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 is a convenient 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 circular mils, A, of a circle with a diameter of d mils, is given by the formula:

Failed to parse (Missing texvc executable; please see math/README to configure.): A= d^2

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 [link]

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

Failed to parse (Missing texvc executable; please see math/README to configure.): d= 0.46

inch = 460 mil

Failed to parse (Missing texvc executable; please see math/README to configure.): A= d^2

Failed to parse (Missing texvc executable; please see math/README to configure.): 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

Failed to parse (Missing texvc executable; please see math/README to configure.): d= 0.46

inch = 460 mil

Failed to parse (Missing texvc executable; please see math/README to configure.): r= {d \over 2}

= 230 mil

Failed to parse (Missing texvc executable; please see math/README to configure.): A= \pi r^2

Failed to parse (Missing texvc executable; please see math/README to configure.): A= \pi \times 230^2 = 52,900 \pi \approx 166,190.25

square mils

Formula 3: Square Inch

Failed to parse (Missing texvc executable; please see math/README to configure.): d= 0.46

inch

Failed to parse (Missing texvc executable; please see math/README to configure.): r= {d \over 2}

= 0.23 inch

Failed to parse (Missing texvc executable; please see math/README to configure.): A= \pi r^2

Failed to parse (Missing texvc executable; please see math/README to configure.): A= \pi \times (0.23)^2 = .0529 \pi \approx 0.16619

square inches

Formula 4: Solving for Circular Mil

Failed to parse (Missing texvc executable; please see math/README to configure.): A= A

Failed to parse (Missing texvc executable; please see math/README to configure.): 211,600

circular milsFailed to parse (Missing texvc executable; please see math/README to configure.): = 52,900 \pi
square mils

1 circular mil Failed to parse (Missing texvc executable; please see math/README to configure.): = {52,900 \pi \over 211,600}

square mils

1 circular mil Failed to parse (Missing texvc executable; please see math/README to configure.): = {\pi \over 4}

square mils

Formula 5: Solving for Circular Mil

1 square mil Failed to parse (Missing texvc executable; please see math/README to configure.): = {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.

AWG circular mil formula [link]

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

Failed to parse (Missing texvc executable; please see math/README to configure.): 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
• Were it possible to use n = -4 in this equation (assuming there was a size larger than 4/0 AWG), the calculated result would be about 255 kcmil, which is similar to the 250 kcmil wire size actually in use

See also [link]

• thou (length)
• square mil
• MCM

References [link]