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 ). It is equal to /4 square mils or approximately . 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 , it is easy to calculate area values in circular mils when the diameter in mils is known.

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

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"Popular Acronyms" . NEMA or MCM."Energy Acronyms", California Energy Commission 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 circular mils, written as 250 kcmil or 250 MCM, which is the first size larger than 0000 AWG used within the NEC.

1,000 circular mil equals approximately , so for many purposes, a ratio of 2 MCM ≈ 1 mm2 can be used with negligible (1.3%) error.

Equivalence to other units of area 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 μm

1000 circular mils = 1 MCM or 1 kcmil, and is (approximately) equal to: 0.5067 mm, so 2 kcmil ≈ 1 mm (a 1.3% error)

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

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

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

The conversion factor from square mils to circular mils is therefore 4/ cmil per square mil:

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).

Square inches

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

Square millimetres

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

Example calculations

A 0000 AWG solid wire is defined to have a diameter of exactly . The cross-sectional area of this wire is:

Formula 1: circular mil

Note: 1 inch = 1000 mils

(This is the same result as the AWG circular mil formula shown below for )

Formula 2: square mil

Formula 3: square inch

Calculating diameter from area

When large diameter wire sizes are specified in kcmil, such as the widely used 250 kcmil and 350 kcmil wires, the diameter of the wire can be calculated from the area without using :

We first convert from kcmil to circular mil

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

Metric equivalent Some tables give conversions to circular millimetres (cmm).Charles Hoare, The A.B.C. of Slide Rule Practice, p. 52, London: Aston & Mander, 1872 Edwin James Houston, A Dictionary of Electrical Words, Terms and Phrases, p. 135, New York: W. J. Johnston, 1889 The area in cmm is defined as the square of the wire diameter in mm. However, this unit is rarely used in practice. One of the few examples is in a patent for a bariatric weight loss device.Greg A. Lloyd, Bariatric Magnetic Apparatus and Method of Manufacturing Thereof, US patent , 9 July 2013.

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

For example, a number 12 gauge wire would use :

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

For example, 0000AWG (4/0AWG), would use ; and the calculated result would be 211,600 circular mils.

Standard large wire sizes in kcmil In North America wires larger than the AWG are available in sizes beginning with a half-inch (500 mil) diameter. However, solid core wire of that size would be quite stiff for most uses as it resists bending and coiling for transport. Therefore, most large wires are made of tightly-bound strands of smaller wire with the same cross-sectional area of conductors. The table below has a diameter column that is for solid wire with no strands. Since standard sizes have a fixed area, a stranded wire would always have a larger diameter than the table shown below.

Large standard wires range from 250 to 400kcmil in increments of 50kcmil, from 400 to 1000 in increments of 100kcmil, and from 1000 to 2000 in increments of 250kcmil.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).

The diameter in the table below is that of a solid rod with the given conductor area in circular mils. Stranded wire is larger in diameter to allow for gaps between the strands, depending on the number and size of strands.

+ Standard kcmil wire sizes& solid copper equivalents Area Diameter NEC copper wireampacity with60/75/90 °Cinsulation (A)NFPA 70 National Electrical Code 2008 Edition . Table 310.16 page 70-148, Allowable ampacities of insulated conductors rated 0 through 2000 volts, 60°C through 90°C, not more than three current-carrying conductors in raceway, cable, or earth (directly buried) based on ambient temperature of 30°C. Extracts from NFPA 70 do not represent the full position of NFPA and the original complete Code must be consulted. In particular, the maximum permissible overcurrent protection devices may set a lower limit. (kcmil, MCM) (mm2) (in) (mm) 250 126.7 0.500 12.70 215 255 290 300 152.0 0.548 13.91 240 285 320 350 177.3 0.592 15.03 260 310 350 400 202.7 0.632 16.06 280 335 380 500 253.4 0.707 17.96 320 380 430 600 304.0 0.775 19.67 355 420 475 700 354.7 0.837 21.25 385 460 520 750 380.0 0.866 22.00 400 475 535 800 405.4 0.894 22.72 410 490 555 900 456.0 0.949 24.10 435 520 585 1000 506.7 1.000 25.40 455 545 615 1250 633.4 1.118 28.40 495 590 665 1500 760.1 1.225 31.11 520 625 705 1750 886.7 1.323 33.60 545 650 735 2000 1013.4 1.414 35.92 560 665 750 Note: For smaller wires, consult . Note: Aluminum wires have a much lower ampacity than copper but are often available in these sizes.

Square mil A square mil is a unit of area, equal to the area of a square with sides of length one mil. A mil is one thousandth of an international inch. This unit of area is usually used in specifying the area of the cross section of a wire or cable.

1 square mil is equal to: 1 millionth of a square inch (1 square inch is equal to 1 million square mils)

about 1.273 circular mils (1 circular mil is equal to about 0.7854 square mils). and

See also Thou (length) Square mil

IEC 60228, the metric wire-size standard used in most parts of the world. American Wire Gauge (AWG), used primarily in the US and Canada Standard Wire Gauge (SWG), the British imperial standard BS3737, superseded by the metric. Stubs Iron Wire Gauge Jewelry wire gauge Body jewelry sizes Electrical wiring Number 8 wire, a term used in the New Zealand vernacular

References