# CGS System of Units Converter

By Dominik Czernia, PhD candidate
Last updated: Aug 16, 2018

The CGS system of units converter is a handy tool that you can use to find relations between SI units and the most popular CGS units. A system of measurement is a set of units and rules relating them to each other. During many years of human history, many systems of measurement have been developed, e.g.:

• the metric system of units - also known as MKS system (meter - kilogram - second) or the International System of Units (SI),
• the imperial system of units (e.g. foot and pound),
• the CGS system of units (centimeter - gram - second).

In the following text, you will find the definitions and conversion factors of CGS units in mechanics and electromagnetism. We have also prepared the table with commonly used physical constants in CGS units compared to SI units.

## CGS units in mechanics

In mechanics, the definitions of the CGS system and of the MKS system are very similar, because they differ only in the scale of two base units. The MKS units use meters `1 m`, kilograms `1 kg` and seconds `1 s`, and the CGS units use centimeters `1 cm = 0.01 m`, grams `1 g = 0.001 kg` and seconds `1 s`. In the table below, we have listed some CGS units with special names and their conversion factors to the MKS units.

Quantity (symbol) CGS unit name (symbol) Equivalent in SI units
acceleration (a) gal (Gal) 10⁻² m/s²
force (F) dyne (dyn) 10⁻⁵ N
energy (E) erg (erg) 10⁻⁷ J
pressure (p) barye (Ba) 10⁻¹ Pa
dynamic viscosity (μ) poise (P) 10⁻¹ Pa*s
kinematic viscosity (ν) stokes (St) 10⁻⁴ m²/s

If you want to express another physical quantity in CGS units system, you just need to use an appropriate formula. For example, since the units of power in the metric system are joules per second `J/s` or watts `W`, the units of power in the CGS units are ergs per second `erg/s` and `1 erg/s = 10⁻⁷ J/s = 10⁻⁷ W`.

## CGS units in electromagnetism

The conversion factors of electromagnetic units in the CGS and International System of Units are more complicated. This is because of the differences in the expressing physical laws of electromagnetism. Moreover, there are a few different CGS subsystems. For example, the factor `Ke` in the Coulomb's law

`F = Ke * q₁ * q₂ / r²`

equals:

• `1 / (4πε₀) = 9 * 10^9 N*m²/C²` in the metric system,
• `1` in the electrostatic CGS (ESU - electrostatic unit) system,
• `c² = 2.997 * 10^10 cm/s` in the electromagnetic CGS (EMU - electrodynamic unit) system,
• `1` in the Gaussian CGS system.

You can see that some CGS subsystems can simplify physical formulas. That's why it is so popular in many areas where there are a lot of theoretical calculations involving electromagnetism equations. In this CGS system of units converter, you can find relations between electromagnetic units of the International System of Units and the Gaussian CGS system. We have listed these with special names in the table below.

Quantity (symbol) Gaussian CGS unit name (symbol) Equivalent in SI units
charge (q) franklin (Fr) 3.336 * 10¹⁰ C
voltage (V) statvolt (statV) 299.8 V
magnetic B field (B) gauss (G) 10⁻³ T
magnetic H field (H) oersted (Oe) 79.577 A/m

## Physical constants in CGS units and MKS units

Differences between the metric system units and CGS units obviously lead to a change in the value of physical constants. You will find some of them in the table below.

Constant (symbol) Value - SI units Value - Gaussian CGS units
Atomic mass unit (u) 1.66*10⁻²⁷ kg 1.66*10⁻²⁴ g
Bohr magneton (μB) 9.27*10⁻²⁴ J/T 9.27*10⁻²¹ erg/G
Bohr radius (a0) 5.29*10⁻¹¹ m 5.29*10⁻⁹ m
Boltzmann constant (kB) 1.38*10⁻²³ J/K 1.38*10⁻¹⁶ erg/K
Electron mass (me) 9.11*10⁻³¹ kg 9.11*10⁻²⁸ g
Elementary charge (e) 1.6*10⁻¹⁹ C 4.8*10⁻¹⁰ Fr
Fine-structure constant (α) 1/137 1/137
Gravitational constant (G) 6.67*10⁻¹¹ N*m²/kg² 6.67*10⁻⁸ dyn*cm²/g²
Planck constant (h) 6.626*10⁻³⁴ J*s 6.626*10⁻²⁷ erg*s
Speed of light in vacuum (c) 2.998*10⁸ m/s 2.998*10¹⁰ cm/s
Dominik Czernia, PhD candidate
Acceleration
SI
m/s²
CGS
Gal
Force
SI
N
CGS
dyne
Energy
SI
J
CGS
erg
Pressure
SI
Pa
CGS
Ba
Dynamic viscosity
SI
kg/(m*s)
CGS
P
Kinematic viscosity
SI
m²/s
CGS
St
Charge
SI
C
CGS
Fr
Voltage
SI
V
CGS
statV
Magnetic B field
SI
T
CGS
G
Magnetic H field
SI
A/m
CGS
Oe
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