In the English system for measuring small lengths such as paper thickness and precision machining dimensions 1/1000 of an inch is used as the unit. It is called mil. For items that are round and have a circular cross section, like most wires, another small unit is used. This unit, called circular mil, is a unit of measure for area. One circular mil is the area of a circle whose diameter is 1 mil. In this respect, the area called a circular mil is

$$\begin{array}{c}1\text{CM}=\frac{1}{4}{(1)}^{2}(\pi )=\frac{\pi}{4}\times {10}^{-6}{\text{in}}^{\text{2}}\\ =\frac{\pi}{4}\times 0.00064516{\text{mm}}^{\text{2}}=0.00050671{\text{mm}}^{\text{2}}\end{array}$$ |

If the diameter of a wire is d mils, then its area is

$$\frac{1}{4}{(d)}^{2}(\pi )={d}^{2}\text{CM}$$ |

By defining the circular mil, in fact, the multiplication by the factor π/4 is included in the unit, making the expression for measurement ...

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