# CGS System of Units Converter

Created by Dominik Czernia, PhD
Reviewed by Bogna Szyk and Steven Wooding
Last updated: Nov 15, 2022

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, numerous systems of measurement have been developed, including:

• Metric system of units – also known as MKS system (meter-kilogram-second) or the International System of Units (SI);
• Imperial system of units (e.g. foot and pound); and
• 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.

Meanwhile, if you work with viscosity, then our Stokes' law calculator and Poise-Stokes converter may come in very handy for you. Be sure to check these tools!

## 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 $\small 1 \text{ m}$, kilograms $\small 1 \text{ kg}$ and seconds $\small 1 \text{ s}$, and the CGS units use centimeters $\small 1 \text{ cm} = 0.01 \text{ m}$, grams $\small 1 \text{ g} = 0.001 \text{ kg}$ and seconds $\small 1 \text{ s}$.

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 the 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 $\small \text{J/s}$ or watts $\small \text{W}$, the units of power in the CGS units are ergs per second $\small \text{erg/s}$ and $\small 1 \text{ erg/s} = 10^{-7} \text{ J/s} = 10^{-7} \text{ W}$.

We prepared calculators that help determine the above physical quantities. For example, check the acceleration calculator to find acceleration using different methods or energy conversion calculator to learn about the variety of energy units.

## 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 $k_{\text{e}}$ (the Coulomb constant) we use in the Coulomb's law calculator and the electrostatic force equation:

$F = k_{\rm e}\frac{q_1 q_2}{r^2},$

equals:

• $1/{\mathrm{4 \pi \epsilon_0}} = 9\!\times\!10^9 \text{ } \mathrm{N\!\cdot\! m^2/C^2}$ in the metric system;

• $1$ in the electrostatic CGS (ESU – electrostatic unit) system;

• $\mathrm{c^2} = 2.997\! \times\!10^{10} \text{ } \mathrm{cm/s}$ in the electromagnetic CGS (EMU – electrodynamic unit) system; and

• $1$ 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 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

1.66×10-24 g

Bohr magneton (μB)

9.27×10-24 J/T

9.27×10-21 erg/G

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
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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