circular mil
General information
Unit of	Area
Symbol	cmil
Derivation	1 cmil = ⁠π/4⁠(0.001 in)2
Conversions
1 cmil in ...	... is equal to ...
SI units	506.7075 μm2
FPS units	7.853982×10−7 in2

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 corresponds to approximately 5.067×10⁻⁴ mm². It is a unit intended for referring to the area of a wire with a circular cross section. As the definition of the unit contains π, it is easy to calculate area values in circular mils when the diameter in mils is known.

The area in circular mils, A, of a circle with a diameter of d mils, is given by the formula: $${\displaystyle \{A\}_{\mathrm {cmil} }=\{d\}_{\mathrm {mil} }^{2}.}$$

In Canada and the United States, the Canadian Electrical Code (CEC) and the National Electrical Code (NEC), respectively, use the circular mil to define wire sizes larger than 0000 AWG. In many NEC publications and uses, large wires may be expressed in thousands of circular mils, which is abbreviated in two different ways: kcmil^[1] or MCM.^[2] For example, one common wire size used in the NEC has a conductor diameter of 0.5 inches, or 500 mils, and thus a cross-section of ${\displaystyle 500^{2}=250{,}000}$ circular mils, written as 250 kcmil or 250 MCM, which is the first size larger than 0000 AWG used within the NEC.

1000 circular mil equals approximately 0.5067 mm², so for many purposes, a ratio of 2 MCM ≈ 1 mm² can be used with negligible (1.3%) error.

As a unit of area, the circular mil can be converted to other units such as square inches or square millimetres.

1 circular mil is approximately equal to:

• 0.7854 square mils (1 square mil is about 1.273 circular mils)
• 7.854 × 10⁻⁷ square inches (1 square inch is about 1.273 million circular mils)
• 5.067 × 10⁻¹⁰ square metres
• 5.067 × 10⁻⁴ square millimetres
• 506.7 μm²

1000 circular mils = 1 MCM or 1 kcmil, and is (approximately) equal to:

• 0.5067 mm², so 2 kcmil ≈ 1 mm² (a 1.3% error)

Therefore, for practical purposes such as wire choice, 2 kcmil ≈ 1 mm² is a reasonable rule of thumb for many applications.

In square mils, the area of a circle with a diameter of 1 mil is:

$${\displaystyle A=\pi r^{2}=\pi \left({\frac {d}{2}}\right)^{2}={\frac {\pi d^{2}}{4}}={\rm {{\frac {\pi \times (1~mil)^{2}}{4}}={\frac {\pi }{4}}~mil^{2}\approx 0.7854~mil^{2}.}}}$$

By definition, this area is also equal to 1 circular mil, so:

$${\displaystyle {\rm {1~cmil={\frac {\pi }{4}}~mil^{2}.}}}$$

The formula for the area of an arbitrary circle in circular mils can be derived by applying this conversion factor to the standard formula for the area of a circle (which gives its result in square mils).

$${\displaystyle {\begin{aligned}A&=\pi r^{2}=\pi \left({\frac {d}{2}}\right)^{2}={\frac {\pi d^{2}}{4}}&&({\text{Area in mil}}^{2})\\&={\frac {\pi d^{2}}{4}}\times {\frac {4~{\textrm {cmil}}}{\pi ~{\textrm {mil}}^{2}}}&&({\text{Convert to cmil}})\\&=d^{2}~\mathrm {cmil/mil^{2}} &&({\text{Result is in cmil}}).\end{aligned}}}$$

To equate circular mils with square inches rather than square mils, the definition of a mil in inches can be substituted:

${\displaystyle {\begin{aligned}{\rm {1~cmil}}&={\rm {{\frac {\pi }{4}}~mil^{2}={\frac {\pi }{4}}~(0.001~in)^{2}}}\\&={\rm {{\frac {\pi }{4{,}000{,}000}}~in^{2}\approx 7.854\times 10^{-7}~in^{2}}}\end{aligned}}}$

Likewise, since 1 inch is defined as exactly 25.4 mm, 1 mil is equal to exactly 0.0254 mm, so a similar conversion is possible from circular mils to square millimetres:

${\displaystyle {\begin{aligned}{\rm {1~cmil}}&={\rm {{\frac {\pi }{4}}~mil^{2}={\frac {\pi }{4}}~(0.0254~mm)^{2}={\frac {\pi \times 0.000\,645\,16}{4}}~mm^{2}}}\\&={\rm {1.6129\pi \times 10^{-4}~mm^{2}\approx 5.067\times 10^{-4}~mm^{2}}}\end{aligned}}}$

A 0000 AWG solid wire is defined to have a diameter of exactly 0.46 inches (11.68 mm). The cross-sectional area of this wire is:

Note: 1 inch = 1000 mils

Zdroj:https://en.wikipedia.org?pojem=Circular_mil
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