Gaussian units constitute ametric system ofunits of measurement. This system is the most common of the several electromagnetic unit systems based on thecentimetre–gram–second system of units (CGS). It is also called theGaussian unit system,Gaussian-cgs units, or often justcgs units.^[a] 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 predominate in most fields, and continue to increase in popularity at the expense of Gaussian units.^[1][b] Alternative unit systems also exist. Conversions between quantities in the Gaussian and SI systems arenot 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 asMaxwell's equations—will change depending on the system of quantities that is employed. As an example, quantities that aredimensionless in one system may have dimension in the other.

The Gaussian unit system is just one of several electromagnetic unit systems within CGS. Others include "electrostatic units", "electromagnetic units", andHeaviside–Lorentz units.

Some other unit systems are called "natural units", a category that includesatomic units,Planck units, and others.

TheInternational System of Units (SI), with the associatedInternational System of Quantities (ISQ), is by far the most common system of units today. Inengineering and practical areas, SI is nearly universal and has been for decades.^[1] In technical, scientific literature (such astheoretical physics andastronomy), Gaussian units were predominant until recent decades, but are now getting progressively less so.^[1][b] The 8th SI Brochure mentions the CGS-Gaussian unit system,^[2] but the 9th SI Brochure makes no mention of CGS systems.

Natural units may be used in more theoretical and abstract fields of physics, particularlyparticle physics andstring theory.

One difference between the Gaussian and SI systems is in the factor4π in various formulas that relate the quantities that they define. With SI electromagnetic units, calledrationalized,^[3][4]Maxwell's equations have no explicit factors of4π in the formulae, whereas theinverse-square force laws –Coulomb's law and theBiot–Savart law –do have a factor of4π attached to ther². With Gaussian units, calledunrationalized (and unlikeHeaviside–Lorentz units), the situation is reversed: two of Maxwell's equations have factors of4π in the formulas, while both of the inverse-square force laws, Coulomb's law and the Biot–Savart law, have no factor of4π attached tor² in the denominator.

(The quantity4π appears because4πr² is thesurface area of the sphere of radiusr, which reflects the geometry of the configuration. For details, see the articlesRelation between Gauss's law and Coulomb's law andInverse-square law.)

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, theampere, is associated with electromagnetic phenomena, with the consequence that a unit of electrical charge (1 coulomb = 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 (thestatcoulomb, statC)can be written entirely as a dimensional combination of the non-electrical base units (gram, centimetre, second), as:

For example,Coulomb's law in Gaussian units has no constant:$${\displaystyle F=\frac{Q_1^{{}_{\mathrm{G}}}{Q}_2^{{}_{\mathrm{G}}}}{r^2},}$$whereF is the repulsive force between two electrical charges,Q^G
₁ andQ^G
₂ are the two charges in question, andr is the distance separating them. IfQ^G
₁ andQ^G
₂ are expressed instatC andr incentimetres, then the unit ofF that is coherent with these units is thedyne.

The same law in the ISQ is:$${\displaystyle F=\frac{1}{4\pi {\epsilon }_0}\frac{Q_1^{{}_{\mathrm{I}}}{Q}_2^{{}_{\mathrm{I}}}}{r^2}}$$whereε₀ is thevacuum permittivity, a quantity that is not dimensionless: it has dimension (charge)² (time)² (mass)⁻¹ (length)⁻³. Withoutε₀, the equation would be dimensionally inconsistent with the quantities as defined in the ISQ, whereas the quantityε₀ does not appear in Gaussian equations. This is an example of how some dimensionalphysical constants can be eliminated from the expressions ofphysical law by the choice of definition of quantities. In the ISQ,1/ε₀ converts or scaleselectric flux density,D, to the correspondingelectric field,E (the latter has dimension offorce percharge), while in the Gaussian system, electric flux density is the same quantity as electric field strength infree space aside from a dimensionless constant factor.

In the Gaussian system, thespeed of lightc appears directly in electromagnetic formulas likeMaxwell's equations (see below), whereas in the ISQ it appears via the productμ₀ε₀ = 1/c².

In the Gaussian system, unlike the ISQ, the electric fieldE^G and themagnetic fieldB^G have the same dimension. This amounts to a factor ofc between howB is defined in the two unit systems, on top of the other differences.^[3] (The same factor applies to other magnetic quantities such as themagnetic field,H, andmagnetization,M.) For example, in aplanar light wave in vacuum,|E^G(r,t)| = |B^G(r,t)| in Gaussian units, while|E^I(r,t)| =c |B^I(r,t)| in the ISQ.

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:E^G,D^G,P^G,B^G,H^G, andM^G. A further point is that theelectric andmagnetic susceptibility 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.)

This section has a list of the basic formulae of electromagnetism, given in both the Gaussian system and theInternational 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).^[5]All formulas except otherwise noted are from Ref.^[3]

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 thedivergence theorem orKelvin–Stokes theorem.

Maxwell's equations in Gaussian system and ISQ

Name	Gaussian system	ISQ
Gauss's law (macroscopic)	${\displaystyle \mathrm{\nabla }\cdot {\mathbf{D}}^{{}_{\mathrm{G}}}=4\pi {\rho }_{\mathrm{f}}^{{}_{\mathrm{G}}}}$	${\displaystyle \mathrm{\nabla }\cdot {\mathbf{D}}^{{}_{\mathrm{I}}}={\rho }_{\mathrm{f}}^{{}_{\mathrm{I}}}}$
Gauss's law (microscopic)	${\displaystyle \mathrm{\nabla }\cdot {\mathbf{E}}^{{}_{\mathrm{G}}}=4\pi {\rho }^{{}_{\mathrm{G}}}}$	${\displaystyle \mathrm{\nabla }\cdot {\mathbf{E}}^{{}_{\mathrm{I}}}=\frac{1}{{\epsilon }_0}{\rho }^{{}_{\mathrm{I}}}}$
Gauss's law for magnetism	${\displaystyle \mathrm{\nabla }\cdot {\mathbf{B}}^{{}_{\mathrm{G}}}=0}$	${\displaystyle \mathrm{\nabla }\cdot {\mathbf{B}}^{{}_{\mathrm{I}}}=0}$
Maxwell–Faraday equation (Faraday's law of induction)	${\displaystyle \mathrm{\nabla }\times {\mathbf{E}}^{{}_{\mathrm{G}}}+\frac{1}{c}\frac{\mathrm{\partial }{\mathbf{B}}^{{}_{\mathrm{G}}}}{\mathrm{\partial }t}=0}$	${\displaystyle \mathrm{\nabla }\times {\mathbf{E}}^{{}_{\mathrm{I}}}+\frac{\mathrm{\partial }{\mathbf{B}}^{{}_{\mathrm{I}}}}{\mathrm{\partial }t}=0}$
Ampère–Maxwell equation (macroscopic)	${\displaystyle \mathrm{\nabla }\times {\mathbf{H}}^{{}_{\mathrm{G}}}-\frac{1}{c}\frac{\mathrm{\partial }{\mathbf{D}}^{{}_{\mathrm{G}}}}{\mathrm{\partial }t}=\frac{4\pi }{c}{\mathbf{J}}_{\mathrm{f}}^{{}_{\mathrm{G}}}}$	${\displaystyle \mathrm{\nabla }\times {\mathbf{H}}^{{}_{\mathrm{I}}}-\frac{\mathrm{\partial }{\mathbf{D}}^{{}_{\mathrm{I}}}}{\mathrm{\partial }t}={\mathbf{J}}_{\mathrm{f}}^{{}_{\mathrm{I}}}}$
Ampère–Maxwell equation (microscopic)	${\displaystyle \mathrm{\nabla }\times {\mathbf{B}}^{{}_{\mathrm{G}}}-\frac{1}{c}\frac{\mathrm{\partial }{\mathbf{E}}^{{}_{\mathrm{G}}}}{\mathrm{\partial }t}=\frac{4\pi }{c}{\mathbf{J}}^{{}_{\mathrm{G}}}}$	${\displaystyle \mathrm{\nabla }\times {\mathbf{B}}^{{}_{\mathrm{I}}}-\frac{1}{c^2}\frac{\mathrm{\partial }{\mathbf{E}}^{{}_{\mathrm{I}}}}{\mathrm{\partial }t}={\mu }_0{\mathbf{J}}^{{}_{\mathrm{I}}}}$

Other electromagnetic laws in Gaussian system and ISQ

Name	Gaussian system	ISQ
Lorentz force	${\displaystyle \mathbf{F}=q^{{}_{\mathrm{G}}}\left({\mathbf{E}}^{{}_{\mathrm{G}}}+\frac{1}{c}\mathbf{v}\times {\mathbf{B}}^{{}_{\mathrm{G}}}\right)}$	${\displaystyle \mathbf{F}=q^{{}_{\mathrm{I}}}\left({\mathbf{E}}^{{}_{\mathrm{I}}}+\mathbf{v}\times {\mathbf{B}}^{{}_{\mathrm{I}}}\right)}$
Coulomb's law	${\displaystyle \mathbf{F}=\frac{q_1^{{}_{\mathrm{G}}}{q}_2^{{}_{\mathrm{G}}}}{r^2}\hat{\mathbf{r}}}$	${\displaystyle \mathbf{F}=\frac{1}{4\pi {\epsilon }_0}\frac{q_1^{{}_{\mathrm{I}}}{q}_2^{{}_{\mathrm{I}}}}{r^2}\hat{\mathbf{r}}}$
Electric field of stationary point charge	${\displaystyle {\mathbf{E}}^{{}_{\mathrm{G}}}=\frac{q^{{}_{\mathrm{G}}}}{r^2}\hat{\mathbf{r}}}$	${\displaystyle {\mathbf{E}}^{{}_{\mathrm{I}}}=\frac{1}{4\pi {\epsilon }_0}\frac{q^{{}_{\mathrm{I}}}}{r^2}\hat{\mathbf{r}}}$
Biot–Savart law[6]	${\displaystyle {\mathbf{B}}^{{}_{\mathrm{G}}}=\frac{1}{c}\oint \frac{I^{{}_{\mathrm{G}}}\times \hat{\mathbf{r}}}{r^2}\mathrm{d}\mathit{\ell }}$	${\displaystyle {\mathbf{B}}^{{}_{\mathrm{I}}}=\frac{{\mu }_0}{4\pi }\oint \frac{I^{{}_{\mathrm{I}}}\times \hat{\mathbf{r}}}{r^2}\mathrm{d}\mathit{\ell }}$
Poynting vector (microscopic)	${\displaystyle \mathbf{S}=\frac{c}{4\pi }{\mathbf{E}}^{{}_{\mathrm{G}}}\times {\mathbf{B}}^{{}_{\mathrm{G}}}}$	${\displaystyle \mathbf{S}=\frac{1}{{\mu }_0}{\mathbf{E}}^{{}_{\mathrm{I}}}\times {\mathbf{B}}^{{}_{\mathrm{I}}}}$

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 thepermittivity is a simple constant.

Expressions for fields in dielectric media

Gaussian system	ISQ
${\displaystyle {\mathbf{D}}^{{}_{\mathrm{G}}}={\mathbf{E}}^{{}_{\mathrm{G}}}+4\pi {\mathbf{P}}^{{}_{\mathrm{G}}}}$	${\displaystyle {\mathbf{D}}^{{}_{\mathrm{I}}}={\epsilon }_0{\mathbf{E}}^{{}_{\mathrm{I}}}+{\mathbf{P}}^{{}_{\mathrm{I}}}}$
${\displaystyle {\mathbf{P}}^{{}_{\mathrm{G}}}={\chi }_{\mathrm{e}}^{{}_{\mathrm{G}}}{\mathbf{E}}^{{}_{\mathrm{G}}}}$	${\displaystyle {\mathbf{P}}^{{}_{\mathrm{I}}}={\chi }_{\mathrm{e}}^{{}_{\mathrm{I}}}{\epsilon }_0{\mathbf{E}}^{{}_{\mathrm{I}}}}$
${\displaystyle {\mathbf{D}}^{{}_{\mathrm{G}}}={\epsilon }^{{}_{\mathrm{G}}}{\mathbf{E}}^{{}_{\mathrm{G}}}}$	${\displaystyle {\mathbf{D}}^{{}_{\mathrm{I}}}={\epsilon }^{{}_{\mathrm{I}}}{\mathbf{E}}^{{}_{\mathrm{I}}}}$
${\displaystyle {\epsilon }^{{}_{\mathrm{G}}}=1+4\pi {\chi }_{\mathrm{e}}^{{}_{\mathrm{G}}}}$	${\displaystyle {\epsilon }^{{}_{\mathrm{I}}}/{\epsilon }_0=1+{\chi }_{\mathrm{e}}^{{}_{\mathrm{I}}}}$

where

• E andD are theelectric field anddisplacement field, respectively;
• P is thepolarization density;
• ${\displaystyle \epsilon }$ is thepermittivity;
• ${\displaystyle {\epsilon }_0}$ is thepermittivity of vacuum (used in the SI system, but meaningless in Gaussian units); and
• ${\displaystyle {\chi }_{\mathrm{e}}}$ is theelectric susceptibility.

The quantities${\displaystyle {\epsilon }^{{}_{\mathrm{G}}}}$ and${\displaystyle {\epsilon }^{{}_{\mathrm{I}}}/{\epsilon }_0}$ are both dimensionless, and they have the same numeric value. By contrast, theelectric susceptibility${\displaystyle {\chi }_{\mathrm{e}}^{{}_{\mathrm{G}}}}$ and${\displaystyle {\chi }_{\mathrm{e}}^{{}_{\mathrm{I}}}}$ are both unitless, but havedifferent numeric values for the same material:$${\displaystyle 4\pi {\chi }_{\mathrm{e}}^{{}_{\mathrm{G}}}={\chi }_{\mathrm{e}}^{{}_{\mathrm{I}}}.}$$

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 thepermeability is a simple constant.

Expressions for fields in magnetic media

Gaussian system	ISQ
${\displaystyle {\mathbf{B}}^{{}_{\mathrm{G}}}={\mathbf{H}}^{{}_{\mathrm{G}}}+4\pi {\mathbf{M}}^{{}_{\mathrm{G}}}}$	${\displaystyle {\mathbf{B}}^{{}_{\mathrm{I}}}={\mu }_0({\mathbf{H}}^{{}_{\mathrm{I}}}+{\mathbf{M}}^{{}_{\mathrm{I}}})}$
${\displaystyle {\mathbf{M}}^{{}_{\mathrm{G}}}={\chi }_{\mathrm{m}}^{{}_{\mathrm{G}}}{\mathbf{H}}^{{}_{\mathrm{G}}}}$	${\displaystyle {\mathbf{M}}^{{}_{\mathrm{I}}}={\chi }_{\mathrm{m}}^{{}_{\mathrm{I}}}{\mathbf{H}}^{{}_{\mathrm{I}}}}$
${\displaystyle {\mathbf{B}}^{{}_{\mathrm{G}}}={\mu }^{{}_{\mathrm{G}}}{\mathbf{H}}^{{}_{\mathrm{G}}}}$	${\displaystyle {\mathbf{B}}^{{}_{\mathrm{I}}}={\mu }^{{}_{\mathrm{I}}}{\mathbf{H}}^{{}_{\mathrm{I}}}}$
${\displaystyle {\mu }^{{}_{\mathrm{G}}}=1+4\pi {\chi }_{\mathrm{m}}^{{}_{\mathrm{G}}}}$	${\displaystyle {\mu }^{{}_{\mathrm{I}}}/{\mu }_0=1+{\chi }_{\mathrm{m}}^{{}_{\mathrm{I}}}}$

where

• B andH are themagnetic fields;
• M ismagnetization;
• ${\displaystyle \mu }$ ismagnetic permeability;
• ${\displaystyle {\mu }_0}$ is thepermeability of vacuum (used in the SI system, but meaningless in Gaussian units); and
• ${\displaystyle {\chi }_{\mathrm{m}}}$ is themagnetic susceptibility.

The quantities${\displaystyle {\mu }^{{}_{\mathrm{G}}}}$ and${\displaystyle {\mu }^{{}_{\mathrm{I}}}/{\mu }_0}$ are both dimensionless, and they have the same numeric value. By contrast, themagnetic susceptibility${\displaystyle {\chi }_{\mathrm{m}}^{{}_{\mathrm{G}}}}$ and${\displaystyle {\chi }_{\mathrm{m}}^{{}_{\mathrm{I}}}}$ are both unitless, but hasdifferent numeric values in the two systems for the same material:$${\displaystyle 4\pi {\chi }_{\mathrm{m}}^{{}_{\mathrm{G}}}={\chi }_{\mathrm{m}}^{{}_{\mathrm{I}}}}$$

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

Electromagnetic fields in Gaussian system and ISQ

Name	Gaussian system	ISQ
Electric field	${\displaystyle {\mathbf{E}}^{{}_{\mathrm{G}}}=-\mathrm{\nabla }{\varphi }^{{}_{\mathrm{G}}}-\frac{1}{c}\frac{\mathrm{\partial }{\mathbf{A}}^{{}_{\mathrm{G}}}}{\mathrm{\partial }t}}$	${\displaystyle {\mathbf{E}}^{{}_{\mathrm{I}}}=-\mathrm{\nabla }{\varphi }^{{}_{\mathrm{I}}}-\frac{\mathrm{\partial }{\mathbf{A}}^{{}_{\mathrm{I}}}}{\mathrm{\partial }t}}$
MagneticB field	${\displaystyle {\mathbf{B}}^{{}_{\mathrm{G}}}=\mathrm{\nabla }\times {\mathbf{A}}^{{}_{\mathrm{G}}}}$	${\displaystyle {\mathbf{B}}^{{}_{\mathrm{I}}}=\mathrm{\nabla }\times {\mathbf{A}}^{{}_{\mathrm{I}}}}$

Electrical circuit values in Gaussian system and ISQ

Name	Gaussian system	ISQ
Charge conservation	${\displaystyle I^{{}_{\mathrm{G}}}=\frac{\mathrm{d}{Q}^{{}_{\mathrm{G}}}}{\mathrm{d}t}}$	${\displaystyle I^{{}_{\mathrm{I}}}=\frac{\mathrm{d}{Q}^{{}_{\mathrm{I}}}}{\mathrm{d}t}}$
Lenz's law	${\displaystyle V^{{}_{\mathrm{G}}}=\frac{1}{c}\frac{\mathrm{d}{\mathrm{\Phi }}^{{}_{\mathrm{G}}}}{\mathrm{d}t}}$	${\displaystyle V^{{}_{\mathrm{I}}}=-\frac{\mathrm{d}{\mathrm{\Phi }}^{{}_{\mathrm{I}}}}{\mathrm{d}t}}$
Ohm's law	${\displaystyle V^{{}_{\mathrm{G}}}=R^{{}_{\mathrm{G}}}{I}^{{}_{\mathrm{G}}}}$	${\displaystyle V^{{}_{\mathrm{I}}}=R^{{}_{\mathrm{I}}}{I}^{{}_{\mathrm{I}}}}$
Capacitance	${\displaystyle Q^{{}_{\mathrm{G}}}=C^{{}_{\mathrm{G}}}{V}^{{}_{\mathrm{G}}}}$	${\displaystyle Q^{{}_{\mathrm{I}}}=C^{{}_{\mathrm{I}}}{V}^{{}_{\mathrm{I}}}}$
Inductance	${\displaystyle {\mathrm{\Phi }}^{{}_{\mathrm{G}}}=c{L}^{{}_{\mathrm{G}}}{I}^{{}_{\mathrm{G}}}}$	${\displaystyle {\mathrm{\Phi }}^{{}_{\mathrm{I}}}=L^{{}_{\mathrm{I}}}{I}^{{}_{\mathrm{I}}}}$

where

• Q is theelectric charge
• I is theelectric current
• V is theelectric potential
• Φ is themagnetic flux
• R is theelectrical resistance
• C is thecapacitance
• L is theinductance

Fundamental constants in Gaussian system and ISQ

Name	Gaussian system	ISQ
Impedance of free space	${\displaystyle Z_0^{{}_{\mathrm{G}}}=\frac{4\pi }{c}}$	${\displaystyle Z_0^{{}_{\mathrm{I}}}=\sqrt{\frac{{\mu }_0}{{\epsilon }_0}}}$
Electric constant	${\displaystyle 1=\frac{4\pi }{Z_0^{{}_{\mathrm{G}}}c}}$	${\displaystyle {\epsilon }_0=\frac{1}{Z_0^{{}_{\mathrm{I}}}c}}$
Magnetic constant	${\displaystyle 1=\frac{Z_0^{{}_{\mathrm{G}}}c}{4\pi }}$	${\displaystyle {\mu }_0=\frac{Z_0^{{}_{\mathrm{I}}}}{c}}$
Fine-structure constant	${\displaystyle \alpha =\frac{(e^{{}_{\mathrm{G}}}{)}^2}{\hslash c}}$	${\displaystyle \alpha =\frac{1}{4\pi {\epsilon }_0}\frac{(e^{{}_{\mathrm{I}}}{)}^2}{\hslash c}}$
Magnetic flux quantum	${\displaystyle {\varphi }_0^{{}_{\mathrm{G}}}=\frac{hc}{2e^{{}_{\mathrm{G}}}}}$	${\displaystyle {\varphi }_0^{{}_{\mathrm{I}}}=\frac{h}{2e^{{}_{\mathrm{I}}}}}$
Conductance quantum	${\displaystyle G_0^{{}_{\mathrm{G}}}=\frac{2(e^{{}_{\mathrm{G}}}{)}^2}{h}}$	${\displaystyle G_0^{{}_{\mathrm{I}}}=\frac{2(e^{{}_{\mathrm{I}}}{)}^2}{h}}$
Bohr radius	${\displaystyle a_{\mathrm{B}}=\frac{{\hslash }^2}{m_{\mathrm{e}}(e^{{}_{\mathrm{G}}}{)}^2}}$	${\displaystyle a_{\mathrm{B}}=\frac{4\pi {\epsilon }_0{\hslash }^2}{m_{\mathrm{e}}(e^{{}_{\mathrm{I}}}{)}^2}}$
Bohr magneton	${\displaystyle {\mu }_{\mathrm{B}}^{{}_{\mathrm{G}}}=\frac{e^{{}_{\mathrm{G}}}\hslash }{2m_{\mathrm{e}}c}}$	${\displaystyle {\mu }_{\mathrm{B}}^{{}_{\mathrm{I}}}=\frac{e^{{}_{\mathrm{I}}}\hslash }{2m_{\mathrm{e}}}}$

Table 1: Common electromagnetism units in SI vs Gaussian^[7]

Quantity	Symbol	SI unit	Gaussian unit (in base units)	Conversion factor
Electric charge	q	C	Fr (cm3/2⋅g1/2⋅s−1)	${\displaystyle \frac{q^{{}_{\mathrm{G}}}}{q^{{}_{\mathrm{I}}}}=\frac{1}{\sqrt{4\pi {\epsilon }_0}}\approx \frac{2.998\times {10}^9\mathrm{F}\mathrm{r}}{1\mathrm{C}}}$
Electric current	I	A	statA (cm3/2⋅g1/2⋅s−2)	${\displaystyle \frac{I^{{}_{\mathrm{G}}}}{I^{{}_{\mathrm{I}}}}=\frac{1}{\sqrt{4\pi {\epsilon }_0}}\approx \frac{2.998\times {10}^9\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{A}}{1\mathrm{A}}}$
Electric potential, Voltage	φ V	V	statV (cm1/2⋅g1/2⋅s−1)	${\displaystyle \frac{V^{{}_{\mathrm{G}}}}{V^{{}_{\mathrm{I}}}}=\sqrt{4\pi {\epsilon }_0}\approx \frac{1\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{V}}{2.998\times {10}^2\mathrm{V}}}$
Electric field	E	V/m	statV/cm (cm−1/2⋅g1/2⋅s−1)	${\displaystyle \frac{{\mathbf{E}}^{{}_{\mathrm{G}}}}{{\mathbf{E}}^{{}_{\mathrm{I}}}}=\sqrt{4\pi {\epsilon }_0}\approx \frac{1\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{V}/\mathrm{c}\mathrm{m}}{2.998\times {10}^4\mathrm{V}/\mathrm{m}}}$
Electric displacement field	D	C/m2	Fr/cm2 (cm−1/2g1/2s−1)	${\displaystyle \frac{{\mathbf{D}}^{{}_{\mathrm{G}}}}{{\mathbf{D}}^{{}_{\mathrm{I}}}}=\sqrt{\frac{4\pi }{{\epsilon }_0}}\approx \frac{4\pi \times 2.998\times {10}^5{\mathrm{F}\mathrm{r}/\mathrm{c}\mathrm{m}}^2}{1{\mathrm{C}/\mathrm{m}}^2}}$
Electric dipole moment	p	C⋅m	Fr⋅cm (cm5/2⋅g1/2⋅s−1)	${\displaystyle \frac{{\mathbf{p}}^{{}_{\mathrm{G}}}}{{\mathbf{p}}^{{}_{\mathrm{I}}}}=\frac{1}{\sqrt{4\pi {\epsilon }_0}}\approx \frac{2.998\times {10}^{11}\mathrm{F}\mathrm{r}\cdot \mathrm{c}\mathrm{m}}{1\mathrm{C}\cdot \mathrm{m}}}$
Electric flux[c]	ΦD	C	Fr (cm3/2⋅g1/2⋅s−1)	${\displaystyle \frac{{\mathrm{\Phi }}_{\mathrm{e}}^{{}_{\mathrm{G}}}}{{\mathrm{\Phi }}_{\mathrm{e}}^{{}_{\mathrm{I}}}}=\sqrt{\frac{4\pi }{{\epsilon }_0}}\approx \frac{4\pi \times 2.998\times {10}^9\mathrm{F}\mathrm{r}}{1\mathrm{C}}}$
Permittivity	ε	F/m	cm/cm	${\displaystyle \frac{{\epsilon }^{{}_{\mathrm{G}}}}{{\epsilon }^{{}_{\mathrm{I}}}}=\frac{1}{{\epsilon }_0}\approx \frac{4\pi \times {2.998}^2\times {10}^9\mathrm{c}\mathrm{m}/\mathrm{c}\mathrm{m}}{1\mathrm{F}/\mathrm{m}}}$
MagneticB field	B	T	G (cm−1/2⋅g1/2⋅s−1)	${\displaystyle \frac{{\mathbf{B}}^{{}_{\mathrm{G}}}}{{\mathbf{B}}^{{}_{\mathrm{I}}}}=\sqrt{\frac{4\pi }{{\mu }_0}}\approx \frac{{10}^4\mathrm{G}}{1\mathrm{T}}}$
MagneticH field	H	A/m	Oe (cm−1/2⋅g1/2⋅s−1)	${\displaystyle \frac{{\mathbf{H}}^{{}_{\mathrm{G}}}}{{\mathbf{H}}^{{}_{\mathrm{I}}}}=\sqrt{4\pi {\mu }_0}\approx \frac{4\pi \times {10}^{-3}\mathrm{O}\mathrm{e}}{1\mathrm{A}/\mathrm{m}}}$
Magnetic dipole moment	m	A⋅m2	erg/G (cm5/2⋅g1/2⋅s−1)	${\displaystyle \frac{{\mathbf{m}}^{{}_{\mathrm{G}}}}{{\mathbf{m}}^{{}_{\mathrm{I}}}}=\sqrt{\frac{{\mu }_0}{4\pi }}\approx \frac{{10}^3\mathrm{e}\mathrm{r}\mathrm{g}/\mathrm{G}}{1\mathrm{A}\cdot {\mathrm{m}}^2}}$
Magnetic flux	Φm	Wb	Mx (cm3/2⋅g1/2⋅s−1)	${\displaystyle \frac{{\mathrm{\Phi }}_{\mathrm{m}}^{{}_{\mathrm{G}}}}{{\mathrm{\Phi }}_{\mathrm{m}}^{{}_{\mathrm{I}}}}=\sqrt{\frac{4\pi }{{\mu }_0}}\approx \frac{{10}^8\mathrm{M}\mathrm{x}}{1\mathrm{W}\mathrm{b}}}$
Permeability	μ	H/m	cm/cm	${\displaystyle \frac{{\mu }^{{}_{\mathrm{G}}}}{{\mu }^{{}_{\mathrm{I}}}}=\frac{1}{{\mu }_0}\approx \frac{1\mathrm{c}\mathrm{m}/\mathrm{c}\mathrm{m}}{4\pi \times {10}^{-7}\mathrm{H}/\mathrm{m}}}$
Magnetomotive force	${\displaystyle \mathcal{F}}$	A	Gi (cm1/2⋅g1/2⋅s−1)	${\displaystyle \frac{{\mathcal{F}}^{{}_{\mathrm{G}}}}{{\mathcal{F}}^{{}_{\mathrm{I}}}}=\sqrt{4\pi {\mu }_0}\approx \frac{4\pi \times {10}^{-1}\mathrm{G}\mathrm{i}}{1\mathrm{A}}}$
Magnetic reluctance	${\displaystyle \mathcal{R}}$	H−1	Gi/Mx (cm−1)	${\displaystyle \frac{{\mathcal{R}}^{{}_{\mathrm{G}}}}{{\mathcal{R}}^{{}_{\mathrm{I}}}}={\mu }_0\approx \frac{4\pi \times {10}^{-9}\mathrm{G}\mathrm{i}/\mathrm{M}\mathrm{x}}{1{\mathrm{H}}^{-1}}}$
Resistance	R	Ω	s/cm	${\displaystyle \frac{R^{{}_{\mathrm{G}}}}{R^{{}_{\mathrm{I}}}}=4\pi {\epsilon }_0\approx \frac{1\mathrm{s}/\mathrm{c}\mathrm{m}}{{2.998}^2\times {10}^{11}\mathrm{\Omega }}}$
Resistivity	ρ	Ω⋅m	s	${\displaystyle \frac{{\rho }^{{}_{\mathrm{G}}}}{{\rho }^{{}_{\mathrm{I}}}}=4\pi {\epsilon }_0\approx \frac{1\mathrm{s}}{{2.998}^2\times {10}^9\mathrm{\Omega }\cdot \mathrm{m}}}$
Capacitance	C	F	cm	${\displaystyle \frac{C^{{}_{\mathrm{G}}}}{C^{{}_{\mathrm{I}}}}=\frac{1}{4\pi {\epsilon }_0}\approx \frac{{2.998}^2\times {10}^{11}\mathrm{c}\mathrm{m}}{1\mathrm{F}}}$
Inductance	L	H	s2/cm	${\displaystyle \frac{L^{{}_{\mathrm{G}}}}{L^{{}_{\mathrm{I}}}}=4\pi {\epsilon }_0\approx \frac{1{\mathrm{s}}^2/\mathrm{c}\mathrm{m}}{{2.998}^2\times {10}^{11}\mathrm{H}}}$

Note: The SI quantities${\displaystyle {\epsilon }_0}$ and${\displaystyle {\mu }_0}$ satisfy⁠${\displaystyle {\epsilon }_0{\mu }_0=1/c^2}$⁠.

The conversion factors are written both symbolically and numerically. The numerical conversion factors can be derived from the symbolic conversion factors bydimensional analysis. For example, the top row says${\displaystyle 1/\sqrt{4\pi {\epsilon }_0}\approx 2.998\times {10}^9\mathrm{F}\mathrm{r}/1\mathrm{C}}$, a relation which can be verified with dimensional analysis, by expanding${\displaystyle {\epsilon }_0}$ andcoulombs (C) inSI base units, and expandingstatcoulombs (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 measuringresistivity in units of seconds. A physical example is: Take aparallel-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 ist seconds, the half-life of the discharge is~0.05t 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.

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 betweennewton-metre andjoule.) The different names help avoid ambiguities and misunderstandings as to what physical quantity is being measured. In particular,all of the following quantities are dimensionally equivalent in Gaussian units, but they are nevertheless given different unit names as follows:^[8]

Any formula can be converted between Gaussian and SI units by using the symbolic conversion factors from Table 1 above.

For example, theelectric field of a stationary point charge has the ISQ formula$${\displaystyle {\mathbf{E}}^{{}_{\mathrm{I}}}=\frac{q^{{}_{\mathrm{I}}}}{4\pi {\epsilon }_0{r}^2}\hat{\mathbf{r}},}$$wherer is distance, and the "I" 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:

Therefore, after substituting and simplifying, we get the Gaussian-system formula:$${\displaystyle {\mathbf{E}}^{{}_{\mathrm{G}}}=\frac{q^{{}_{\mathrm{G}}}}{r^2}\hat{\mathbf{r}},}$$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${\displaystyle 1/c^2}$ by${\displaystyle {\epsilon }_0{\mu }_0}$ (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.^{[9][10][11][d]}

Table 2A: Replacement rules for translating formulas from Gaussian to ISQ

Name	Gaussian system	ISQ
electric field,electric potential,electromotive force	${\displaystyle \left({\mathbf{E}}^{{}_{\mathrm{G}}},{\phi }^{{}_{\mathrm{G}}},{\mathcal{E}}^{{}_{\mathrm{G}}}\right)}$	${\displaystyle \sqrt{4\pi {\epsilon }_0}\left({\mathbf{E}}^{{}_{\mathrm{I}}},{\phi }^{{}_{\mathrm{I}}},{\mathcal{E}}^{{}_{\mathrm{I}}}\right)}$
electric displacement field	${\displaystyle {\mathbf{D}}^{{}_{\mathrm{G}}}}$	${\displaystyle \sqrt{\frac{4\pi }{{\epsilon }_0}}{\mathbf{D}}^{{}_{\mathrm{I}}}}$
charge,charge density,current, current density,polarization density, electric dipole moment	${\displaystyle \left(q^{{}_{\mathrm{G}}},{\rho }^{{}_{\mathrm{G}}},I^{{}_{\mathrm{G}}},{\mathbf{J}}^{{}_{\mathrm{G}}},{\mathbf{P}}^{{}_{\mathrm{G}}},{\mathbf{p}}^{{}_{\mathrm{G}}}\right)}$	${\displaystyle \frac{1}{\sqrt{4\pi {\epsilon }_0}}\left(q^{{}_{\mathrm{I}}},{\rho }^{{}_{\mathrm{I}}},I^{{}_{\mathrm{I}}},{\mathbf{J}}^{{}_{\mathrm{I}}},{\mathbf{P}}^{{}_{\mathrm{I}}},{\mathbf{p}}^{{}_{\mathrm{I}}}\right)}$
magneticB field,magnetic flux, magnetic vector potential	${\displaystyle \left({\mathbf{B}}^{{}_{\mathrm{G}}},{\mathrm{\Phi }}_{\mathrm{m}}^{{}_{\mathrm{G}}},{\mathbf{A}}^{{}_{\mathrm{G}}}\right)}$	${\displaystyle \sqrt{\frac{4\pi }{{\mu }_0}}\left({\mathbf{B}}^{{}_{\mathrm{I}}},{\mathrm{\Phi }}_{\mathrm{m}}^{{}_{\mathrm{I}}},{\mathbf{A}}^{{}_{\mathrm{I}}}\right)}$
magneticH field,magnetic scalar potential,magnetomotive force	${\displaystyle \left({\mathbf{H}}^{{}_{\mathrm{G}}},{\psi }^{{}_{\mathrm{G}}},{\mathcal{F}}^{{}_{\mathrm{G}}}\right)}$	${\displaystyle \sqrt{4\pi {\mu }_0}\left({\mathbf{H}}^{{}_{\mathrm{I}}},{\psi }^{{}_{\mathrm{I}}},{\mathcal{F}}^{{}_{\mathrm{I}}}\right)}$
magnetic moment,magnetization,magnetic pole strength	${\displaystyle \left({\mathbf{m}}^{{}_{\mathrm{G}}},{\mathbf{M}}^{{}_{\mathrm{G}}},p^{{}_{\mathrm{G}}}\right)}$	${\displaystyle \sqrt{\frac{{\mu }_0}{4\pi }}\left({\mathbf{m}}^{{}_{\mathrm{I}}},{\mathbf{M}}^{{}_{\mathrm{I}}},p^{{}_{\mathrm{I}}}\right)}$
permittivity, permeability	${\displaystyle \left({\epsilon }^{{}_{\mathrm{G}}},{\mu }^{{}_{\mathrm{G}}}\right)}$	${\displaystyle \left(\frac{{\epsilon }^{{}_{\mathrm{I}}}}{{\epsilon }_0},\frac{{\mu }^{{}_{\mathrm{I}}}}{{\mu }_0}\right)}$
electric susceptibility, magnetic susceptibility	${\displaystyle \left({\chi }_{\mathrm{e}}^{{}_{\mathrm{G}}},{\chi }_{\mathrm{m}}^{{}_{\mathrm{G}}}\right)}$	${\displaystyle \frac{1}{4\pi }\left({\chi }_{\mathrm{e}}^{{}_{\mathrm{I}}},{\chi }_{\mathrm{m}}^{{}_{\mathrm{I}}}\right)}$
conductivity,conductance,capacitance	${\displaystyle \left({\sigma }^{{}_{\mathrm{G}}},S^{{}_{\mathrm{G}}},C^{{}_{\mathrm{G}}}\right)}$	${\displaystyle \frac{1}{4\pi {\epsilon }_0}\left({\sigma }^{{}_{\mathrm{I}}},S^{{}_{\mathrm{I}}},C^{{}_{\mathrm{I}}}\right)}$
resistivity,resistance,inductance,memristance,impedance	${\displaystyle \left({\rho }^{{}_{\mathrm{G}}},R^{{}_{\mathrm{G}}},L^{{}_{\mathrm{G}}},M^{{}_{\mathrm{G}}},Z^{{}_{\mathrm{G}}}\right)}$	${\displaystyle 4\pi {\epsilon }_0\left({\rho }^{{}_{\mathrm{I}}},R^{{}_{\mathrm{I}}},L^{{}_{\mathrm{I}}},M^{{}_{\mathrm{I}}},Z^{{}_{\mathrm{I}}}\right)}$
magnetic reluctance	${\displaystyle {\mathcal{R}}^{{}_{\mathrm{G}}}}$	${\displaystyle {\mu }_0{\mathcal{R}}^{{}_{\mathrm{I}}}}$

Table 2B: Replacement rules for translating formulas from ISQ to Gaussian

Name	ISQ	Gaussian system
electric field,electric potential,electromotive force	${\displaystyle \left({\mathbf{E}}^{{}_{\mathrm{I}}},{\phi }^{{}_{\mathrm{I}}},{\mathcal{E}}^{{}_{\mathrm{I}}}\right)}$	${\displaystyle \frac{1}{\sqrt{4\pi {\epsilon }_0}}\left({\mathbf{E}}^{{}_{\mathrm{G}}},{\phi }^{{}_{\mathrm{G}}},{\mathcal{E}}^{{}_{\mathrm{G}}}\right)}$
electric displacement field	${\displaystyle {\mathbf{D}}^{{}_{\mathrm{I}}}}$	${\displaystyle \sqrt{\frac{{\epsilon }_0}{4\pi }}{\mathbf{D}}^{{}_{\mathrm{G}}}}$
charge,charge density,current, current density,polarization density, electric dipole moment	${\displaystyle \left(q^{{}_{\mathrm{I}}},{\rho }^{{}_{\mathrm{I}}},I^{{}_{\mathrm{I}}},{\mathbf{J}}^{{}_{\mathrm{I}}},{\mathbf{P}}^{{}_{\mathrm{I}}},{\mathbf{p}}^{{}_{\mathrm{I}}}\right)}$	${\displaystyle \sqrt{4\pi {\epsilon }_0}\left(q^{{}_{\mathrm{G}}},{\rho }^{{}_{\mathrm{G}}},I^{{}_{\mathrm{G}}},{\mathbf{J}}^{{}_{\mathrm{G}}},{\mathbf{P}}^{{}_{\mathrm{G}}},{\mathbf{p}}^{{}_{\mathrm{G}}}\right)}$
magneticB field,magnetic flux, magnetic vector potential	${\displaystyle \left({\mathbf{B}}^{{}_{\mathrm{I}}},{\mathrm{\Phi }}_{\mathrm{m}}^{{}_{\mathrm{I}}},{\mathbf{A}}^{{}_{\mathrm{I}}}\right)}$	${\displaystyle \sqrt{\frac{{\mu }_0}{4\pi }}\left({\mathbf{B}}^{{}_{\mathrm{G}}},{\mathrm{\Phi }}_{\mathrm{m}}^{{}_{\mathrm{G}}},{\mathbf{A}}^{{}_{\mathrm{G}}}\right)}$
magneticH field,magnetic scalar potential,magnetomotive force	${\displaystyle \left({\mathbf{H}}^{{}_{\mathrm{I}}},{\psi }^{{}_{\mathrm{I}}},{\mathcal{F}}^{{}_{\mathrm{I}}}\right)}$	${\displaystyle \frac{1}{\sqrt{4\pi {\mu }_0}}\left({\mathbf{H}}^{{}_{\mathrm{G}}},{\psi }^{{}_{\mathrm{G}}},{\mathcal{F}}^{{}_{\mathrm{G}}}\right)}$
magnetic moment,magnetization,magnetic pole strength	${\displaystyle \left({\mathbf{m}}^{{}_{\mathrm{I}}},{\mathbf{M}}^{{}_{\mathrm{I}}},p^{{}_{\mathrm{I}}}\right)}$	${\displaystyle \sqrt{\frac{4\pi }{{\mu }_0}}\left({\mathbf{m}}^{{}_{\mathrm{G}}},{\mathbf{M}}^{{}_{\mathrm{G}}},p^{{}_{\mathrm{G}}}\right)}$
permittivity, permeability	${\displaystyle \left({\epsilon }^{{}_{\mathrm{I}}},{\mu }^{{}_{\mathrm{I}}}\right)}$	${\displaystyle \left({\epsilon }_0{\epsilon }^{{}_{\mathrm{G}}},{\mu }_0{\mu }^{{}_{\mathrm{G}}}\right)}$
electric susceptibility, magnetic susceptibility	${\displaystyle \left({\chi }_{\mathrm{e}}^{{}_{\mathrm{I}}},{\chi }_{\mathrm{m}}^{{}_{\mathrm{I}}}\right)}$	${\displaystyle 4\pi \left({\chi }_{\mathrm{e}}^{{}_{\mathrm{G}}},{\chi }_{\mathrm{m}}^{{}_{\mathrm{G}}}\right)}$
conductivity,conductance,capacitance	${\displaystyle \left({\sigma }^{{}_{\mathrm{I}}},S^{{}_{\mathrm{I}}},C^{{}_{\mathrm{I}}}\right)}$	${\displaystyle 4\pi {\epsilon }_0\left({\sigma }^{{}_{\mathrm{G}}},S^{{}_{\mathrm{G}}},C^{{}_{\mathrm{G}}}\right)}$
resistivity,resistance,inductance,memristance,impedance	${\displaystyle \left({\rho }^{{}_{\mathrm{I}}},R^{{}_{\mathrm{I}}},L^{{}_{\mathrm{I}}},M^{{}_{\mathrm{I}}},Z^{{}_{\mathrm{I}}}\right)}$	${\displaystyle \frac{1}{4\pi {\epsilon }_0}\left({\rho }^{{}_{\mathrm{G}}},R^{{}_{\mathrm{G}}},L^{{}_{\mathrm{G}}},M^{{}_{\mathrm{G}}},Z^{{}_{\mathrm{G}}}\right)}$
magnetic reluctance	${\displaystyle {\mathcal{R}}^{{}_{\mathrm{I}}}}$	${\displaystyle \frac{1}{{\mu }_0}{\mathcal{R}}^{{}_{\mathrm{G}}}}$

After the rules of the table have been applied and the resulting formula has been simplified, replace all combinations${\displaystyle {\epsilon }_0{\mu }_0}$ by${\displaystyle 1/c^2}$.