Gaussian units constitute a

metric system The metric system is a system of measurement that standardization, standardizes a set of base units and a nomenclature for describing relatively large and small quantities via decimal-based multiplicative unit prefixes. Though the rules gover ...

units of measurement A unit of measurement, or unit of measure, is a definite magnitude (mathematics), magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other qua ...

. This system is the most common of the several electromagnetic unit systems based on the

centimetre–gram–second system of units The centimetre–gram–second system of units (CGS or cgs) is a variant of the metric system based on the centimetre as the unit of length, the gram as the unit of mass, and the second as the unit of time. All CGS mechanical units are unamb ...

(CGS). It is also called the Gaussian unit system, Gaussian-cgs units, or often just cgs units. The term "cgs units" is ambiguous and therefore to be avoided if possible: there are several variants of CGS, which have conflicting definitions of electromagnetic quantities and units.

SI units The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official st ...

predominate in most fields, and continue to increase in popularity at the expense of Gaussian units. Alternative unit systems also exist. Conversions between quantities in the Gaussian and SI systems are direct unit conversions, because the quantities themselves are defined differently in each system. This means that the equations that express physical laws of electromagnetism—such as

Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, Electrical network, electr ...

—will change depending on the system of quantities that is employed. As an example, quantities that are

dimensionless Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that align with another sy ...

in one system may have dimension in the other.

Alternative unit systems

The Gaussian unit system is just one of several electromagnetic unit systems within CGS. Others include "

electrostatic units Electrostatics is a branch of physics that studies slow-moving or stationary electric charges. Since classical times, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word (), mean ...

", "

electromagnetic units In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...

", and

Heaviside–Lorentz units Heaviside–Lorentz units (or Lorentz–Heaviside units) constitute a system of units and quantities that extends the CGS with a particular set of equations that defines electromagnetic quantities, named for Oliver Heaviside and Hendrik Antoon L ...

. Some other unit systems are called "

natural units In physics, natural unit systems are measurement systems for which selected physical constants have been set to 1 through nondimensionalization of physical units. For example, the speed of light may be set to 1, and it may then be omitted, equa ...

", a category that includes

atomic units The atomic units are a system of natural units of measurement that is especially convenient for calculations in atomic physics and related scientific fields, such as computational chemistry and atomic spectroscopy. They were originally suggested ...

Planck units In particle physics and physical cosmology, Planck units are a system of units of measurement defined exclusively in terms of four universal physical constants: ''Speed of light, c'', ''Gravitational constant, G'', ''Reduced Planck constant, ħ ...

, and others. The

International System of Units The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official s ...

(SI), with the associated

International System of Quantities The International System of Quantities (ISQ) is a standard system of Quantity, quantities used in physics and in modern science in general. It includes basic quantities such as length and mass and the relationships between those quantities. This ...

(ISQ), is by far the most common system of units today. In

engineering Engineering is the practice of using natural science, mathematics, and the engineering design process to Problem solving#Engineering, solve problems within technology, increase efficiency and productivity, and improve Systems engineering, s ...

and practical areas, SI is nearly universal and has been for decades."CGS"
in ''How Many? A Dictionary of Units of Measurement'', by Russ Rowlett and the

University of North Carolina at Chapel Hill The University of North Carolina at Chapel Hill (UNC, UNC–Chapel Hill, or simply Carolina) is a public university, public research university in Chapel Hill, North Carolina, United States. Chartered in 1789, the university first began enrolli ...

In technical, scientific literature (such as

theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict List of natural phenomena, natural phenomena. This is in contrast to experimental p ...

and

astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...

), Gaussian units were predominant until recent decades, but are now getting progressively less so. The 8th SI Brochure mentions the CGS-Gaussian unit system, but the 9th SI Brochure makes no mention of CGS systems. Natural units may be used in more theoretical and abstract fields of physics, particularly

particle physics Particle physics or high-energy physics is the study of Elementary particle, fundamental particles and fundamental interaction, forces that constitute matter and radiation. The field also studies combinations of elementary particles up to the s ...

and

string theory In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...

Major differences between Gaussian and SI systems

"Rationalized" unit systems

One difference between the Gaussian and SI systems is in the factor in various formulas that relate the quantities that they define. With SI electromagnetic units, called ''rationalized'',Kowalski, Ludwik, 1986
"A Short History of the SI Units in Electricity"
''The Physics Teacher'' 24(2): 97–99
Alternate web link (subscription required)
/ref>

have no explicit factors of in the formulae, whereas the inverse-square force laws –

Coulomb's law Coulomb's inverse-square law, or simply Coulomb's law, is an experimental scientific law, law of physics that calculates the amount of force (physics), force between two electric charge, electrically charged particles at rest. This electric for ...

and the

Biot–Savart law In physics, specifically electromagnetism, the Biot–Savart law ( or ) is an equation describing the magnetic field generated by a constant electric current. It relates the magnetic field to the magnitude, direction, length, and proximity of the ...

– have a factor of attached to the . With Gaussian units, called ''unrationalized'' (and unlike

), the situation is reversed: two of Maxwell's equations have factors of in the formulas, while both of the inverse-square force laws, Coulomb's law and the Biot–Savart law, have no factor of attached to in the denominator. (The quantity appears because is the surface area of the sphere of radius , which reflects the geometry of the configuration. For details, see the articles '' Relation between Gauss's law and Coulomb's law'' and ''

Inverse-square law In science, an inverse-square law is any scientific law stating that the observed "intensity" of a specified physical quantity is inversely proportional to the square of the distance from the source of that physical quantity. The fundamental ca ...

''.)

Unit of charge

A major difference between the Gaussian system and the ISQ is in the respective definitions of the quantity charge. In the ISQ, a separate base dimension, electric current, with the associated SI unit, the

ampere The ampere ( , ; symbol: A), often shortened to amp,SI supports only the use of symbols and deprecates the use of abbreviations for units. is the unit of electric current in the International System of Units (SI). One ampere is equal to 1 c ...

, is associated with electromagnetic phenomena, with the consequence that a unit of electrical charge (1

coulomb The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI). It is defined to be equal to the electric charge delivered by a 1 ampere current in 1 second, with the elementary charge ''e'' as a defining c ...

= 1 ampere × 1 second) is a physical quantity that cannot be expressed purely in terms of the mechanical units (kilogram, metre, second). On the other hand, in the Gaussian system, the unit of electric charge (the

statcoulomb The statcoulomb (statC), franklin (Fr), or electrostatic unit of charge (esu) is the unit of measurement for electrical charge used in the centimetre–gram–second electrostatic units variant (CGS-ESU) and Gaussian systems of units. In term ...

, statC) be written entirely as a dimensional combination of the non-electrical base units (gram, centimetre, second), as: For example,

in Gaussian units has no constant:

F = \frac ,

where is the repulsive force between two electrical charges, and are the two charges in question, and is the distance separating them. If and are expressed in

statC The statcoulomb (statC), franklin (Fr), or electrostatic unit of charge (esu) is the unit of measurement for electrical charge used in the centimetre–gram–second electrostatic units variant (CGS-ESU) and Gaussian systems of units. In term ...

and in

centimetre upright=1.35, Different lengths as in respect to the electromagnetic spectrum, measured by the metre and its derived scales. The microwave is in-between 1 meter to 1 millimeter. A centimetre (International spelling) or centimeter (American ...

s, then the unit of that is coherent with these units is the

dyne The dyne (symbol: dyn; ) is a derived units of measurement, unit of force (physics), force specified in the centimetre–gram–second system of units, centimetre–gram–second (CGS) system of units, a predecessor of the modern International S ...

. The same law in the ISQ is:

F = \frac \frac

where is the

vacuum permittivity Vacuum permittivity, commonly denoted (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric const ...

, a quantity that is not dimensionless: it has dimension ( charge)² (

time Time is the continuous progression of existence that occurs in an apparently irreversible process, irreversible succession from the past, through the present, and into the future. It is a component quantity of various measurements used to sequ ...

)² (

mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...

)⁻¹ (

length Length is a measure of distance. In the International System of Quantities, length is a quantity with Dimension (physical quantity), dimension distance. In most systems of measurement a Base unit (measurement), base unit for length is chosen, ...

)⁻³. Without , the equation would be dimensionally inconsistent with the quantities as defined in the ISQ, whereas the quantity does not appear in Gaussian equations. This is an example of how some dimensional

physical constant A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that cannot be explained by a theory and therefore must be measured experimentally. It is distinct from a mathematical constant, which has a ...

s can be eliminated from the expressions of

physical law Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena. The term ''law'' has diverse usage in many cases (approximate, accurate, broad, or narrow) ...

by the choice of definition of quantities. In the ISQ, converts or scales electric flux density, , to the corresponding

electric field An electric field (sometimes called E-field) is a field (physics), physical field that surrounds electrically charged particles such as electrons. In classical electromagnetism, the electric field of a single charge (or group of charges) descri ...

, (the latter has dimension of

force In physics, a force is an influence that can cause an Physical object, object to change its velocity unless counterbalanced by other forces. In mechanics, force makes ideas like 'pushing' or 'pulling' mathematically precise. Because the Magnitu ...

per charge), while in the Gaussian system, electric flux density is the same quantity as electric field strength in

free space A vacuum (: vacuums or vacua) is space devoid of matter. The word is derived from the Latin adjective (neuter ) meaning "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressur ...

aside from a dimensionless constant factor. In the Gaussian system, the

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...

appears directly in electromagnetic formulas like

(see below), whereas in the ISQ it appears via the product .

Units for magnetism

In the Gaussian system, unlike the ISQ, the electric field and the

magnetic field A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular ...

have the same dimension. This amounts to a factor of between how is defined in the two unit systems, on top of the other differences. (The same factor applies to other magnetic quantities such as the

, , and

magnetization In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Accordingly, physicists and engineers usually define magnetization as the quanti ...

, .) For example, in a planar light wave in vacuum, in Gaussian units, while in the ISQ.

Polarization, magnetization

There are further differences between Gaussian system and the ISQ in how quantities related to polarization and magnetization are defined. For one thing, in the Gaussian system, ''all'' of the following quantities have the same dimension: , , , , , and . A further point is that the

electric Electricity is the set of physical phenomena associated with the presence and motion of matter possessing an electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by Maxwel ...

and

magnetic susceptibility In electromagnetism, the magnetic susceptibility (; denoted , chi) is a measure of how much a material will become magnetized in an applied magnetic field. It is the ratio of magnetization (magnetic moment per unit volume) to the applied magnet ...

of a material is dimensionless in both the Gaussian system and the ISQ, but a given material will have a different numerical susceptibility in the two systems. (Equation is given below.)

List of equations

This section has a list of the basic formulae of electromagnetism, given in both the Gaussian system and the International System of Quantities (ISQ). Most symbol names are not given; for complete explanations and definitions, please click to the appropriate dedicated article for each equation. A simple conversion scheme for use when tables are not available may be found in Garg (2012).A. Garg, 2012, "Classical Electrodynamics in a Nutshell" (Princeton University Press). All formulas except otherwise noted are from Ref.

Maxwell's equations

Here are Maxwell's equations, both in macroscopic and microscopic forms. Only the "differential form" of the equations is given, not the "integral form"; to get the integral forms apply the

divergence theorem In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, reprinted in is a theorem relating the '' flux'' of a vector field through a closed surface to the ''divergence'' of the field in the volume ...

Kelvin–Stokes theorem Stokes' theorem, also known as the Kelvin–Stokes theorem after Lord Kelvin and George Stokes, the fundamental theorem for curls, or simply the curl theorem, is a theorem in vector calculus on \R^3. Given a vector field, the theorem relates th ...

Other basic laws

Dielectric and magnetic materials

Below are the expressions for the various fields in a dielectric medium. It is assumed here for simplicity that the medium is homogeneous, linear, isotropic, and nondispersive, so that the

permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter (epsilon), is a measure of the electric polarizability of a dielectric material. A material with high permittivity polarizes more ...

is a simple constant. where * and are the

and displacement field, respectively; * is the polarization density; *

\varepsilon

is the

; *

\varepsilon_0

is the permittivity of vacuum (used in the SI system, but meaningless in Gaussian units); and *

\chi_\mathrm

is the

electric susceptibility In electricity (electromagnetism), the electric susceptibility (\chi_; Latin: ''susceptibilis'' "receptive") is a dimensionless proportionality constant that indicates the degree of polarization of a dielectric material in response to an applie ...

. The quantities

\varepsilon^

and

\varepsilon^/\varepsilon_0

are both dimensionless, and they have the same numeric value. By contrast, the

\chi_\mathrm^

and

\chi_\mathrm^

are both unitless, but have for the same material:

4\pi \chi_\mathrm^ = \chi_\mathrm^\,.

Next, here are the expressions for the various fields in a magnetic medium. Again, it is assumed that the medium is homogeneous, linear, isotropic, and nondispersive, so that the permeability is a simple constant. where * and are the

s; * is

; *

\mu

magnetic permeability In electromagnetism, permeability is the measure of magnetization produced in a material in response to an applied magnetic field. Permeability is typically represented by the (italicized) Greek letter ''μ''. It is the ratio of the magnetic ...

; *

\mu_0

is the permeability of vacuum (used in the SI system, but meaningless in Gaussian units); and *

\chi_\mathrm

is the

. The quantities

\mu^

and

\mu^/\mu_0

are both dimensionless, and they have the same numeric value. By contrast, the

\chi_\mathrm^

and

\chi_\mathrm^

are both unitless, but has in the two systems for the same material:

4\pi \chi_\mathrm^ = \chi_\mathrm^

Vector and scalar potentials

The electric and magnetic fields can be written in terms of a vector potential and a scalar potential :

Electrical circuit

where * is the

electric charge Electric charge (symbol ''q'', sometimes ''Q'') is a physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative''. Like charges repel each other and ...

* is the

electric current An electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is defined as the net rate of flow of electric charge through a surface. The moving particles are called charge c ...

* is the

electric potential Electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as electric potential energy per unit of electric charge. More precisely, electric potential is the amount of work (physic ...

* is the

magnetic flux In physics, specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B over that surface. It is usually denoted or . The SI unit of magnetic flux is the we ...

* is the

electrical resistance The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual paral ...

* is the

capacitance Capacitance is the ability of an object to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are two closely related ...

* is the

inductance Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The electric current produces a magnetic field around the conductor. The magnetic field strength depends on the magnitude of the ...

Fundamental constants

Electromagnetic unit names

{, class="wikitable plainrowheaders defaultcenter col5left" , + Table 1: Common electromagnetism units in SI vs Gaussian ! scope="col" , Quantity ! scope="col" , Symbol ! scope="col" , SI unit ! scope="col" , Gaussian unit(in base units) ! scope="col" , Conversion factor , - ! scope="row" ,

Electric charge Electric charge (symbol ''q'', sometimes ''Q'') is a physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative''. Like charges repel each other and ...

, , C , Fr(cm^3/2⋅g^1/2⋅s⁻¹) ,

\frac{q^{_\mathrm{G}{q^{_\mathrm{I} = \frac{1}{\sqrt{4\pi\varepsilon_0 \approx \frac{2.998 \times 10^9 \, \mathrm{Fr{1\, \mathrm{C

, - ! scope="row" ,

Electric current An electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is defined as the net rate of flow of electric charge through a surface. The moving particles are called charge c ...

, , A , statA(cm^3/2⋅g^1/2⋅s⁻²) ,

\frac{I^{_\mathrm{G}{I^{_\mathrm{I} = \frac{1}{\sqrt{4\pi\varepsilon_0 \approx \frac{2.998 \times 10^9 \, \mathrm{statA{1\, \mathrm{A

, - ! scope="row" ,

Electric potential Electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as electric potential energy per unit of electric charge. More precisely, electric potential is the amount of work (physic ...

Voltage Voltage, also known as (electrical) potential difference, electric pressure, or electric tension, is the difference in electric potential between two points. In a Electrostatics, static electric field, it corresponds to the Work (electrical), ...

, , V , statV(cm^1/2⋅g^1/2⋅s⁻¹) ,

\frac{V^{_\mathrm{G}{V^{_\mathrm{I} = \sqrt{4\pi\varepsilon_0} \approx \frac{1\, \mathrm{statV{2.998 \times 10^2 \, \mathrm{V

, - ! scope="row" ,

Electric field An electric field (sometimes called E-field) is a field (physics), physical field that surrounds electrically charged particles such as electrons. In classical electromagnetism, the electric field of a single charge (or group of charges) descri ...

, , V/ m , statV/ cm(cm^−1/2⋅g^1/2⋅s⁻¹) ,

\frac{\mathbf{E}^{_\mathrm{G}{\mathbf{E}^{_\mathrm{I} = \sqrt{4\pi\varepsilon_0} \approx \frac{1 \, \mathrm{statV/cm{2.998 \times 10^4 \, \mathrm{V/m

, - ! scope="row" , Electric displacement field , , C/ m² , Fr/ cm²(cm^−1/2g^1/2s⁻¹) ,

\frac{\mathbf{D}^{_\mathrm{G}{\mathbf{D}^{_\mathrm{I} = \sqrt{\frac{4\pi}{\varepsilon_0 \approx \frac{4\pi\times 2.998 \times 10^5 \, \mathrm{Fr/cm}^2}{ 1 \, \mathrm{C/m}^2}

, - ! scope="row" ,

Electric dipole moment The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system: that is, a measure of the system's overall Chemical polarity, polarity. The International System of Units, SI unit for electric ...

, , C⋅ m , Fr⋅ cm(cm^5/2⋅g^1/2⋅s⁻¹) ,

\frac{\mathbf{p}^{_\mathrm{G}{\mathbf{p}^{_\mathrm{I} = \frac{1}{\sqrt{4\pi\varepsilon_0 \approx \frac{2.998 \times 10^{11} \, \mathrm{Fr}{\cdot}\mathrm{cm{1 \, \mathrm{C}{\cdot}\mathrm{m

, - ! scope="row" ,

Electric flux In electromagnetism, electric flux is the total electric field that crosses a given surface. The electric flux through a closed surface is directly proportional to the total charge contained within that surface. The electric field E can exert ...

, , C , Fr(cm^3/2⋅g^1/2⋅s⁻¹) ,

\frac{\Phi^{_\mathrm{G_{\mathrm{e}{\Phi^{_\mathrm{I_{\mathrm{e} = \sqrt{\frac{4\pi}{\varepsilon_0 \approx \frac{4\pi\times 2.998 \times 10^9 \, \mathrm{Fr{1 \, \mathrm{C

, - ! scope="row" ,

Permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter (epsilon), is a measure of the electric polarizability of a dielectric material. A material with high permittivity polarizes more ...

, , F/ m , cm/cm ,

\frac{\varepsilon^{_\mathrm{G}{\varepsilon^{_\mathrm{I} = \frac{1}{\varepsilon_0} \approx \frac{4\pi \times 2.998^2 \times 10^{9} \, \mathrm{cm/cm{1 \, \mathrm{F/m

, - ! scope="row" , Magnetic B field , , T , G(cm^−1/2⋅g^1/2⋅s⁻¹) ,

\frac{\mathbf{B}^{_\mathrm{G}{\mathbf{B}^{_\mathrm{I} = \sqrt{\frac{4\pi}{\mu_0 \approx \frac{10^4 \, \mathrm{G{1 \, \mathrm{T

, - ! scope="row" , Magnetic H field , , A/ m , Oe(cm^−1/2⋅g^1/2⋅s⁻¹) ,

\frac{\mathbf{H}^{_\mathrm{G}{\mathbf{H}^{_\mathrm{I} = \sqrt{4\pi\mu_0} \approx \frac{4\pi \times 10^{-3} \, \mathrm{Oe{1 \, \mathrm{A/m

, - ! scope="row" ,

Magnetic dipole moment In electromagnetism, the magnetic moment or magnetic dipole moment is the combination of strength and orientation of a magnet or other object or system that exerts a magnetic field. The magnetic dipole moment of an object determines the magnitude ...

, , A⋅ m² ,

erg The erg is a unit of energy equal to 10−7joules (100Nano-, nJ). It is not an SI unit, instead originating from the centimetre–gram–second system of units (CGS). Its name is derived from (), a Greek language, Greek word meaning 'work' or ' ...

/ G(cm^5/2⋅g^1/2⋅s⁻¹) ,

\frac{\mathbf{m}^{_\mathrm{G}{\mathbf{m}^{_\mathrm{I} = \sqrt{\frac{\mu_0}{4\pi \approx \frac{10^3 \, \mathrm{erg/G{1 \, \mathrm{A}{\cdot}\mathrm{m}^2}

, - ! scope="row" ,

Magnetic flux In physics, specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B over that surface. It is usually denoted or . The SI unit of magnetic flux is the we ...

, , Wb , Mx(cm^3/2⋅g^1/2⋅s⁻¹) ,

\frac{\Phi^{_\mathrm{G_{\mathrm{m}{\Phi^{_\mathrm{I_{\mathrm{m} = \sqrt{\frac{4\pi}{\mu_0 \approx \frac{10^8 \, \mathrm{Mx{1 \, \mathrm{Wb

, - ! scope="row" , Permeability , , H/ m , cm/cm ,

\frac{\mu^{_\mathrm{G}{\mu^{_\mathrm{I} = \frac{1}{\mu_0} \approx \frac{1 \, \mathrm{cm/cm{4\pi \times 10^{-7} \, \mathrm{H/m

, - ! scope="row" , Magnetomotive force ,

\mathcal F

, A , Gi(cm^1/2⋅g^1/2⋅s⁻¹) ,

\frac{\mathcal F^{_\mathrm{G}{\mathcal F^{_\mathrm{I} = \sqrt{4\pi\mu_0} \approx \frac{4\pi \times 10^{-1} \, \mathrm{Gi{1 \, \mathrm{A

, - ! scope="row" ,

Magnetic reluctance Magnetic reluctance, or magnetic resistance, is a concept used in the analysis of magnetic circuits. It is defined as the ratio of magnetomotive force (mmf) to magnetic flux. It represents the opposition to magnetic flux, and depends on the ...

\mathcal R

, H⁻¹ , Gi/ Mx(cm⁻¹) ,

\frac{\mathcal R^{_\mathrm{G}{\mathcal R^{_\mathrm{I} = \mu_0 \approx \frac{4\pi \times 10^{-9} \, \mathrm{Gi/Mx{1 \, \mathrm{H}^{-1

, - ! scope="row" , Resistance , , Ω , s/ cm ,

\frac{R^{_\mathrm{G}{R^{_\mathrm{I} = 4\pi\varepsilon_0 \approx \frac{1 \, \mathrm{s/cm{2.998^2 \times 10^{11}  \, \Omega}

, - ! scope="row" ,

Resistivity Electrical resistivity (also called volume resistivity or specific electrical resistance) is a fundamental specific property of a material that measures its electrical resistance or how strongly it resists electric current. A low resistivity i ...

, , Ω⋅ m , s ,

\frac{\rho^{_\mathrm{G}{\rho^{_\mathrm{I} = 4\pi\varepsilon_0 \approx \frac{1 \, \mathrm{s{2.998^2 \times 10^{9}  \, \Omega{\cdot}\mathrm{m

, - ! scope="row" ,

Capacitance Capacitance is the ability of an object to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are two closely related ...

, , F , cm ,

\frac{C^{_\mathrm{G}{C^{_\mathrm{I} = \frac{1}{4\pi\varepsilon_0} \approx \frac{2.998^2 \times 10^{11} \, \mathrm{cm{1 \, \mathrm{F

, - ! scope="row" ,

Inductance Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The electric current produces a magnetic field around the conductor. The magnetic field strength depends on the magnitude of the ...

, , H , s²/ cm ,

\frac{L^{_\mathrm{G}{L^{_\mathrm{I} = 4\pi\varepsilon_0 \approx \frac{1 \, \mathrm{s}^2/\mathrm{cm{2.998^2 \times 10^{11} \, \mathrm{H

Note: The SI quantities

\varepsilon_0

and

\mu_0

satisfy . The conversion factors are written both symbolically and numerically. The numerical conversion factors can be derived from the symbolic conversion factors by dimensional analysis. For example, the top row says \approx {2.998 \times 10^9 \,\mathrm{Fr \,/\, {1\,\mathrm{C, a relation which can be verified with dimensional analysis, by expanding

\varepsilon_0

and

s (C) in

SI base units The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which all ...

, and expanding

s (or franklins, Fr) in Gaussian base units. It is surprising to think of measuring capacitance in centimetres. One useful example is that a centimetre of capacitance is the capacitance between a sphere of radius 1 cm in vacuum and infinity. Another surprising unit is measuring

resistivity Electrical resistivity (also called volume resistivity or specific electrical resistance) is a fundamental specific property of a material that measures its electrical resistance or how strongly it resists electric current. A low resistivity i ...

in units of seconds. A physical example is: Take a parallel-plate capacitor, which has a "leaky" dielectric with permittivity 1 but a finite resistivity. After charging it up, the capacitor will discharge itself over time, due to current leaking through the dielectric. If the resistivity of the dielectric is seconds, the half-life of the discharge is seconds. This result is independent of the size, shape, and charge of the capacitor, and therefore this example illuminates the fundamental connection between resistivity and time units.

Dimensionally equivalent units

A number of the units defined by the table have different names but are in fact dimensionally equivalent – i.e., they have the same expression in terms of the base units cm, g, s. (This is analogous to the distinction in SI between

newton-metre The newton-metre or newton-meter (also non-hyphenated, newton metre or newton meter; symbol N⋅m or N m) is the unit of torque (also called ) in the International System of Units (SI). One newton-metre is equal to the torque resulting fr ...

and

joule The joule ( , or ; symbol: J) is the unit of energy in the International System of Units (SI). In terms of SI base units, one joule corresponds to one kilogram- metre squared per second squared One joule is equal to the amount of work d ...

.) The different names help avoid ambiguities and misunderstandings as to what physical quantity is being measured. In particular, of the following quantities are dimensionally equivalent in Gaussian units, but they are nevertheless given different unit names as follows: {, class="wikitable plainrowheaders" style="text-align: center;" , + Dimensionally equivalent units , - ! scope="col" , Quantity ! scope="col" , Gaussian symbol ! scope="col" , In Gaussian
base units ! scope="col" , Gaussian unit
of measure , - ! scope="row" ,

, , cm^−1/2⋅g^1/2⋅s⁻¹ , statV/cm , - ! scope="row" , Electric displacement field , , cm^−1/2⋅g^1/2⋅s⁻¹ ,

/cm² , - ! scope="row" , Polarization density , , cm^−1/2⋅g^1/2⋅s⁻¹ ,

/cm² , - ! scope="row" ,

Magnetic flux density A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular ...

, , cm^−1/2⋅g^1/2⋅s⁻¹ , G , - ! scope="row" , Magnetizing field , , cm^−1/2⋅g^1/2⋅s⁻¹ , Oe , - ! scope="row" ,

Magnetization In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Accordingly, physicists and engineers usually define magnetization as the quanti ...

, , cm^−1/2⋅g^1/2⋅s⁻¹ , dyn/ Mx

General rules to translate a formula

Any formula can be converted between Gaussian and SI units by using the symbolic conversion factors from Table 1 above. For example, the electric field of a stationary point charge has the ISQ formula

\mathbf{E}^{_\mathrm{I = \frac{q^{_\mathrm{I}{4\pi \varepsilon_0 r^2} \hat{\mathbf{r ,

where is distance, and the "" superscript indicates that the electric field and charge are defined as in the ISQ. If we want the formula to instead use the Gaussian definitions of electric field and charge, we look up how these are related using Table 1, which says:

\begin{align}
\frac{\mathbf{E}^{_\mathrm{G}{\mathbf{E}^{_\mathrm{I} &= \sqrt{4\pi\varepsilon_0}\,, \\
\frac{q^{_\mathrm{G}{q^{_\mathrm{I} &= \frac{1}{\sqrt{4\pi\varepsilon_0\,.
\end{align}

Therefore, after substituting and simplifying, we get the Gaussian-system formula:

\mathbf{E}^{_\mathrm{G = \frac{q^{_\mathrm{G}{r^2}\hat{\mathbf{r\,,

which is the correct Gaussian-system formula, as mentioned in a previous section. For convenience, the table below has a compilation of the symbolic conversion factors from Table 1. To convert any formula from the Gaussian system to the ISQ using this table, replace each symbol in the Gaussian column by the corresponding expression in the SI column (vice versa to convert the other way). Replace

1/c^2

\varepsilon_0 \mu_0

(or vice versa). This will reproduce any of the specific formulas given in the list above, such as Maxwell's equations, as well as any other formula not listed. {, class="wikitable plainrowheaders" , + Table 2A: Replacement rules for translating formulas from Gaussian to ISQ , - ! scope="col" , Name ! scope="col" , Gaussian system ! scope="col" , , - ! scope="row" ,

electromotive force In electromagnetism and electronics, electromotive force (also electromotance, abbreviated emf, denoted \mathcal) is an energy transfer to an electric circuit per unit of electric charge, measured in volts. Devices called electrical ''transducer ...

\left(\mathbf{E}^{_\mathrm{G, \varphi^{_\mathrm{G, \mathcal E^{_\mathrm{G\right)

\sqrt{4\pi\varepsilon_0}\left(\mathbf{E}^{_\mathrm{I, \varphi^{_\mathrm{I, \mathcal E^{_\mathrm{I\right)

, - ! scope="row" , electric displacement field ,

\mathbf{D}^{_\mathrm{G

\sqrt{\frac{4\pi}{\varepsilon_0\mathbf{D}^{_\mathrm{I

, - ! scope="row" , charge,

charge density In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in co ...

, current,

current density In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional ...

, polarization density,

electric dipole moment The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system: that is, a measure of the system's overall Chemical polarity, polarity. The International System of Units, SI unit for electric ...

\left(q^{_\mathrm{G, \rho^{_\mathrm{G, I^{_\mathrm{G, \mathbf{J}^{_\mathrm{G,\mathbf{P}^{_\mathrm{G, \mathbf{p}^{_\mathrm{G\right)

\frac{1}{\sqrt{4\pi\varepsilon_0\left(q^{_\mathrm{I, \rho^{_\mathrm{I, I^{_\mathrm{I, \mathbf{J}^{_\mathrm{I,\mathbf{P}^{_\mathrm{I,\mathbf{p}^{_\mathrm{I\right)

, - ! scope="row" , magnetic field,

magnetic vector potential In classical electromagnetism, magnetic vector potential (often denoted A) is the vector quantity defined so that its curl is equal to the magnetic field, B: \nabla \times \mathbf = \mathbf. Together with the electric potential ''φ'', the ma ...

\left(\mathbf{B}^{_\mathrm{G, \Phi_\mathrm{m}^{_\mathrm{G,\mathbf{A}^{_\mathrm{G\right)

\sqrt{\frac{4\pi}{\mu_0\left(\mathbf{B}^{_\mathrm{I, \Phi_\mathrm{m}^{_\mathrm{I,\mathbf{A}^{_\mathrm{I\right)

, - ! scope="row" , magnetic field,

magnetic scalar potential Magnetic scalar potential, ''ψ'', is a quantity in classical electromagnetism analogous to electric potential. It is used to specify the magnetic H-field in cases when there are no free currents, in a manner analogous to using the electric ...

, magnetomotive force ,

\left(\mathbf{H}^{_\mathrm{G, \psi^{_\mathrm{G, \mathcal F^{_\mathrm{G\right)

\sqrt{4\pi\mu_0}\left(\mathbf{H}^{_\mathrm{I, \psi^{_\mathrm{I, \mathcal F^{_\mathrm{I\right)

, - ! scope="row" ,

magnetic moment In electromagnetism, the magnetic moment or magnetic dipole moment is the combination of strength and orientation of a magnet or other object or system that exerts a magnetic field. The magnetic dipole moment of an object determines the magnitude ...

, magnetic pole strength ,

\left(\mathbf{m}^{_\mathrm{G, \mathbf{M}^{_\mathrm{G, p^{_\mathrm{G\right)

\sqrt{\frac{\mu_0}{4\pi\left(\mathbf{m}^{_\mathrm{I, \mathbf{M}^{_\mathrm{I, p^{_\mathrm{I\right)

, - ! scope="row" ,

,
permeability ,

\left(\varepsilon^{_\mathrm{G, \mu^{_\mathrm{G\right)

\left(\frac{\varepsilon^{_\mathrm{I}{\varepsilon_0}, \frac{\mu^{_\mathrm{I}{\mu_0}\right)

, - ! scope="row" ,

\left(\chi_\mathrm{e}^{_\mathrm{G, \chi_\mathrm{m}^{_\mathrm{G\right)

\frac{1}{4\pi}\left(\chi_\mathrm{e}^{_\mathrm{I, \chi_\mathrm{m}^{_\mathrm{I\right)

, - ! scope="row" , conductivity, conductance,

\left(\sigma^{_\mathrm{G, S^{_\mathrm{G, C^{_\mathrm{G\right)

\frac{1}{4\pi\varepsilon_0}\left(\sigma^{_\mathrm{I,S^{_\mathrm{I,C^{_\mathrm{I\right)

, - ! scope="row" ,

, resistance,

, memristance, impedance ,

\left(\rho^{_\mathrm{G,R^{_\mathrm{G,L^{_\mathrm{G,M^{_\mathrm{G,Z^{_\mathrm{G\right)

4\pi\varepsilon_0\left(\rho^{_\mathrm{I,R^{_\mathrm{I,L^{_\mathrm{I,M^{_\mathrm{I,Z^{_\mathrm{I\right)

, - ! scope="row" ,

magnetic reluctance Magnetic reluctance, or magnetic resistance, is a concept used in the analysis of magnetic circuits. It is defined as the ratio of magnetomotive force (mmf) to magnetic flux. It represents the opposition to magnetic flux, and depends on the ...

\mathcal{R}^{_\mathrm{G

\mu_0\mathcal{R}^{_\mathrm{I

{, class="wikitable plainrowheaders" , + Table 2B: Replacement rules for translating formulas from ISQ to Gaussian , - ! scope="col" , Name ! scope="col" , ! scope="col" , Gaussian system , - ! scope="row" ,