The barn is a unit of area and is used in particle physics with the symbol b.
It represents approximately the area of the cross-section of a uraneum nucleus, so is very small compared to most other recognised units of area.
It is also used to measure the interaction of a nucleus with an electric field gradient in nuclear quadrupole and magnetic resonance.
The circular mil is a unit designed specifically to measure the area of a wire with a circular cross section. It has the symbol cmil.
An inch is 1000 mils. This makes the circular mil particularly useful for measuring cross sections of wire as there is no need to use the symbol π so the process is simplified.
A circular mil is a very small unit so not advised to use for large areas!