zmVault/circular-mil.md

Circular Mil

A 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}