# Circular Mil

> A [**circular mil**](https://en.wikipedia.org/wiki/Circular_mil)
> is a unit of area, equal to the area of a circle with a diameter of one mil
> (one thousandth of an inch or 0.0254 mm).
> It is equal to π/4 square mils...
> 
> The area in circular mils, A, of a circle with a diameter of d mils, is given by the formula:
> 
> $$
> A_{\rm{cmil}} = ( d_{\rm{mil}} )^{2}
> $$

> In square mils, the area of a circle with a diameter of 1 mil is:
> 
> $$
> \begin{align}
> A &= \pi r^{2} \\
> &= \pi \left( \frac{d}{2} \right)^{2} \\
> &= \frac{\pi d^{2}}{4} \\
> &= \frac{ \pi \times (1~\rm{mil})^{2} }{4} \\
> &= \frac{\pi}{4}~\rm{mil}^{2} \\
> &\approx 0.7854~\rm{mil}^{2} \\
> \end{align}
> $$
> 
> By definition, this area is also equal to 1 circular mil, so
> 
> $$
> \rm{ 1~cmil = \frac{\pi}{4}~mil^{2} }
> $$
> 
> The conversion factor from square mils to circular mils is therefore 4/π cmil per square mil:
> 
> $$
> \rm{ 1~mil^{2} = \frac{4}{\pi} }~cmil
> $$

> The formula to calculate the area in circular mil
> for any given AWG (American Wire Gauge) size
> is as follows.
> $A_{n}$ represents the area of number $n$ AWG.
> 
> $$
> A_{n}=\left( 5 \times 92^{(36-n)/39} \right)^{2}
> $$
> 
> For example, a number 12 gauge wire would use $n=12$:
> 
> $$
> \left( 5 \times 92^{(36-12)/39} \right)^{2}
> = 6530~\rm{cmil}
> $$