CGS and Gaussian Units are the bane of my existence, so I decided to make a page that compiles all the useful information I can find about them in one place.

Base Units

The Seven SI Base Units are as follows:

1. Time: second (s)
2. Length: metre (m)
3. Mass: kilogram (kg)
4. Current: ampere (A)
5. Temperature: Kelvin (K)
6. Amount: mole (mol)
7. Luminous Intensity: candela (cd)

Kelvin, mol, candela are not part of the “mechanical” units and do not change in CGS. As a result, CGS just defines 3 Base Units

1. Time: second (s)
2. Length: centimetre (cm)
3. Mass: gram (g)

So, one fundamental difference between SI and CGS is that there is no base units for current (or charge). Instead, the units for those quantities are defined in terms of the CGS base units.

Definition of CGS Gaussian Units

In the SI unit system, the quantity $\mu_0 \equiv 4 \pi \cdot 10^{-7} N/A^2$. However, the Gaussian Unit System defines the following for the permitivity of free space:

\begin{equation} \epsilon_0 \equiv \frac{1}{4 \pi} \end{equation}

In this way, we never need to see $\epsilon_0$ in any of our equations. This is chosen so that the Coulomb force law becomes

\begin{equation} F = \frac{q_1 q_2}{r^2} \end{equation}

Additionally, the relationship between the speed of light and the permitivity and permeability constants is $c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$ which allows us to replace the permeability constant with

\begin{equation} \mu_0 = \frac{4 \pi}{c^2} \text{s}^{2} \text{cm}^{-2} \end{equation}

Derived Units

• dyn = g cm s$^{-2}$
• erg = dyn cm = g cm$^2$ s$^{-2}$
• gauss = dyn esu$^{-1}$ = g$^{1/2}$ cm$^{-1/2}$ s$^{-1}$
• gauss$^2$ = g cm$^{-1}$ s$^{-2}$ = erg cm$^{-3}$
• esu = g$^{1/2}$ cm$^{3/2}$ s$^{-1}$ = dyn$^{1/2}$ cm
• stat volt = erg esu$^{-1}$ = g$^{1/2}$ cm$^{1/2}$ s$^{-1}$

Fundamental Constants and Common Conversions

• $e = -4.80 \times 10^{-10}$ esu
• 1 barn $\equiv 10^{-24}$ cm$^2$
• $\sigma = 6.65 \times 10^{-25}$ cm$^2 = 0.665$ barn is the Thomson Cross-Section of Electron
• 1 debye = $10^{-18}$ esu cm
• 1 erg = $10^{-7}$ J
• 1 pc = $3.086 \times 10^18$ cm