Circular mil

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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). It corresponds to 5.067×10-4 mm². It is a convenient[citation needed] unit for referring to the area of a wire with a circular cross section, because the area in circular mils can be calculated without reference to pi (π).

The area in square inches of a circle with a diameter of d mils, is given by the formula:

1 CM= 1/4*Pi()*d^2 square inches.

Note: the rest of this articule have to be revised. I'll do that as soon has is possible for me!

Electricians in Canada and the United States are familiar with the circular mil because the National Electrical Code (NEC) uses 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: MCM[1] or kcmil.[2] For example, one common wire size used in the NEC has a cross-section of 250,000 circular mils, written as 250 kcmil or 250 MCM, which is the first size larger than 0000 AWG used within the NEC.

Equivalence to other units of area

Although square mils are rarely used, it is convenient to convert between square inches and circular mils. As a classic example taken from the NEC, a 0000 AWG solid wire is defined to have a diameter of exactly 0.46 inch.

Formula 1: Circular Mil

Note: 1 inch = 1000 mils
d=0.46 inch = 460 mils
A=d^{2}
A=460^{2} = 211,600 circular mils
(This is the same result as the AWG circular mil formula shown below for n=-3)

Formula 2: Square Mil

d=0.46 inch = 460 mils
r={d \over 2} = 230 mils
A=\pi r^{2}
A=\pi \times 230^{2}=52,900\pi \approx 166,190.25 square mils

Formula 3: Square Inch

d=0.46 inch
r={d \over 2} = 0.23 inch
A=\pi r^{2}
A=\pi \times (0.23)^{2}=.0529\pi \approx 0.16619 square inches

Formula 4: Solving for Circular Mil

A=A
211,600 circular mils=52,900\pi square mils
1 circular mil ={52,900\pi \over 211,600} square mils
1 circular mil ={\pi \over 4} square mils

Formula 5: Solving for Square Mil

1 square mil ={4 \over \pi } circular mils

Therefore, the following conversions apply:

  • To obtain square mils   ⇒ (# of circular mils) × π ÷ 4
  • To obtain square inches ⇒ (# of circular mils) × π ÷ 4,000,000
  • To obtain circular mils ⇒ (# of square mils)   × 4 ÷ π
  • To obtain circular mils ⇒ (# of square inches) × 4,000,000 ÷ π

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
  • 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.

When large diameter wire sizes are specified in kcmil, such as the ubiquitous 250 kcmil or 350 kcmil wires, the wire's diameter can be easily determined with the following formula:

Formula 6: Diameter

Note: We first convert from kcmil to circular mil
A=250 kcmil
A=250,000 circular mils
d={\sqrt {A}}
d={\sqrt {250,000}} = 500 mils = 0.500 inch

Thus, this wire would have a diameter of a half inch or 12.7 mm.

AWG circular mil formula

The formula to calculate the circular mil for any given AWG (American Wire Gauge) size is as follows. An represents the circular mil area for the AWG size n.

A_{n}=(5\times 92^{{\frac {36-n}{39}}})^{2}
  • For example, a number 12 gauge wire would use n = 12; and the calculated result would be 6529.946789 circular mils

Sizes with multiple zeros are successively larger than the number 0 gauge size and can be denoted using "number of zeros/0"; for example 4/0 for the number 0000 gauge. For an m/0 AWG wire size, use

n = −(m−1) = 1−m in the above formula.

For example, the number 0000 gauge or 4/0 gauge, would use n = −3; and the calculated result would be 211,600 circular mils. If 5/0 AWG existed (it does not), the calculated result would be about 267 kcmil, which is similar to the 250 kcmil wire size actually in use.

Standard sizes

Standard sizes are from 250 to 400 in increments of 50 kcmil, 400 to 1000 in increments of 100 kcmil, and from 1000 to 2000 in increments of 250 kcmil.[3]

Fictitious AWG equivalents are as follows. The diameter is assuming solid wire, which is not practical. Stranded wire is 5% larger in diameter to allow for gaps between the strands.

Standard kcmil wire sizes
& solid copper equivalents
kcmil
MCM 		mm² Diameter Fictitious AWG
equivalent
in. mm
250 126.7 0.500 12.70 4.7/0
300 152.0 0.548 13.91 5.5/0
350 177.3 0.592 15.03 6.2/0
400 202.7 0.632 16.06 6.7/0
500 253.4 0.707 17.96 7.7/0
600 304.0 0.775 19.67 8.5/0
700 354.7 0.837 21.25 9.2/0
750 380.0 0.866 22.00 9.5/0
800 405.4 0.894 22.72 9.7/0
900 456.0 0.949 24.10 10.2/0
1000 506.7 1.000 25.40 10.7/0
1250 633.4 1.118 28.40 11.7/0
1500 760.1 1.225 31.11 12.4/0
1750 886.7 1.323 33.60 13.1/0
2000 1013.4 1.414 35.92 13.7/0

See also

References

  1. ↑ "Power Plant Siting Acronyms", California Energy Commission
  2. ↑ "Popular Acronyms". NEMA
  3. ↑ NFPA 70-2011 National Electrical Code 2011 Edition. Table 310.15(B)(17) page 70-155, Allowable Ampacities of Single-Insulated Conductors Rated Up to and Including 2000 Volts in Free Air, Based on Ambient Air Temperature of 30°C (86°F).
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