1.8 × 10-6
Faraday constant			96 485.3383(83)C·mol-1	8.6 × 10-8
first radiation constant			3.741 771 38(64) × 10-16 W·m2	1.7 × 10-7
	for spectral radiance		1.191 042 82(20) × 10-16 W · m2 sr-1	1.7 × 10-7
Loschmidt constant	at T=273.15 K and p=101.325 kPa		2.686 7773(47) × 1025 m-3	1.8 × 10-6
gas constant			8.314 472(15) J·K-1·mol-1	1.7 × 10-6
molar Planck constant			3.990 312 716(27) × 10-10 J · s · mol-1	6.7 × 10-9
molar volume of an ideal gas	at T=273.15 K and p=100 kPa		22.710 981(40) × 10-3 m3 ·mol-1	1.7 × 10-6
	at T=273.15 K and p=101.325 kPa		22.413 996(39) × 10-3 m3 ·mol-1	1.7 × 10-6
Sackur-Tetrode constant	at T=1 K and p=100 kPa		-1.151 7047(44)	3.8 × 10-6
	at T=1 K and p=101.325 kPa		-1.164 8677(44)	3.8 × 10-6
second radiation constant			1.438 7752(25) × 10-2 m·K	1.7 × 10-6
Stefan-Boltzmann constant			5.670 400(40) × 10-8 W·m-2·K-4	7.0 × 10-6
Wien displacement law constant		4.965 114 231...	2.897 7685(51) × 10-3 m · K	1.7 × 10-6

Cover of brochure The International System of Units. ... The unified atomic mass unit (u), or dalton (Da), is a small unit of mass used to express atomic and molecular masses. ... Avogadros number, also called Avogadros constant (NA) is a large constant used in chemistry and physics. ... Ludwig Boltzmann The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ... In physics and chemistry, the Faraday constant is the amount of electric charge of one mole of electrons. ... Avogadros number, also called Avogadros constant (NA), named after Amedeo Avogadro, is a constant used in chemistry and physics. ... The gas constant (also known as the universal or ideal gas constant, usually denoted by symbol R) is a physical constant used in equations of state to relate various groups of state functions to one another. ... An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of negligible volume, with no intermolecular forces. ... In a simple derivation based on the ideal gas law, the entropy S is not an extensive variable as it must be, leading to an apparent paradox known as the Gibbs paradox. ... The Stefan-Boltzmann constant (also Stefans constant), denoted with a Greek letter σ, is a derivable physical constant, the constant of proportionality between the total energy radiated per unit surface area of a black body in unit time and the fourth power of the thermodynamic temperature, as per the... The wavelength corresponding to the peak emission in various black body spectra as a function of temperature Wiens displacement law is a law of physics that states that there is an inverse relationship between the wavelength of the peak of the emission of a black body and its temperature. ...

Table of adopted values

Quantity		Symbol	Value (SI units)	Relative Standard Uncertainty
conventional value of Josephson constant2			483 597.9 × 109 Hz · V-1	defined
conventional value of von Klitzing constant3			25 812.807 Ω	defined
molar mass	constant		1 × 10-3 kg · mol-1	defined
	of carbon-12		12 × 10-3 kg · mol−1	defined
standard acceleration of gravity (gee, free fall on Earth)			9.806 65 m·s-2	defined
standard atmosphere			101 325 Pa	defined

Cover of brochure The International System of Units. ... The magnetic flux quantum Φ0 is the quantum of magnetic flux passing through a superconductor. ... The quantum Hall effect is a quantum mechanical version of the Hall effect, observed in two-dimensional systems of electrons subjected to low temperatures and strong magnetic fields, in which the Hall conductance σ takes on the quantized values where e is the elementary charge and h is Plancks... Carbon 12 is a stable isotope of the element carbon. ... Gravity is a force of attraction that acts between bodies that have mass. ... The acceleration due to gravity denoted g (also gee) is a non-SI unit of acceleration defined as exactly 9. ... Free fall in its strictest sense is the condition of acceleration which is due only to gravity. ...

Notes

¹The values are given in the so-called concise form; the number in brackets is the standard uncertainty, which is the value multiplied by the relative standard uncertainty.
²This is the value adopted internationally for realizing representations of the volt using the Josephson effect.
³This is the value adopted internationally for realizing representations of the ohm using the quantum Hall effect.
Josephson junction array chip developed by NIST as a standard volt. ... The Josephson effect is a term given to the phenomenon of current flow across two superconductors separated by a very thin insulating barrier. ... The ohm (symbol: Ω) is the SI unit of electric resistance. ... The quantum Hall effect is a quantum-mechanical version of the Hall effect, observed in two-dimensional systems of electrons subjected to low temperatures and strong magnetic fields, in which the Hall conductance σ takes on the quantized values where e is the elementary charge and h is Plancks constant. ...

See also

• Fundamental physical constant
• Astronomical constant
• Scientific constants named after people
• Fine-tuned universe
• Physical law
• CODATA
• Natural units
• Atomic units
• Planck units

In physics, fundamental physical constants are, in the strictest sense, physical constants that are independent of systems of units and hence are dimensionless numbers. ... An astronomical constant is a physical constant used in astronomy. ... This is a list of physical and mathematical constants named after people. ... The deepest visible-light image of the cosmos. ... A physical law, scientific law, or a law of nature is a scientific generalization based on empirical observations of physical behavior. ... CODATA (Committee on Data for Science and Technology) was established in 1966 as an interdisciplinary committee of the International Council of Science (ICSU), formerly the International Council of Scientific Unions. ... In physics, Planck units are physical units of measurement originally proposed by Max Planck. ... Atomic units (au) form a system of units convenient for electromagnetism, atomic physics, and quantum electrodynamics, especially when the focus is on the properties of electrons. ... In physics, Planck units are a system of physical units of measurement. ...

References

• CODATA Recommendations - 2002 CODATA Internationally recommended values of the Fundamental Physical Constants
• John D. Barrow, 2002. The Constants of Nature; From Alpha to Omega - The Numbers that Encode the Deepest Secrets of the Universe. Pantheon Books. ISBN 0-375-42221-8.